modelling activity generation processes

MODELLING ACTIVITY GENERATION PROCESSES

Khandker Mohammed Nurul Habib

A thesis submitted in conformity with the requirements for the degree of Doctor of Philosophy

Department of Civil Engineering University of Toronto

© Copyright by Khandker Mohammed Nurul Habib, 2007

In the name of Allah, Most Gracious, Most Merciful.

Modelling Activity Generation Processes Khandker Mohammed Nurul Habib Doctor of Philosophy Department of Civil Engineering University of Toronto 2007

ABSTRACT Any operational activity-based travel demand model can be divided into two major components: activity generation and activity scheduling. Although considerable progress in behavioural theory and modelling techniques has been achieved for the activity scheduling component, activity generation in many ways is an overlooked or under researched area. This thesis concentrates on this critical issue from the theoretical perspective as well as empirical model development. Based on a comprehensive literature review this thesis develops a conceptual framework for modelling activity generation, considering it as a process. The consideration of the activity generation as a process is to ensure the dynamic interrelationship with the activity scheduling process as well as meaningful integration with other medium- to long-term household decisions (employment, housing, automobile ownership etc.) processes. The conceptual framework leads to a step by step procedure for investigating behavioural hypotheses and developing empirical models. Use of week-long activity diary survey (CHASE: Computerized Household Activity Scheduling Elicitor) data allows the investigation of behavioural elements within an econometric modelling II

frameworks of activity generation. The classification of activities into skeletal versus non-skeletal types allows adoption of different modelling techniques consistent with the dynamics and behavioural linkages between short-term travel demands with the mediumto long-term household decisions. Investigation of non-skeletal activities reveals that activity sequencing is more the job of activity scheduling than activity generation. For modelling the non-skeletal activity-agenda, this thesis adopts the concept of activity utility and proposes a large scale demand system modelling technique. It is demonstrated that a multi-day modelling framework is necessary to ensure both withinday as well as day-to-day dynamics in activity-agenda formation. At the same time it is also necessary to ensure that the activity classification is sufficiently disaggregate so that the trade-offs involved in time allocation to different activities during activity generation process is properly addressed. Long-term development will require operationalization of the proposed activity generation models to improve the policy sensitivity of activitybased travel demand model as well as allow better integration of the travel demand model within an Integrated Land Use Transportation and Environment (ILUTE) framework.

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ACKNOWLEDGEMENTS I am indebted to a great number of people who generously offered friendship, inspiration, advise, and encouragement throughout my Ph.D study. First of all, I offer my sincere gratitude to my teacher and thesis supervisor, Professor Eric J. Miller, with whom it has been an honour and a pleasure to work. I am indebted to him for a great number of things: for sharing his knowledge, for his friendly treatment, for the opportunities he provided me, for giving me complete freedom, for his patience, for his accessibility, for his invaluable suggestions and many more reasons to note down. Eric, you do have a profound and ever lasting influence in my career life. Thanks to the members of my doctoral committee: Professor Baher Abdulhai, Professor Amer Shalaby and Professor Christopher Kennedy – for their critical review of different aspects of this research and helping me to improve the thesis. Special thanks to the external member of the committee, Professor Dick Ettema for his critical reviews and suggestions. Dick Ettema has not only been a very insightful committee member, but also a source of inspiration in my research. I also wish to thank Professor Roger H. von Haefen for influencing and helping me to use advanced econometric methods in this dissertation. In related to this, I would also like to thank Professor Chandra Bhat for creating a thought-provoking discussion on large-scale demand system modelling that in many ways forced me to dig deeper into my research topics. Special thanks to Professor Kay Axhausen for all of the encouragements and his invitation to extend my research works to European context.

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During my years in Toronto, I have been lucky to have a lot of great friends and colleagues. Thank you to all the friends and colleagues who have made my student life in Toronto a whole lot more enjoyable. Juan Carrasco, Beatriz and little Mariana were the central alters of my ego-centric social network in Toronto. Thanks to Antoine, Ilan, Marek, Marianne, Matt, Prachi and many others with whom I have shared stimulating conversations and the camaraderie of student life. Last but not least I am indebted to my parents, siblings and nephews (Shabab, Ishmam and Tasha) for their affections and love.

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TABLE OF CONTENTS ABSTRACT

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CHAPTER 01: INTRODUCTION

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1.1 Objectives…………………………………………………………………………......3 1.2 Relevance……………………………………………………………………………...4 1.3 Approach………………………………………………………………………………5 1.4 Thesis Outline ............................................................................................................... 5

CHAPTER 02: LITERATURE REVIEW

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2.1 Introduction…………………………………………………………………………....7 2.2 Evolution of Travel Demand Modelling Approaches................................................... 8 2.3 Activity-based Approach to Travel Demand Modelling .............................................. 9 2.3.1 Utility-Maximizing Models.................................................................. 11 2.3.2 Computational Process or Rule-Based Models .................................... 13 2.3.3 Hybrid Models...................................................................................... 16 2.4 Modelling Activity Generation ................................................................................... 19 2.5 The Concept of Activity Utility .................................................................................. 21 2.5.1 Forms of Utility .................................................................................... 22 2.5.2 Relative versus Absolute Utility........................................................... 24 2.5.3 Components of Activity Utility ............................................................ 25 2.6 Summary and Commentary ........................................................................................ 29 2.7 Future Directions ........................................................................................................ 31

CHAPTER 03: MODELLING ACTIVITY GENERATION PROCESSES THE CONCEPTUAL FRAMEWORK

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3.1 Introduction…………………………………………………………………………..33 3.2 Activity-Agenda as Activity Generation Component................................................. 34 3.3 Time Budget for Modelling Activity-Agenda Formation........................................... 41 3.4 Application of Activity Utility for Modelling Activity-Agenda................................. 44 3.5 Necessary Output of Activity Generation Model to the Activity Scheduling Model. 47 3.6 Integration within Integrated Land Use Transportation and Environment Modelling Framework............................................................................................................. 48 VI

3.7 Conclusions…………………………………………………………………………..49

CHAPTER 04: SOURCE OF DATA FOR EMPIRICAL INVESTIGATIONS 51 4.1 Introduction…………………………………………………………………………..51 4.2 TAPS: Toronto Activity Panel Survey ....................................................................... 52 4.3 CHASE: Computerized Household Activity Scheduling Elicitor .............................. 55 4.4 Wave 1 CHASE Survey of TAPS............................................................................... 60 4.5 Use of Wave 1 CHASE Survey Data as Prime Data Source in Activity Generation Process Investigation ............................................................................................. 63 4.6 Conclusions…………………………………………………………………………..65

CHAPTER 05: MODELLING SKELETAL ACTIVITY GENERATION

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5.1 Introduction…………………………………………………………………………..67 5.2 Modelling Workers’ Skeletal Component of Daily Activity-Agenda ........................ 71 5.3 Mathematical Formulations of the Component Models ............................................. 72 5.3.1 Multilevel Linear Model for Episode Duration.................................... 73 5.3.2 Event History Analysis Models............................................................ 76 5.4 Empirical Estimation Results of SWDAS Components ............................................. 79 5.4.1 ‘Gap Duration before Work’: The Work Start Time............................ 80 5.4.2 Work Duration...................................................................................... 82 5.4.3 ‘Gap Duration after Work before Night Sleep’: The Night Sleep Start Time .......................................................................................................................... 84 5.4.4 Night Sleep Duration ............................................................................ 86 5.5 Conclusions…………………………………………………………………………..88

CHAPTER 06: INVESTIGATING SEQUENCING OF NON-SKELETAL ACTIVITIES IN ACTIVITY-AGENDA FORMATION

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6.1 Introduction…………………………………………………………………………..90 6.2 Causal Structures for Start Time and Duration Relationship of Non-Skeletal Activities …………………………………………………………………………93 6.2.1 Start Time of the Activity Episode is Planned First ............................. 93 6.2.2 Duration of the Activity Episode is Planned First................................ 94 VII

6.3 Modelling Techniques and Estimation Procedures..................................................... 96 6.3.1 Causal Structure: Start Time
Duration ............................................ 96 6.3.2 Causal Structure: Duration
Start Time .......................................... 101 6.4 Description of Data for Empirical Investigation....................................................... 104 6.5 Estimation Results of the Models ............................................................................. 108 6.5.1 Household Obligation Activities ........................................................ 111 6.5.2 Drop off / Pick up Type Activities ..................................................... 113 6.5.3 Shopping Activity............................................................................... 115 6.5.4 Service Type Activity......................................................................... 117 6.5.5 At-Home Recreation Type Activity ................................................... 119 6.5.6 Out-of-Home Recreation Type Activity............................................. 121 6.5.7 Social Activity .................................................................................... 123 6.5.8 Summary............................................................................................. 124 6.6 Conclusions………………………………………………………………………....125

CHAPTER 07: MODELLING ACTIVITY-AGENDA FORMATION

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7.1 Introduction………………………………………………………………………....128 7.2 Utility Theory and Large Scale Demand System Modelling.................................... 128 7.3 The Specification of Utility Function of Activity-Agenda ....................................... 131 7.3.1 Estimation Procedure.......................................................................... 134 7.3.2 Accommodating Heteroskedascity ..................................................... 138 7.4 Data for Empirical Estimation .................................................................................. 139 7.5 Estimation Results of Empirical Models .................................................................. 143 7.6 Summary and Conclusions ....................................................................................... 151

CHAPTER 08: INVESTIGATING THE RHYTHM OF ACTIVITYAGENDA FORMATION

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8.1 Introduction…………………………………………………………………………154 8.2 Econometric Formulation for Day-Specific Activity-Agenda.................................. 155 8.3 Data for Empirical Estimation .................................................................................. 156 8.4 Interpretations and Comparisons of the Models ....................................................... 161 8.5 Summary and Conclusions ....................................................................................... 166

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CHAPTER 09: INVESTIGATING INTER-ACTIVITY CORRELATION IN TIME ALLOCATION BEHAVIOUR OF ACTIVITY-AGENDA FORMATION

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9.1 Introduction…………………………………………………………………………168 9.2 Model Specification and Estimation ......................................................................... 170 9.2.1 Bayesian Estimation Procedure .......................................................... 171 9.3 Data for Empirical Estimation .................................................................................. 174 9.4 Interpretation of the Model ....................................................................................... 176 9.5 Key Findings and Conclusions ................................................................................. 184

CHAPTER 10: CONCLUSIONS AND DISCUSSIONS

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10.1 Summary…………………………………………………………………………..185 10.2 Complexity of Behavioural Process versus Our Understanding............................. 199 10.3 Understanding versus Empirical Modelling ........................................................... 200 10.4 Future Research Efforts .......................................................................................... 202 10.4.1 Further Investigation Necessary ...................................................... 202 10.4.2 Data Requirement ............................................................................. 204 10.5 Final Remarks ......................................................................................................... 206

BIBLIOGRAPHY……………………………………………………………...207

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LIST OF TABLES Table 4. 1 Summary of Methods and Instruments used for TAPS ................................... 53 Table 4. 2 Core Survey Elements of TAPS Waves .......................................................... 54 Table 5. 1 Models for ‘Gap Duration before Work’ ......................................................... 80 Table 5. 2 Models for ‘Work Duration’............................................................................ 82 Table 5. 3 Models for ‘Gap Duration after Work before Night Sleep’............................. 84 Table 5. 4 Models for ‘Night Sleep Duration’.................................................................. 86 Table 6. 1 Activity Type: Household Obligations .......................................................... 111 Table 6. 2 Activity Type: Drop off / Pick Up ................................................................. 113 Table 6. 3 Activity Type: Shopping................................................................................ 115 Table 6. 4 Activity Type: Services ................................................................................. 117 Table 6. 5 Activity Type: At-Home Recreation.............................................................. 119 Table 6. 6 Activity Type: Out-of-Home Recreation....................................................... 121 Table 6. 7 Activity Type: Social ..................................................................................... 123 Table 6. 8 Summary of Start Time and Duration Relationships..................................... 125 Table 7. 1 The Disaggregate Generic Activity Classification ........................................ 141 Table 7. 2 Model with Activity Specific Dummy in Additional Utility Component .... 145 Table 7. 3 Model with Activity Specific Dummy Variable in Baseline Utility Component ......................................................................................................................................... 146 Table 7. 4 Heteroskedastic Model with Activity Specific Dummy in Baseline Utility Component...................................................................................................................... 148 Table 8. 1 Models for Daily and Weekly Activity-Agenda Formation .......................... 159 Table 9. 1 Activity Classification ................................................................................... 175 Table 9. 2 Estimated Models of Time Allocation........................................................... 177 Table 9. 3 Activity Specific Dummy Variables in Baseline Utility Component............ 181 Table 9. 4 Activity Specific Dummy Variables in Additional Utility Component ........ 182

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LIST OF FIGURES Figure 3. 1 Maslow’s Need Hierarchy .............................................................................. 36 Figure 3. 2 The Schematic Diagram of Activity Generation Process............................... 41 Figure 3. 3 Defining Time Budget for Modelling Activity-Agenda Formation ............... 44 Figure 6. 1 Causal Structure: Start Time is Conditional to Duration Selection................ 94 Figure 6. 2 Causal Structure: Duration is Conditional to Start Time Selection................ 95 Figure 6. 3 Observed Duration Distribution According to Time of Day........................ 107 Figure 7. 1 Relative Importance of Individual Activity Type in Agenda Formation ..... 150 Figure 8. 1 Observed Maximum Frequencies of the Activity Types.............................. 157 Figure 8. 2 Relative Importance of Individual Activity Types in Day-Specific Agenda Formation........................................................................................................................ 165 Figure 9. 1 Relative Importance of Individual Activity Types in Time Allocations...... 179

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CHAPTER 01: INTRODUCTION This thesis addresses some critical issues regarding one of the long-neglected parts of activity-based travel demand models: activity generation. In addressing these under-researched issues, it attempts to develop a comprehensive modelling framework, while at the same time it investigates a variety of behavioural assumptions. Activity generation components of the activity-based models do the task of modelling the activity planning. Almost all current activity-based models place their main emphasis on activity scheduling and treat activity planning/generation either as a given input or through the use of a relatively adhoc model. It is important, however, that the activity generation model should be robust and comprehensive. The scope of the activity planning/generation is often inter-mingled with that of the activity scheduling in the existing literature. It is a growing tendency that activity scheduling should be considered as a process (Doherty et al, 2001), but it is also true that “To efficiently reach a desired goal state (e.g. engaging in a valued activity) in a complex environment requires that a course of action is predetermined” (Gärling et al, 1997). The determination or planning of the course of action is also a dynamic phenomenon, which can also be referred as the activity generation process. Although there still remains some degree of arbitrariness in dividing the scopes of activity generation and activity scheduling, it is worth investigating this issue using detailed behavioural data. If the observed information allow us to segregate the activity planning and the activity scheduling processes, it is of great interest that the issues related to the activity planning / generation process should be investigated through devising hypotheses, investigating critical issues, and developing a comprehensive modelling framework. This approach in almost self-evident, “Since choices made by people are targeted, modelling these choices requires behavioural assumptions…………………………………………………………………. …………..Theoretically founded behavioural assumptions are essential for the 1

development of models of travel choice which can be used to forecast travel demand. These assumptions should furthermore be coordinated with the development of mathematical-statistical modelling tools” (Gärling et al, 1998) Virtually no empirical efforts have been devoted to analyse these issues related to the activity planning / generation with explicit consideration of the generation as a process. There are some studies dealing with particularly the activity generation but almost all of them overlook the behavioural processes of evolving the activity demands over time and the comprehensive activity-agenda formation considering explicit interactions with the activity scheduling process (e. g. Scott, 2000; Srinivasan, 2004). This dissertation attempts to fill that gap. The central thesis is that the activity generation component acts as a container in activity-based travel demand models, where the interactions among different long-, medium-, and short-term decision processes take place. And in the same way, it acts as an interface between the travel demand model and the other components of an Integrated Land Use Transportation and Environment (ILUTE) model. Recognizing the dynamics of activity planning, it requires considering activity planning/generation as a process. Our insight into this process, together with development of a comprehensive modelling capacity, will increase our understanding of complex travel behaviour as well as increasing the forecasting / predicting capacity of our travel demand models. As activity-travel behaviour is complex and multi-faceted, it poses considerable challenge to devise the analysis/modelling framework for the activity generation process. A number of issues need to be investigated before reaching the point of developing an operational empirical model. Among these, one major unresolved issue is the measurement of the benefit/loss in planning/participating in activities. Gärling et al (1997)s’ ‘valued activity’ is not often compared by the ‘values’ per se for modelling the plans of the courses of actions (the activity generation) because the definition of activity ‘values’, in other words, the activity utility, is not yet resolved. This dissertation addresses the first challenge of devising an analysis/modelling framework using the behavioural assumptions of decision dynamics. For the second challenge of defining activity utility this dissertation draws upon knowledge from different areas. Based on the 2

analysis/modelling framework, as well as the activity utility concept, it develops a comprehensive modelling framework for the activity generation process. The implications of this thesis are widespread, and serve to define a comprehensive research agenda for the author.

1.1 Objectives Miller (2005c) in his propositional paper argues that, while the integrated nature of transportation and land-use is well understood, the modelling framework for integrating relatively short-run activity-travel behaviour with longer-run residential location, job and auto ownership choices (among other decisions) is not well developed. Overcoming this shortcoming, it is further argued, requires the logical extension of the activity-based paradigm. The research presented in this dissertation attempts to address this broader issue with a holistic approach of developing a modelling framework while at the same time empirically investigating critical questions, before developing operational models. Key objectives of the thesis are: 1. Clearly defining the role of activity generation module in the activitybased travel demand model. 2. Defining the definition and scope of the activity utility concept. 3. Defining the decision dynamics within the activity generation models: skeleton versus non-skeleton activity decisions. 4. Devising a modelling framework for skeletal activity plans. 5. Investigating temporal arrangement of non-skeletal activities in activity planning (activity-agenda formation). 6. Developing an econometric framework for activity-agenda formation of non-skeletal activities. 7.

Investigating day-to-day dynamics in activity-agenda formation.

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8. Investigating complementary and substitutive effects in time allocation to different non-skeletal activity types. The long-term objective towards which this thesis contributes is to develop an operational model of the household activity generation process capable of supporting multi-day activity travel scheduling, together with the meaningful and seamless integration of the activity-based travel demand model within the ILUTE framework.

1.2 Relevance This research has both theoretical and applied implications. Theoretically, it represents the first attempt to gain an understanding of the complex phenomena of the activity planning/generation process by capturing the multidimensionality of the activity planning decisions in terms of the dynamics and the context, the scope of which goes beyond a typical day. Defining the activity utility to develop coherent models for activity planning and scheduling would constitute a significant contribution to the travel behaviour literature. The results of the investigation of the issues related to the planning and classification of flexible types of activities would be a valuable contribution to the time-use as well as travel demand modelling literature. Developing a mathematical modelling framework for activity-agenda formation would contribute to the literature of travel demand modelling techniques. From an applied perspective, this research contributes to development of an operational model of activity-travel generation as a part of an activity-based travel demand model to assess the deep-rooted impacts of emerging policies that past activity generation models are simply incapable of providing. Many emerging transportation and land-use policies such as Travel Demand Management (TDM), Transportation System Management (TSM), and application of Intelligent Transportation System (ITS), etc. have profound impacts that go beyond influencing daily activity scheduling-rescheduling decisions to include medium- to long-term activity planning decisions. This thesis provides a path to develop a comprehensive modelling framework that can address the wide-spread impacts of these policy measures, either within the context of a stand-alone travel demand model, or as a component within an Integrated Land Use Transportation and Environment (ILUTE) modelling framework. 4

1.3 Approach The research in this dissertation focuses on the whole of the activity planning process, as being separable from the activity scheduling-rescheduling process, while explicitly recognizing the interdependencies between these two processes, as well as the interdependencies among planning decisions of different dynamics. The research approach follows an inductive process of step by step investigations into a coordinated sequence of research questions. It is influenced by the complexity of the research topics and the objective of developing a comprehensive modelling framework. The inductive process of step by step investigation and thereby developing behavioural hypotheses before operational modelling ensures that the critical issues are addressed properly. This thesis draws upon multiple disciplines, especially with respect to the efforts to combine social-scientific and spatio-temporal behavioural theory with advanced statistical-econometric techniques. This combination of behavioural and econometric approaches is still somewhat rare in the literature, wherein behavioural scientists and econometricians are in many cases separate contributors to the literature, and the importance of the combination of behavioural theory and advanced mathematical methods are often restricted to the papers’ concluding remarks.

1.4 Thesis Outline This dissertation consists of ten chapters. The second chapter presents a literature review on overall activity-based modelling approaches, theories and empirical works. After reviewing the key concepts it compares the empirical models of activity-based travel demand. Based on the gaps and limitations of activity-based travel demand models it further concentrates on the theoretical aspects of behavioural models, especially the concept of activity utility. The third chapter presents a conceptual modelling framework for the activitytravel generation process based on the concepts and insights developed in the previous chapter. This chapter provides the theoretical background for the investigations and empirical model development in the following chapters. Chapter four discusses data issues, and presents a description of the activity diary 5

data used for empirical investigation and model development, along with preliminary statistics characterizing the database. Chapter five presents the empirical models for the fixed or skeletal parts of the daily activity generation process. The skeletal parts define the total time availability for the non-skeletal activities that are the focus of the following chapters. Before developing the modelling framework for non-skeletal activities, the sixth chapter investigates the temporal arrangement of the non-skeletal activities to decide whether the activity general model of the non-skeletal activity should consider the sequencing of the activities or not. Motivated by the findings of the previous chapter, the seventh chapter develops an advanced econometric framework for the activity-agenda formation of non-skeletal activities using the concept of activity utility defined in chapter four and the total time budget defined by the skeletal activities modelled in chapter five. Chapter eight further investigates day-to-day dynamics in activity-agenda formation by developing day-specific models compared to the week-long model presented in the previous chapter. In chapters six through eight, the classification of nonskeletal activities is considered as given, but it is important to investigate this classification because it defines the time allocation behaviour with respect to different objectives. So, the ninth chapter presents the investigation of time allocation behaviour in different non-skeletal activities in order to find the complementary or substitutive effects among them, if any. Finally, chapter ten summarizes the main findings of the thesis, particularly as related to the development of a unifying framework for future model development.

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CHAPTER 02: LITERATURE REVIEW 2.1 Introduction This thesis finds its base in existing literature of activity-based travel demand modelling. Its objective is to fill some gaps in this literature and to help move the theoretical state-of-the-art into empirical application. The amount of literature on activitybased travel demand modelling has been growing significantly over the past two decades. But criticisms and a sense of frustration exist among travel demand modelling researchers. According to Recker (2001), “most probably because of the inherent overwhelming complexities of treating the “whole” of travel, the approach has not been embraced by the main stream of transport researchers as offering a viable practical paradigm of travel demand modelling. There may indeed be wisdom in judgment in that, despite efforts over the past decades, activity-based modelling advancement has been relegated largely to either descriptive or proscriptive study, falling well short of being able to be used in the context of actual forecasting changes in travel behaviour ”. Despite this criticism research in this field has already reached a significant maturity level that has resulted in several operational models as practicing tools in many jurisdictions across in the USA, Canada, the Netherlands and Japan. Comprehensive operational activity-based travel demand models such as Albatross, CEMDEP, FAMOS, TASHA and many others provide evidence of the viability of activity-based theories in practical transportation analysis applications. However, continuous efforts to update the behavioural validity as well as computational efficiency of operational models are ongoing phenomena. The literature review presented in this chapter deals with the evolutionary process of travel demand modelling approaches that have been explored to date; the underlying theory of activity-based analysis and techniques used in the name of activity-based analysis; critical investigation of the gaps in empirical evidence of theoretically consistent and interconnected approaches; and the possibility of emerging methods such as activity utility. Thus, this chapter reviews the existing literature as a 7

whole and outlines the basis of focusing on specific issues that are the subjects of the subsequent chapters. More concentrated and focused reviews of relevant literatures are then included as required within subsequent chapters.

2.2 Evolution of Travel Demand Modelling Approaches Urban passenger travel demand analysis is one of the key tasks in transportation planning. The Urban Transportation Modelling System (UTMS) has been using as universal framework of analyzing urban passenger travel demand since the 1950s (Meyer and Miller, 2001). UTMS divides travel demand into four sequential steps: trip generation, trip distribution, modal split and trip assignment. The unit of analysis in UTMS is the trip and trips are considered as the product of human behaviour. But the fact is that the trip is more of a consequence than a direct demand. UTMS uses physical analogy for deciding where people travel. The movement of people over space is compared with “gravity flow” from trip production location to trip attraction location. Thus UTMS is not based on any coherent theory of travel behaviour. Also the approaches in UTMS are spatially and demographically aggregate. Even a household based trip generation model of a UTMS cannot capture intra-household interactions. Despite these criticisms UTMS was the only option to travel demand modelers until the 1970s. Since the 1970s the advent of new concepts and theories have given the opportunity to shift the travel demand modelling approach from the traditional trip-based approach to more of a derived demand approach (considering trips as derived demand rather than direct demand) and from an aggregate demand analysis approach to more of a disaggregate microsimulation approach. The two revolutionary breakthroughs that initiated this paradigm shift are rapid progress in econometric random utility-based individual choice models and activity-based travel demand modelling. Since the 1970s the econometric models of individual’s choice analysis and activity-based travel demand modelling have gone hand in hand. Though these two are often two individual areas of research, the activity-based travel demand modelling in many cases relies on econometric choice and demand analysis techniques. Based on these general comments, the next section provides an overview of the historical evolution of activity-based travel demand modelling.

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2.3 Activity-based Approach to Travel Demand Modelling The state-of-the-art in activity-based travel demand modelling has experienced significant progress over the last two decades. The activity-based approach to travel demand modelling begins with the premise that people travel so as to participate in outof-home activities that are dispersed over the space (work, shopping, school, social, recreation etc.). It is considered that, in order to develop policy sensitive and behaviourally rich travel demand models, one must explicitly model the evolution of daily activity patterns in which people engage. The anticipated outcomes of this approach are a deeper understanding of personal travel behaviour, improved policy analysis and improved forecasting. Sociologist Stuart Chapin (1974, 1978), environmentalists Cullen and Godson (1975) and planner Hägerstrand (1970) formulated the basis of activity based travel demand modelling. Based on these seminal works Ian Haggie (in Jones et al, 1983) proposed the need for understanding travel phenomena as a part of complex activity patterns. The consensus has grown that in order to model travel demand we have to look deeper to find the reason of travel other than considering the trip as a unit of demand. The importance of space as provider of opportunity to involve in different activities as well as constraints that restrict our activity desires together with limitations of time are recognized to analyze travel demand. It is also understood that activities emerge from basic needs of survival and selfrealization (Arentze and Timmermans, 2000). Out of all the different constraints (capability constraints, coupling constraints, authority constraints etc.) and opportunities (opportunity over space to involve in different sorts of activities, e.g. shopping centres, recreational centres, work places etc. and also temporal opportunities, e.g. time availability, time constraints of the activity centres etc.) a set of activities is selected that defines a path in space and time. This process is explained by Hägerstrand using the concept of the time-space prism. So, it is clear from the very beginning that there are two basic component of conceptualizing activity-based travel demand model. The one component deals with the basic needs or self-realizations that instigate us to involve in different activities; this can be termed the activity generation component. The other component is the spatio-temporal opportunities and constraints that finally define the actual participation in different 9

activities, which can be termed activity scheduling. More specifically the desire or need to participate in different activities indicates the activity generation, and the allocation of time and space to specific activity needs within limited action space and time limitation indicate activity scheduling. Obviously the interactions between these two components are two-way. Sometimes spatio-temporal opportunities instigate different activity needs, and sometimes different activity needs exceed the spatio-temporal opportunities and thereby people change their life style. These are the basic underpinnings of the concept of activity-based travel demand analysis. Since the beginning of this new trend, researchers have been involved in developing models for activity-travel demand along with explanatory analyses to understand behavioural process. CARLA is one of the earliest examples of modelling efforts based on activity approach (Jones et al 1983). CARLA explicitly recognizes the difference between activity generation and scheduling. However, the way of dividing the generation and scheduling process and the technique of modelling adopted by various modelers has resulted in different modelling approaches. Arentze and Timmermans (2000) classify the activity-based travel demand modelling approaches into several categories: 1. Single facet model 2. Constraint-based model 3. Utility-maximization model 4. Computational process model 5. Microsimulation model Single facet models deal with some specific attributes of activity patterns but not the activity pattern as a whole. Abundant literature is available that deals with specific issues of activity-travel patterns, e.g. frequency, duration, start time etc. Such models can be parts of an overall activity-based modelling system. Constraint-based models deal with overall activity-travel demand comprehensively and use the spatio-temporal constraints to 10

select activity patterns for the individuals. However, the question is how to develop alternative activity-patterns for those individuals before selecting a particular pattern (i.e. the choice set for activity pattern). The generation process of activity-travel patterns can be based on optimization of some utility calculation that falls into the third category (utility-maximization), it may follow some specific behavioural rules or decision trees that fall into the fourth category (computational process model), or the patterns can be generated using Monte Carlo simulation techniques that fall into the fifth category (microsimulation). So, here the activity-based modelling techniques are classified into three broad categories: 1. Utility-maximization technique 2. Computational process or Rule-based model 3. Hybrid model: combination of utility theory, rules, microsimulation and all other type models

2.3.1 Utility-Maximizing Models The utility-maximization approach is mainly based on random utility maximization (RUM) theory. Advances in discrete choice theory and overall econometric methods allow applying RUM theory in activity-travel demand modelling. The basic assumptions are that people are rational utility maximizers and possess complete information about all possible alternatives is available. The alternatives are represented by the bundle of attributes (both of choice makers as well as the alternative) and people select the alternatives in order to maximize the overall utility (see Ben-Akiva and Lerman, 1985 for a comprehensive description of theory and application of RUM-based discrete choice theory). The Adler and Ben-Akiva (1979) model is one of the earliest examples of this type of model. They assume that an individual chooses a complete one-day activity pattern from a number of alternative patterns in order to maximize the total activity pattern utility. The competing patterns are characterized by types of modes, number of destinations and purposes, time expenditure to various purposes, travel time by 11

corresponding modes etc. The individual’s socio-economic characteristics are also used to specify his/her tastes and preferences. Selecting the utility maximizing pattern among a number of alternative patterns is considered as a discrete choice problem and the multinomial logit model is used. The Recker et al (1986a, 1986b) model, STARCHILD is an example of more generalized activity-based model that uses the concept of utility maximization. Their framework is explicitly activity-based. Travel is considered as the mechanism that allows scheduling of activities and the complex travel behaviour is the resultant of complex activity scheduling behaviour. It models the demands for individual activities with the consideration of inter-activity and intra-household correlations, other than considering a complete pattern as unit of choice. Kawakami and Isobe (1982, 1988, 1989) developed utility-based models for workers’ activity-travel demand. Their models are also activity pattern based, but the whole activity patterns are not considered as individual choice units. Rather the patterns are built up step by step as trees of decisions for activities before work and after work activity choices. For each component (before and after work) hierarchical decision structures are adopted to select choice of non-work activity, then choice of activity-travel pattern and finally the exact destination. These hierarchical choice problems are formulated as a nested logit based RUM model. Ben-Akiva and Bowman (1995, 1996) criticized Kawakami and Isobe’s model for not considering the interdependencies of activity-travel behaviour across the day. In contrast, they proposed frameworks for both workers and non-workers for daily activityschedules into a set of home-based tours hierarchically defined through the choice of activity patterns, choice of primary tour, choice of destination and mode for primary tour, choice of the time for secondary tour, destination and mode for secondary tour. This hierarchical decision structure is also modelled as RUM-based nested logit model. This framework was later implemented in the Portland model (Bowman et al 1998). Wen and Koppelman (1999) proposed a similar framework but incorporated the household context of decision-making and activity-travel behaviour. Their modelling structure consists of two hierarchical structures: first – the number of maintenance stops, assigning stops to husbands and wives, vehicle allocation; second – individual level of 12

decisions on number of home-based tours and choice of maintenance stop to the tours. Similar efforts were taken in the Mid-Ohio Regional Planning Commission (MORPC) Model, (Vovsha et al, 2004); the Atlanta Regional Commission (ARC) Model, (Bradley and Vovsha, 2005); and the Tel-Aviv model, (Shiftan and Ben-Akiva, 2006). Finally, according to Arentze and Timmermans (2000), these types of models are closer to the tour-based model that originated in 1970s in the Netherlands than activity-based models. The general approach of these types of models is encapsulating trips into tours, with all travel is viewed as parts of round trip journeys based at home.

2.3.2 Computational Process or Rule-Based Models The assumption of overall pattern-based utility maximization in utility-based model as described above raises some fundamental behavioural issues. The psychological argument against global utility maximization is that people do not always take optimal decisions rather they frequently take sub-optimal decisions. The key reasons of suboptimal decisions may be: a satisficing approach rather than maximizing, limitation in information acquisition, and limitations in information retention. So, considering patternbased utility maximization may be one option of many variations of human behaviour but it rather fails to elucidate in much detail how utility maximization is accomplished (Gärling et al, 1994). Such an approach tends to be confined to specifying what factors affect the final choice, but the process of evolution of choice sets and final decisions are left unspecified. Psychologists Newell and Simon (1972) first proposed that human decision making process rather follow sets of IF----THEN---ELSE rules. The rules indicate a reason-based behavioural process that overwrites cost-benefit calculation type maximization (like RUM). Tversky and Kehneman (1981) argue that various kinds of context influence the heuristics or rules of human decision making process. Such behavioural rules or production system specify the decision making process as functions of sets of conditions. Application of production system theory in activity-based travel demand modelling gave rise to a new modelling approach often referred as computational process or rule-based model. Hayes-Roth and Hayes-Roth (1978, 1979) first applied this theory in describing the activity scheduling process. Their model architecture is based on the theory that 13

people make decisions at different levels of the decision making process and the changes between the levels are opportunistic. Their model is a full comprehensive decision making framework that incorporates problem solving strategy, cognitive architecture of data storage and retrieval. The operational version of the model is a production system model that uses a set of rules to map the interacting environment for decision making, having a set of planned activities and time scope for each of them. Decision rules are abstracted from a data set collected based on a “think-aloud” data collection technique. The “think-aloud” technique refers to the data collection method in which the subject is asked to list all possible considerations and decisions in activity planning. CARLA, developed by Jones et al, (1983) is an earlier example of this type of model that uses a combinatorial algorithm to generate feasible activity patterns. CARLA is often broadly classified as a separate category of activity-based model (constraintbased model) (Arentze and Timmermans, 2000). But it uses a combinatorial algorithm where alternative feasible activity patterns are first generated and then a number of heuristic rules are used to reduce the number of alternative activity patterns. It uses a decision tree structure for the activity scheduling process. It does not use a RUM approach for generation and scheduling. It mainly uses the time-constraints for different activity types to model the activity scheduling process. Gärling et al (1989) proposed a computation process model of activity-scheduling process named SCHEDULER. The conceptual model of SCHEDULER is implemented for predicting activity patterns of commuters after introducing tele-commuting using GIS for input of spatial information (Golledge et al, 1994). Following this model Kwan (1997) developed the GIS based activity-scheduling model GISCAS. These models are based on several rules that an individual uses for selecting activity type, destination and start time from an agenda for a specific time period. The models consider that individuals and households always try to attain certain goals using activities as the means of achieving their goals as the environment offers opportunities and constraints. The agenda is considered as a Long-Term Calendar (LTC) that collects different activities together with their attributes, including duration and priority. The scheduler module draws the activities from LTC to give them sequences, chooses locations, resolves conflicts by changing the sequences, and stores the processed schedule in Short-Term Calendar (STC) for 14

execution. AMOS (Activity Mobility Option Simulator) is a rule-based dynamic microsimulation model for household activity-travel over time and space (Kitamura et al, 1993, 1996; Pendyala et al, 1995, 1998). AMOS is developed as a part of SAMS (Sequenced Activity Mobility Simulator) that was applied in Washington D.C. The model is developed to assess short term responses to various TCMs (Transportation Control Measures). Major components of the model are: Baseline Activity Travel Pattern Synthesizer, Response Option Generator, Activity-Travel Pattern Adjuster and Evaluation Module. The Baseline Activity Travel Pattern Synthesizer generates activitytravel pattern for the individual from trip diary data using socio-economic characteristics of the individual, characteristics of the transportation network, land use characteristics and desired policy initiatives. The Response Option Generator creates different responses to proposed or implemented TCMs. Considering the responses the Activity Travel Pattern Adjuster adjusts the generated pattern and presents it to Evaluation Module to evaluate the adjusted pattern. This process is iterated until the pattern satisfies the Evaluation Module’s requirement. SMASH (Simulation Model of Activity Scheduling Heuristics) model is also a rule-based model like AMOS, (Ettema et al, 1993, 2000). It simulates the responses of people in terms of adjusting their activity scheduling process due to introduction of various policy measures. It models activity scheduling as a step-wise process. The schedule is repeatedly adjusted until it meets the person’s requirements. The decisions to change schedules are modelled as a discrete choice problem using a nested logit model. Thus it depicts activity scheduling as a heuristic search procedure. ALBATROSS is a comprehensive and operational rule-based activity-based model (Arentze and Timmermans, 2000, 2004a, 2004b). It deals with all types of decisions comprehensively: long-term, medium-term and short-term decisions. The longterm decisions influence the medium-term decisions and the medium-term decisions influence the short-term decisions. The long-term decisions are marriage, birth, location choice, etc. the medium-term decisions are life-style decisions and the short-term decisions are daily activity calendar, scheduling etc. A decision tree algorithm, CHAID, is used to define an exhaustive set of mutually exclusive rules for each decision step. It 15

uses the concept of fixed or skeleton activities to start the daily activity scheduling then fills the gaps within the daily activity skeleton by different flexible activities using different rules. The skeleton and flexible activities are drawn from decisions tree calibrated using an observed activity-diary data set. The problem of AMOS and SMASH type models are that they are good for modelling short-term policy analyses but not for long-term demand forecasting. The models need to be customized to specific policy responses by introducing specific rules. Defining rules from observed data does not necessarily guarantee temporal and spatial transferability. These types of models are mainly concerned with the activity scheduling process and the baseline schedules (generation or demand) are provided as input. Comprehensive rule-based models like SCHEDULER and CARLA also face the similar problem of identifying multifaceted rules to deal with all sorts of interactions between the person and the environment. They also start with given activity patterns; that is inputs are generated in a very empirical manner that lacks a proper theoretical basis. Complete dependence on rules also makes such models very static; in addition the handling of preference heterogeneity is really a difficult task. On the other hand ALBATROSS is totally based on a decision tree approach. The decision trees are derived from observed data and may need proper theoretical justification in order to link the latent versus observed activity-travel behaviour.

2.3.3 Hybrid Models There is also a category of activity-based model that uses both the concept of rules and utility maximization; we refer to these types of models as hybrid models. This type of model is becoming popular due to flexibility in handling different behavioural and spatio-temporal issues. The hybrid approach allows considering different types of modelling techniques for different components of the overall modelling structure. It also allows using the microsimulation approach in an activity-based framework. PCATS (Prism-Constrained Activity Travel Simulator) uses temporal, spatial and modal constraints to simulate activity-travel behaviour, (Fujii et al, 1997; Kitamura and Fujii, 1998; Kitamura et al, 1998). PCAT is the prerequisite of another component, PCATS-RUM, which is an example of hybrid model. PCATS creates the choice set using behavioural rules to give input to PCATS-RUM. The latter component uses the principle 16

of utility maximization. So, although the authors of PCATS describe it as a rule-based model, it uses both rule and utility maximization concepts, (Arentze and Timmermans, 2000). It divides the day into two periods: open and blocked periods. The blocked periods are defined by fixed commitments like work activities and the time-space prism is defined by the window of opportunities between blocked periods to be filled by flexible activities. A nested logit model is used to fill the open periods with flexible activities. PCAT-RUM defines the schedule that maximizes the utility of activities to fill the open periods subjected to time-space and modal constraints. PCATS has been further improved and used to develop an activity-based microsimulation model for Florida, named FAMOS, (Pendyala et al, 2004). The difference between these models and the utility-maximization models (as discussed in sub section 2.3.1) is that these models do not use the whole-day utility maximization approach, rather utility maximization for the open period is considered, along with recognition of the existence of different spatio-temporal constraints. It also considers the concept of activity utility as the unit to sum up for getting total pattern level utility, rather than pattern utility as the unit of analysis. TASHA (Travel Activity Scheduler for Household Agent) is another example of a hybrid model (Miller and Roorda, 2003). The scheduler component of this model is rule based, the generation component uses microsimulation from observed distribution of activities, and the mode choice component of this model is utility based. The utility structure of the mode choice component also uses different rules to incorporate the possibility of ride sharing, joint tours, etc. (Miller et al, 2005). TASHA is developed based on the concepts of projects. A project is a collection of activities with common goal(s). Life is defined as consisting of several projects. Each project generates candidate activities for scheduling, called a project agenda. Activity episodes are inserted into each project agenda with preliminary time sequences with other episodes of the project agenda. Once the project agendas are formed the schedule of the individual is constructed by drawing the activity episodes from the project agendas. Activity attributes are modified, travel is added, or episodes may be deleted using scheduling rules. CEMDAP (Comprehensive Econometric Model of Daily Activity Pattern) uses a conglomeration of a number of econometric models to simulate the activity-travel 17

patterns of household members. It does not simultaneously model the daily activity pattern as a whole; rather it uses sequential and nested decision structures, where separate models are used to predict different activity attributes at different levels. It defines the activity-travel pattern into three levels: stop, tour and pattern. It uses utility based econometric models for each level but certain types of constraints or rules are also used to restraint the maximum number of tours and maximum number of stops in any tour. However, the stronger feature of this model compared to other operational activity-based model is the use of 22 advanced econometric models justified to the statistical properties of the base data (Timmermans, 2006).

Above all, the common trend in activity-based modelling is the use of the microsimulation approach. In the transportation community microsimulation is often understood to refer specifically to the microscopic analysis of route choice, network performance and traffic flows only. Common examples of traffic microsimulation models include CORSIM, TRANSIMS, PARAMICS etc. (see Barrett et al, 1995). Such models tend to be applied to systems in which the equilibrium condition is not clear and closed form solutions for the equilibrium states are not available. But the more generic concept of microsimulation involves the microscopic resolution of any system where individual entities are modelled as individual agents. In activity-based modelling the agent is considered as an intelligent entity (individual person or household) that shows autonomous behaviour in response to stimuli from its external environment. Actually the agent-based approach to activity-based modelling truly represents a paradigm shift in how we can think about, analyse and model travel demand that holds promise to significantly change our transportation analysis capabilities (Miller, 2005a). Many operational activity-based models are microsimulation based. ALBATROSS, AMOS, CEMDEP, FAMOS, TASHA, SMASH: these all exploit the basic concept of microsimulation, and as our understanding of activity-travel behaviour increases this consistently makes it easier to take the microscopic or agent-based modelling framework. And vice versa; microsimulation provides a conceptual and computational framework for thinking about and implementing activity/agent-based models. 18

2.4 Modelling Activity Generation All activity-based models as discussed above can be broadly divided into two parts: an activity generation component and an activity scheduling component, (Habib and Miller 2006). The activity generation component captures the desire to participate in different activity types, while the activity scheduling component defines the final activity sets with all attributes that to fit the actual time period (the modelling span: day, week etc.). Of course there are two-way feedback relationships between generation and scheduling, although the modularization into these two major parts has become a norm in activity-based modelling approach. Bhat and Koppelman (1993) commented 13 years ago that the activity generation component was the most under-researched area in activitybased modelling literature, and this statement is still true. This becomes clear by investigating the generation components of the existing operational models discussed in the previous section. Alder and Ben-Akiva (1979) consider complete activity patterns as input. The input patterns are drawn from observed data, but they do not model the way in which a specific agenda is developed. Rather, these patterns are considered as given. STARCHILD Recker et al (1986a, 1986b) considers separate generation and scheduling components. The generation component is considered as activity program formation. It considers the duration and locational attributes of the activity episodes at the generation level. These are influenced by mode availability and activity chaining opportunities that are schedule level decisions. So a clear distinction between generation and scheduling in terms of feedback and updating does not exist. All other pattern-level utility maximization models described in subsection 2.3.1 suffer the criticism of considering the generation component as a given input from observed data. These models mainly model the activity scheduling process as choices to select alternatives from the given input either comprehensively or sequentially. The rule-based model CARLA draws patterns from observed data to give input to the component that adjusts the pattern to comply with different constraints. The generation process is mainly overlooked and considered as a given input. AMOS and SMASH also use the same approach of considering the generation process as external input to the model. ALBATROSS, on the other hand, deals comprehensively with both 19

generation and scheduling. It refers to the daily activity generation component as activity program generation and an individual activity program is derived from the household activity calendar. The household activity calendar contains different activities related to long-, medium- and short-term household decisions. But activities are drawn from calendar based on rules, not based on explicit benefit measures like activity utility. Rules are often adhoc and static in nature, especially when used for activity generation. The lack of a specific unit for measuring benefit/loss in participation and the need of participation indicates an absence of behavioural trade-offs in the activity demand generation model. FAMOS and TASHA use Monte-Carlo simulation to generate different activity demands drawn from observed distributions. This is another way of considering the generation component as given input. The input is generated through a simple microsimulation process. The behavioural elements of the model are concentrated in the scheduling process. These models put most of their efforts into the scheduling process rather than the generation process. These models also fail to incorporate any measurement of the benefit of activity participation. In the case of CEMDAP, the activity generation component is similar to trip generation models of traditional four-stage model systems and lack proper time definition, characterization of activity-travel patterns, etc. (Timmermans, 2006). It also lacks a specific unit for measuring benefit/loss in participation and the need for participation. Bhat and Koppelman (1993) discuss the definitions and relationships between the activity generation and activity scheduling processes in detail. According to their definition, activity generation indicates the activity demand and tentative fixing of activity attributes to provide input to the activity scheduler. Apparent complications in the scheduling process attract researchers to put maximum concentration on the activityscheduling process and take adhoc or arbitrary measures for the activity generation stage. But from the travel demand point of view the generation process is the most critical part that not only reflects the responses to different transportation policies but also defines the interactions among different long-, medium- and short-term household decisions (Habib and Miller, 2005). One of the major reasons for overlooking behavioural processes in activity generation is the lack of a consistent theoretical foundation. This lack is prevalent 20

in terms of: 1. Sound theoretical understanding and 2. The abstraction used to model the process. Achieving a sound theoretical understanding is related to the conceptualization of time. The definition of time is very important in activity-based modelling because modelling activity-travel demand is in many ways a time use or time allocation issue, (Gärling et al 1999). A crude conceptualization of time leads to the ambiguous or adhoc representation of the dynamics of activity-travel behaviour in activity-based models, (Litwin, 2005). These all raise the crucial question: “What should be the appropriate modelling span (a single day or a week)?” On the other hand the application of a theoretical foundation in modelling demands appropriate translation of theoretical concepts into modelling technique. Since all of our demands are related to desires for fulfilling various needs (Maslow, 1970), in the case of activity demand, all our activities are one way or another related to obtaining some return(s) for fulfilling these needs. Abstraction of the return(s) from different activities can be compared to the benefit/losses gained from an activity and measured in terms of the microeconomic concept of utility. In this case utility indicates ‘activity utility’. The other behavioural/theoretical aspects of activity demand, e.g. priority, flexibility, etc. all can be related to ‘activity utility’, (Miller, 2005c). Axhausen and Gärling (1992) identified 14 year ago that the research into defining ‘activity utility’ and the evolution of ‘activity utility’ over time is an important but unresolved research question. Nine years after Timmermans et al (2001) raise the same frustration of insufficient research on this topic. In order to conceptualize the utility theory for activitybased analysis, it is necessary to review the generic concept of utility per se. Given this, the next section concentrates on this issue.

2.5 The Concept of Activity Utility The benefit, pleasure, aversion of unexpected consequences, etc. derived from engaging in any activity episode can be referred as the ‘activity utility’, (Kraan, 1997; 21

Miller, 2005c). Nash (1950) describes the concept of utility as an anticipation or expectation or desirability. In economic terms, an individual derives a certain level of utility either directly or indirectly from the participation in an activity. Timmermans et al (2001) suggests that the individual gains some benefit from each activity and the net benefit derived from an activity can be termed as ‘utility’. The conventional activity-pattern based utility maximization is often criticized for its lack of behavioural validity. It is argued that the complexity of real life in addition to our limited information processing and problem solving capacity, formation of habit, idiosyncrasy etc. often makes us satisficers rather than global optimizers (Kapteyn et al, 1979; Simon, 1990; Tversky and Simonson, 1993). But this criticism is not against the concept of utility; rather the way utility theory is applied. So, it is desirable to investigate how individuals assign utility to individual activity episodes (Axhausen and Gärling, 1992). Another common criticism of the concept of utility theory is that it is an indirect or latent measure which we do not observe, (Kapteyn et al 1979). In response to this criticism we can argue that in modelling human decision making processes in diverse choice situations, and especially when we do not observe the mental process of the actors, the only way is to base the model on the observed outcome of the choice process and rationally justify the choice process assumed. The concept of activity utility is the same approach to model how individuals assign value to different activity episodes. The concept can be derived from the economic theory of utility.

2.5.1 Forms of Utility The concept of utility was first adopted as a psychological entity, which is measurable in its own right. In the case of activity utility, it indicates the expectation of the actor upon completion of an activity. According to this concept, the term utility indicates the ‘expected utility’ per se, (Fishburn, 1988). Over time this hedonistic conception of a psychological entity, measurable its own right, has been evolved to a behaviouristic interpretation as a simple level for the explicit value of a function that describes an actor’s behaviour, (Strotz, 1953). According to Winston (1987) some activity may generate positive or negative satisfaction when undertaken, while the accomplishment of some activity may yield positive or negative satisfaction. The utility of activities can be devised to differentiate the on-going satisfaction (positive or negative) 22

of doing something and the final satisfaction upon the completion of the activity. This decomposition may allow us to incorporate minor details of behavioural components and different trade-offs within our modelling frameworks. Recker et al (1986a) argue that the utility of any decision depends on the outcome of the decision and the decision process itself. So the utility of an activity can be divided into two parts: process utility and goal utility, (Winston, 1987; Axhausen and Gärling, 1992). For example, thinking of a commuter’s work trip; the commuter’s aim is to reach the office, but to reach the office he has to travel. Reaching the office is important to start the work that generates the salary (goal utility), but the travel to the office may not be pleasant to him due to traffic congestion and might create dissatisfaction (process utility). Thus the work trip of the commuter may provide two different types of utility to him. Another example may be ‘eating dinner’. Eating dinner is intended to satiate hunger (goal utility) but to satiate hunger one has to eat and the satisfaction (process utility) from eating depends on the type of food, place of eating, travel necessary to reach the restaurant, etc. It is clear that a trade-off is involved between goal and process. For example, travel distance and time limitation (negative process utility) may compel one to go to a nearby restaurant for lunch that one does not like more than another, more attractive one, which is far away. Although some authors only recognize the process utility of activity, (Juster, 1990), according to Winston (1987), conflicting preferences between process and goal utility can arise, especially in cases when they have opposite signs, for example, when: “Saving or jogging everyday or otherwise suffering now for a future reward”. Practically we do not observe utility, we observe actions. Utility of activity is latent: it can be perceived but cannot be seen in quantifiable form. Aarts and Dijksterhuis (2000) argue that the typical goals of activities often lead to habit formation. Their investigation of automatic activation of goal directed behaviour also reveals that the goal and process attributes of the motivation for activity participation do exist. But for such a latent variable (i.e., utility) the dichotomous division into goal and process needs detailed behavioural data to estimate or formulate. Given the behavioural data, the formulation of the utility of activity can be specified in two distinct ways: ‘ordinal utility’ and ‘cardinal utility’. Ordinal utility 23

indicates the mathematical expression of the utility function, while cardinal utility implies a particular numerical value of the utility function, (Ben-Akiva and Lerman, 1985). The comparison of different alternatives can be based on the cardinal numbers of utility values or the ordinal expressions. However, the incorporation of error in perception, variability of individuals’ choice, etc. may result in the realization of ordinal utility in the form of cardinal numbers. This then raises another issue of the comparative value of utility versus absolute value of utility. The concept of the comparison of utilities is deeply rooted in the economics and management science literatures. In economics, the comparison of utility in ordinal form is done through econometric formulation of choice preference modelling. In almost all of these formulations, the utility of an alternative is compared with the utility of another one in an absolute form. But there is also some literature focusing on the concept of relative utility per se rather than comparing absolute values. The next section discusses this issue.

2.5.2 Relative versus Absolute Utility Although in econometric models sometimes it is assumed that the individual’s utility is independent of the behaviour of other people or of its own past experience, the majority of psychology and sociology assumes that human choice or preferences are variable and interdependent. They usually term this theory as relative deprivation theory, adaptation level theory or reference group theory (Davis, 1959; Stadt et al, 1985). Kehneman and Tversky’s ‘prospect theory’ also indicates that people evaluate decisions with respect to reference points (normally status quo) and judge their decisions in terms of gain or loss. In management science a similar concept is termed the theory of relative interest (Coleman, 1973; Gupta, 1989). Based on such deprivation theory or theory of relative interest, the notion of relative utility in comparison to absolute utility is developed. This concept is that the utility of any activity is perceived only relative to some reference point. In a multi-facet choice situation, people always face some sort of negotiation or conflict resolution process, where their choice of a particular type of activity, in fact, indicates their relative preference over the other available options. Zhang et al (2004) argue that an individual’s evaluation of an alternative is always relative to the other alternatives, even when there is no alternative, in which case the comparison is made with previous experience of the 24

same or similar alternative(s). They used the concept of relative interest proposed by Coleman (1973) and modified by Gupta (1989). The relative interest of an individual i to an alternative j is the ratio of utility difference between alternative j and the least preferred alternative j0 to the summation of utility differences between alternative j and all other available alternatives. So in the case of the single alternative its value is 1 and the value decreases with increasing number of alternatives to the minimum value of zero. Zhang et al (2004) used relative utility for choice maximization purposes and describe the relative utility of an alternative j as the product of relative interest of that alternative and the summation of utility difference between the preferred alternative and every other individual alternative. Although this concept of relative utility is promising, Stadt et al (1985) argue that there is no way to prove that utility is completely relative. A review of related literature indicates that when people are not subjected to strict constraints, the comparison of individual utility of alternatives is appealing, but when people are shaped by a higher number of constraints and the need for an immediate decision for implementation, the concept of relative utility is more appealing. However, the conceptualization of any form of utility function is related to the other attributes of activities. Activity attributes, such as priority, flexibility, urgency, which shape the choice of activities, can be a function of activity utility, among other factors, (Miller, 2005d). Since the concept of activity utility is still an evolving one, the next section concentrates on the components that can comprise the utility of activity.

2.5.3 Components of Activity Utility Some authors consider the full activity/travel pattern as the unit of analysis; hence they derive the utility function for a full activity/travel pattern rather than an individual activity or activity episode. Alder and Ben-Akiva (1979) derived a utility function of travel pattern as a function of scheduling convenience, net non-home activity duration, activity site attributes, and residual income after travel expenses and socio-economic variables, and used a multinomial logit model to relate utility scores for alternative travel patterns. Supernak (1992) draws temporal utility profiles of actions as a whole and compares the cumulative utility of activity profiles for the selection of activity pattern. He agrees that the daily choice scenarios involving chains of activities constrained 25

temporarily, geographically and logistically is quite complex. In addition to these, the dynamic interrelationships among different activities apparently make the derivation of a utility function of activities more complex. It is conceivable that such complexity of measuring utility function increases the complexity of estimating travel demands, (Kapteyn et al, 1980). In such a complex situation, the utility of an activity episode can be perceived as consisting of two distinct parts, as proposed by Winston: goal and process utility. Recker et al (1986a, 1986b) argue that the utility of a particular activity can be determined only within the context of an entire agenda. In response to this, we can argue that the context of agenda can be easily incorporated within the goal utility component of the activity, which may be separate from the process utility component. That means the goal utility of an activity reflects the project or agenda level trade-offs, while the process utility of an activity reflects the scheduling or execution level trade-offs. The term goal utility is in fact synonymous to direct utility and the term process utility is synonymous to indirect utility as described in classical micro-economic theories. In activity travel analysis, division of utility in such a manner may ensure the inter-linkages among different activities at different levels of decision making process. The next subsections discuss these two components in detail. 2.5.3.1 Goal Utility The goal utility of an activity depends on the type of activity. Miller (2005b) gives the definition of four generic types of activities in which we can fit all activities. These are Biological or Physiological activities that address basic needs for a biological and human (psychologically different from other beings) being and are necessary for personal maintenance; Social / Cultural / Religious activities involving more than one actor, either intra-household or inter-household, that address psychological satisfaction; Cognitive activities related to mental development; and Labour activities that are instrumental actions associated with the acquisition and maintenance of physical resources. Doherty (2003) argues that any physical or mental activity must have an end goal of satisfying needs. This activity classification is mainly based on the needs and the goals of activities are to satisfy these needs. So, it is more conducive to divide activities in general according to underlying 26

needs. But the problem of any generic typology is that there are some activities whose goals are only indirectly related to a need or are related to multiple needs. For example, consider grocery shopping. This activity has the goal to buy goods. These goods may be food, which is related to the physiological need of eating, or may be a book, which is related to the cognitive need of learning. For such activities with a common goal, the activities have more or less a sequential pattern. For example, to satisfy the need of eating one may need to perform the activity of shopping (whose goal is to buy food), then he/she may need to perform the activity of cooking (whose goal is to get the food fit for eating) and then he/she has to perform the activity of eating (whose goal is to satiate hunger). Similarly for the need of learning, one has to go to a library, borrow books and read the books (multiple types of activities). Axhausen (1998) divides life in terms of project, agenda, episodes, etc. A project is a set of activities with common goal(s); an agenda is the collection of activities to be scheduled within a time frame; and an episode is an individual instance of an activity with a specific start and end time, together with other attributes. Thinking of our life in terms of projects, different projects may be composed of different types of activities having different needs at the end. So, the comparison of activities for sequencing may have several stages: First stage: comparison of activities having the same ultimate goal; Second stage: intra-project comparison, meaning the comparison of activities having different ultimate goals within a project; Third stage: inter-project comparison, meaning comparison of activities corresponding to different projects. It is clear that for the first stage comparison ‘the priority with respect to potentiality’ that means precondition or precedence is the appropriate tool but for the second or third stage of comparison the goal utility function of activities may be an appropriate measuring tool. Here, the goal of any activity not only targets the satiation of the need but also incorporates some project and agenda level attributes. So to devise the goal utility we need to identify both the goal of the project and the goal of the individual activity episode that belongs to the project. For example, the goal of a dinner party project is to arrange a social get-together, and goal of shopping that belongs to the dinner party project may be to buy food. It is necessary to identify both of these goals because buying food may seem to be very important but one may cancel this activity for the sake of another project that is 27

more important than the dinner party project. So, to devise the generic goal utility function of an activity episode, we need the generic classification of projects as well as the activities. 2.5.3.2 Process Utility The process utility of an activity episode refers to the utility gained (either positive or negative) during the process of execution of the episode, which is the indirect utility of the activity episode. Although the execution of an episode is the final stage of the overall process, it is conceivable that one should have some idea about the execution of an activity at the project level. For example, the duration of an activity episode is finally fixed during its execution, but one should have an idea about the duration at the beginning when one thinks about that activity, what is referred to here as project level thinking. So there is a trade-off in defining activity episode attributes at different levels of decision making based on these two components of utility. Again, frequently the process utility may have an opposite sign relative to the goal utility. Joh (2004) argues that this direct part of utility of activity episodes may be opposite to the other component, except for some recreational activities. This conception in fact justifies the diminishing pattern of increasing total marginal utility (summation of goal and process utility) of activity episodes with respect to time. The derivations of utility of activity episodes as found in the literature are mostly focused on the indirect satisfaction from the activity episode and are based on the concept of classical economic theory of diminishing utility with time. This means the longer the time spent on an activity the more satisfaction one obtains, with decreasing marginal utility. The theory behind this concept is that the people tend to spend as much time as they can for a particular activity, but the extra utility obtained from spending extra time on that activity decreases over time, leading eventually to instigating a new activity of higher utility. Based on this concept some authors suggest that utility of an activity episode depends on the ‘characteristics’, ‘type’, ‘duration’, ‘location’ and ‘frequency’ of the activity episode, (Kraan, 1997). Golob (1981) suggests two types of constraints that shape the utility of activities are ‘income budget’ and ‘available time’. Again Kraan (1997) argues that income and time budget varies between individuals and depends on ‘employment type’, ‘age’, ‘sex’ etc. of socio-economic and demographic characteristics. 28

Kitamura (1984) argues that activity choice and time allocation are obviously interrelated. Bhat and Misra (1999) also use the same concept to derive utility of discretionary activities. Recker et al (1986b) suggest that the utility of participating in an activity is realized when the participation takes place and argue that the utility of participation in an activity is nothing but the utility of time spent for the participation. Joh et al (2001) argue that the utilities of activity episodes are associated with some selected characteristics of activities as well as characteristics of individuals and households. Kitamura (1984) argues that the utility of activity depends on many observed and unobserved microscopic factors; time allocation to various activities should be modelled by using the concept of random utility. But in any of these studies the concept of utility is not precisely specified. Sometimes the process and goal utility are considered together and sometimes the utility consideration includes only the process utility (Joh et al, 2001)

2.6 Summary and Commentary Activity-based travel demand modelling originated with the concept that travel is not always a direct demand but rather it is a derived demand. Work of Hägerstrand, Chapin, Cullen and Godson provide the basic theory of an activity-based approach to travel demand modelling. These early papers influenced travel demand modellers to move from a trip-based travel demand approach to a tour-based approach and then an activity-based approach. The basic tenet of the activity-based approach is modelling the behaviour of the traveler rather than simply replicating the observed trips mechanistically. Human behaviour is complex and multifaceted, and cannot be explained by absolute theories like those in physics and chemistry. The psychological theories explaining travel behaviour are still evolving. Hence, modelling activity-based travel demand also follows the same evolutionary process. However the paradigm shift from trip-based to activity-based modelling has already taken place. A number of activitybased models are working in several jurisdictions of USA, Canada, Europe, Japan, etc. The activity-based models, either conceptual or operational, documented in the literature can be categorized into various types. The most common division is utilitybased versus rule-based models. The pure utility-based models are in general based on the concept of utility maximization. The assumption is that an individual chooses a 29

specific activity-pattern in order to maximize the pattern level utility. On the other hand rule-based models oppose the concept of utility maximization in favor of the concept that our behaviour is more satisficing than maximizing in nature. Rule-based models use behaviour rules (IF----THEN---IF type structure) in order to model the activity-travel decision making process. Hybrid models also exist that use combinations of utility maximization and behavioural rules. Hybrid models possess flexibility in terms of applying different statistical or econometric techniques together with behavioural rules to model multi-faceted activity-travel behaviour. These models often use microsimulation to model at the disaggregate level of the individual, as well as typically using Monte-Carlo simulation techniques for some parts of the overall modelling structure. Despite recent progress, limitations exist in all of these models. These limitations can be broadly categorized as: 1. Crude conceptualization of time (also modelling time frame as well as dynamics in activity behaviour) and 2. Lack of consistent theoretical foundations. All activity-based travel demand models can be divided into two parts: the activity generator and the activity scheduler. The activity-based modelling literature to date has mainly focused to the activity scheduling process. This is also true in the operational activity-based models. All activity-based models consider the activity generation component as either an external input provider to the scheduler, simulate the activity-demand from observed distributions, or generate the activity demand in ways that are similar to trip generation approaches of traditional four-stage model. Although some of the theoretical models have an explicit generation stage in terms of agenda level, the model for activity generation process or the agenda formation is missing. The activity scheduling process is complex and multidimensional, and the focus of the research community on the scheduling process indicates our concern for replicating observed behaviour. But the activity generation level is by no means less important than the scheduling process. The lack of appropriate interactions (two-way) between activity generator and activity scheduler in activity-based models is not consistent with the basic tenet of the 30

derived demand concept of travel demand. It not only reduces the policy sensitivities or forecasting capabilities of the models but also affects the proper integration of activitybased travel demand models within an integrated land-use and transportation modelling framework. It is important to distinguish the capability of explaining observed behaviour and the capability of replicating the actual behaviour that can forecast emergent patterns. This is one of the main reasons why our activity-based models fail to forecast the increasing trip rates that have been observed in North America (Roorda et al, 2007; Pendyala, 2006). The relatively weak treatment of the activity generation component is mainly due to the lack of appropriate and consistent theory as well as a lack of proper data for validating theoretical models. All operational models discussed in this chapter are for a typical day, and very few activity diaries collect week-long data, except for few examples, (Habib and Miller, 2006). In terms of theoretical understanding, the theory of activity utility is a critical one. Considering the multidimensional interactions involved in different levels of activity decision making process it seems almost inevitable that the utility-based measure for activity episode unit should be considered in activity-based travel demand models (Miller, 2005d).

2.7 Future Directions From the literature review presented in this chapter it becomes clear that although the contribution to the complex field of activity scheduling is substantial, the activitytravel generation process is an under-researched area. But from the behavioural as well as model integration points of view activity generation models are crucial to the future development of activity-based models. The three critical points that demand more contributions from the research community are: 1. What should be the appropriate modelling span that can capture the rhythms of activity behaviour in terms of appropriate two-way relationships between activity generation and activity scheduling process, integration of activity-based travel demand model within an integrated land-use and transportation model?

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2. What should be the appropriate measure and the measuring unit for benefit/loss in planning/participating in individual activity types? 3. What should be the appropriate disaggregation of activity typology so that the measuring unit remains semantic as well as the inter-activity trade-offs in planning and execution can be captured within a reasonable time frame or modelling span? Specifically, what is most important is concentrating on the activity generation process separate from activity scheduling. Defining activity utility as a measuring unit of benefit/loss in planning/participating in individual activity types and investigating the use of this measure in modelling activity generation process is also a promising step. Investigating different modelling time frames using appropriate econometric modelling techniques that utilize the concept of utility is also attractive to fill the apparent gaps in the existing literature of activity-based modelling. This investigative approach also can open the opportunity of investigating the preliminary arrangements of different activity types along the time scale in the activity planning stage. The most critical and pressing starting point can be redefining the activity generation component as the “activity generation process”. The concept of considering generation as a process can endogenize the inherent dynamics in activity-travel demand and different trade-offs in activity planning and decision making process will become easier and clearer to be dealt with.

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CHAPTER 03: MODELLING ACTIVITY GENERATION PROCESSES - THE CONCEPTUAL FRAMEWORK 3.1 Introduction The impetus for moving towards activity-based travel demand modelling approach is to model the causal processes from which travel demand is derived. The causal processes of travel demand and their dynamics are integrated within various spatio-temporal and socio-economic systems involved in trade-offs between earning and consumption of resources and commodities. In general terms, resources are spent to purchase commodities for consumption. Time and energy are spent to earn resources. Modelling demand, especially travel demand requires consideration of such trade-offs. But complications arise for the role of time within resource-commodity trade-offs. Time plays both roles of resource and commodity. This dual role of time is often difficult to distinguish, especially in case of activity-travel demand modelling. Becker (1965), Johnson (1966), DeSerpa (1971), Evan (1972) and many others investigate the theoretical aspects of the role of time in overall demand system modelling. All of these theoretical studies either directly or indirectly suggest that time use is intricately related to all other consumption processes. In the case of travel demand modelling, we are mainly concerned with an individual’s time and space allocation processes. Income and consumption of goods and services are often considered to be external factors to the travel demand system. One of the main reasons of disentangling the time-use decision from the other consumption processes is the short duration of the modelling span. All operational activity-based models are for a typical day time-period. The main argument is that for such a short period of time the effects of other consumption processes often act as predetermined or external factors. This simplification of reality is often unavoidable, especially due to the cost and difficulties to collect the information necessary to develop behavioural models (Axhausen, 1998). In addition, treating all of these processes as a whole rather complicates the modelling works and hinders the widespread practical use of activity-based travel demand models (Recker, 2001). So, the challenge for activity-based travel demand modellers is to capture the 33

rhythm of activity/travel behaviour sufficiently and to make the model capable of being integrated within a larger modelling framework with appropriate feedbacks to the other modules of medium- or long-term decisions, such as the Integrated Land Use Transportation and Environment (ILUTE) framework, (Salvini, 2003). This chapter deals with these critical issues in a holistic way. It provides the conceptual background of the empirical investigations of this dissertation. The term “conceptual framework” does not necessarily imply a complete blue print for a practical model of activity generation. The topics of this dissertation are complex and several key parts of the processes are latent in nature. As mentioned in Chapter 2, this is a longneglected topic in activity-based travel demand modelling literature. Keeping this in mind, this dissertation has not jumped into proposing a complete empirical model for activity generation processes at this time. Rather it investigates critical and underresearched behavioural elements using an advanced activity-diary survey data, working towards identifying the critical features of an activity generation component of an activity-based travel demand model. Hence, the investigation process adopted in this dissertation is inductive in nature. This chapter acts as the springboard to developing different hypotheses that lead to a deeper understanding of the behavioural processes. At the end, based on the results of empirical investigations, the thesis identifies the critical features that should be considered to overcome the practical limitations of the activity generation model in terms of modelling framework as well as appropriate techniques. The chapter has been organized as follows: first, it concentrates on the activity generation component (i.e., agenda formation); second, it deals with time definition and modelling time frame; third, it defines the concept of activity utility within activity agenda modelling; and, finally, the importance of agenda formation, modelling time span and utility concept within an overall integrated urban modelling framework is discussed. Identification of key areas for empirical investigations concludes the chapter.

3.2 Activity-Agenda as Activity Generation Component It is identified in the literature review in Chapter 2 that the generation component of activity-based models often lacks a proper theoretically consistent framework. This results in modellers taking arbitrary or adhoc measures for generating activity episodes for the activity scheduler. But activity demand is not an arbitrary or random phenomena; 34

it has deep roots in basic human physiology, psychology, sociology and many other branches of basic social science. Maslow (1970) in his seminal book identifies that basic human needs act as motivations that influence us to engage in different types of activities. The theory that needs act as motivation is very promising for the development of a semantic framework for the activity generation process. Maslow categorizes the basic and abstract needs of all human beings into three broad categories: conative, cognitive and aesthetic. He concentrates on the first two categories only and defines each one as the collections of individual needs with specific hierarchies. Figure 3.1 shows the individual categories graphically. He confesses that it is often difficult to separate the two categories distinctively because of their overlapping and two-directional relationships. But this theory provides an excellent basis for defining the activity generation process. Consistent with Maslow, Miller (2005a) argues that our life is not a random jumble of events but rather is a sequence of coherent and logically interconnected set of actions. So modelling activity generation should be based on these basic needs and each type of need may involve multiple types of activities.

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“Preconditions” for satisfaction of needs: • Freedom of speech

Meaning SelfUnderstanding

• Freedom of movement

Actualization

• Self-defense • Justice

Knowledge

Esteem

Curiosity

(self-respect, esteem of others)

Cognitive Needs

• Fairness •……….

Love (affections, belongingness, family, social) Safety (security, stability, freedom from fear, etc.) Physiological (air, water, food)

Conative Needs

Figure 3. 1 Maslow’s Need Hierarchy Source: Miller (2005c)

Consistent with this concept, Axhausen (1998) proposes a way of classifying the evolution of activity demands. He proposed that life can be divided into a series of projects. A project consists of a collection of activities, and, as per Miller’s (2005b) definition, projects are logically interconnected set of actions that have common goal(s). Maslow’s proposition of motivational theory as our actions (activities) are directed / motivated by needs defines the goal(s). Although the needs may vary from place to place or even time to time, the basic nature of human needs remain the same. Hence anyone’s life can be divided into a number of projects. For example, the ‘work project’ has the main goal to earn money which is necessary to acquire all commodities/services required to satisfy other needs. Miller (2005b, 2005c, 2005d) elaborates the use of this needsmotivated concept of project to define all activities of household members (considering the household as the fundamental level of spatial aggregation). Defining life in terms of projects is theoretically sound and consistent but raises another issue, which is defining 36

the sets of activities that form the projects. Bhat and Koppelman (2000) and Arentze and Timmermans (2004) both define ‘activity’ as the collection of all actions of a certain category. Miller (2005d) argues that this definition of activity is very loose in nature. He also argues that it is almost arbitrary to have a formal and technical definition of ‘activity’. He believes it is more conducive to bundle inter-related actions under the heading of ‘project’ than the term ‘activity’. This debate indicates that either project or activity in general can rarely be a measuring unit; rather it is the action we actually plan or perform that should be the measuring unit. The tangible form of our actions is the specific amount of time spent for a specific objective, which is commonly referred to as ‘activity episode’. So activity episode is the occurrence of an activity with some attributes (start time, end time, mode etc.). Grouping activity episodes according to common goal(s) can be logically consistent with the concept of project. Given these definitions, the question of episode sequencing within the project arises. Different projects can be composed of different numbers of activity episodes with different execution sequences. For example, let us group all social activities under the heading of social project. Social activities may be of different types. Consider a single example of a birthday party. It requires a number of different activities to be performed, for example, buying goods, inviting friends, preparing the venue and food, etc. The execution process of all of these activities involving the social event has a longitudinal time sequence. So, from the modelling point of view we need to introduce an intermediate stage between project level and execution of activities. Such an intermediate level is often referred to as the project agenda level (Miller, 2005b). The above discussions clarify that the evolutionary process of activity demand at any particular point of time in our life cycle can be explained by consistent and logical theory. This theory defines the process by which activity demand evolves over time, and hence is termed as the activity-generation process in this thesis. But from the modelling points of view, it poses two challenges: “Can we justify the theory by empirical evidence?” “What should be the optimum time frame that can conform to the dynamics of both 37

generation and scheduling processes?” Miller (2005b) divides the longitudinal (temporal) profile of any project into two main components: project task list and project-agenda. Project task list refers to the set of activities ordered by sequence that must be executed for the project. Project-agenda is the set of specified activities that a particular project is currently looking to schedule. This concept is intuitive and theoretically consistent. This concept of project-agenda further raises another issue, which is the scheduling time frame. Theoretically the project-agenda should be defined to be scheduled within certain time period. For example, the activities like buying goods, inviting friends/family member etc. are to be performed before the birthday party. If we consider the execution process of the activities within a specific time frame as ‘activity scheduling’ process, the project-agendas act as an interface between projects and the scheduler. But the question is that “Can we really capture such minute details through surveys?” Which is synonymous to the question raised by Axhausen (1998): “Can we obtain the data we would like to have?” The answer may be ‘yes’ or may be ‘no’. It depends on the data collection procedure, which often becomes too costly to conduct. Even a state-of-the-art activity data collection tool such as CHASE reveals that we really do not observe project-based agenda formation processes (Doherty and Miller, 2000; Doherty et al., 2004). We can at best observe with CHASE activity episodes they first appear with a provisional schedule, prior to subsequent scheduling. So the empirical application of this framework needs simplifications because we do not observe data at such a precise level. Although the behavioural process of developing such activity collection is missing, we can fairly hypothesize that, derived from different projects, the candidate activity episodes are selected through the process of mental simulations of various scheduling scenarios (Litwin, 2005). Since we do not observe the mental simulation processes of the individual decision-makers, we can also fairly hypothesize that for a particular person, the collection 38

of candidate episodes for scheduling within a specific time period that we observe in activity diary surveys is the optimum set of activity information that she/he desires to schedule. The collection of candidate episodes to be scheduled within a particular time period as a whole is defined as the activity-agenda in this thesis. By definition it refers to the collection of individual project-based agendas as defined by Miller (2005d). Thus this definition of activity-agenda is not conceptually conflicting with the original definition of project agendas as mentioned before and it is also consistent with many empirical models of activity-scheduling. The empirical activity-based travel demand model, TASHA, for example (Miller and Roorda, 2003), has a class that contains the candidate activity episodes derived from different projects for scheduling. In general terms, the activity-agenda is a generic set of ‘things to do’ within a planned period of time that does not necessarily involve a sequence and it is synonymous to the B-space time dimension defined by Litwin (2005). B-space refers to a mental space filled with a variety of activity decisions that an individual decision-maker might have. According to his definition, the activity information contained by B-space is derived from the decision-maker’s life experience, where each activity enters as an independent dimension within it. So we can argue that within this sub-component of behavioural framework, individual decision-makers desire to select the activity episode bundle that seems to be optimal in terms of the possibility of scheduling within the specified time period (time budget). This optimality does not refer to the global optimization of activity behaviour, which is consistently and strongly denied by behavioural psychologists (Gärling et al., 1989; Gärling and Garvill, 1993; Gärling et al., 1994). Rather it refers to the optimality of a sub-module of the overall activity decision framework, a proposition which, it is argued, is behaviourally plausible. Figure 3.2 presents the schematic framework of the general modelling structure for the activity generation process. This conceptual framework explains the activity generation process in a sequential way that is tractable in terms of modelling approach. The top-most box of the figure contains all projects that conform to our life cycle. These projects can be thought as life cycle events like marriage, birth, entering school, job, deaths etc. The projects are longitudinal in time scale and generate different types of activity episodes for execution in specific time periods of life. In this framework the 39

project is a loosely defined concept in order to compartmentalize the life cycle events. The definition and classification of projects may vary from person to person. So, the concept of project is more of synonymous to the general definition of activity. Projects define different activity episodes to be performed / executed within a specific time range. For a specific time range (part of a day, a single day, a week etc.), different candidate activity episodes corresponding to different projects compete to be scheduled. Combinations of candidate activity episodes within the time frame can create a number of possible sets, which we refer to as activity-agenda. A mental simulation regarding all possible scenarios helps to devise possible agenda sets. It is logical to assume that as a rational being people select the optimum set of activity episodes (activity-agenda) out of all possible sets to start the execution process (activity scheduling). This process is continuous by its own definition. At the end of the scheduled time period there must be a feedback towards the agenda formation level to accommodate the reality of our realized actions and experiences by adjusting combinations of activity episodes to form activity-agendas. This feedback process acknowledges the learning and adaptation process regarding our interaction with the environment that evolves over time This conceptual framework raises two further questions: “What should be the appropriate time scale or time budget for modelling activity agenda formation process?” “What is the measuring unit to define the optimum activity-agenda?”

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Project 01 Project 02 Project 03 Project….. Project….. Project….. Project N

Agenda1 Optimum Agenda: Scheduler

Episode a Episode b Episode c Episode d Episode g Episode k ………… ………… Episode z

Agenda 2 Agenda ---Agenda n Episode p Episode q ………... Episode x Episode y Episode z

Figure 3. 2 The Schematic Diagram of Activity Generation Process The next two sections answer these two questions consecutively.

3.3 Time Budget for Modelling Activity-Agenda Formation A long debate has occurred concerning the appropriate modelling span that can capture all necessary dynamics in activity-travel behaviour. The traditional approach in many UTMSs (particularly in Canada) has been peak period modelling. But the activity-

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based microsimulation approach provides theoretically consistent means to undertake 24hour modelling. All operational activity-based models are of typical weekday travel. But the rhythm of our activity-travel behaviour circulates within the time span of more than a single day, (Axhausen et al, 2002). The decision to model typical-day activity-travel is mainly due to insufficient data to calibrate/validate longer time period models, as well as the computational requirements associated with such extended models. But the so-called ‘typical day’ cannot capture the day-to-day rhythm in activity behaviour. It is certainly the case that travel behaviour, which is the outcome of activity behaviour, exhibits considerable variation across the days. For any urban transportation network, the traffic load is neither uniformly distributed across the day nor across the week, (Ben-Akiva, 1985). The temporal variation of transportation network performance is symbiotic to the rhythm of travellers’ activity behaviour that causes the travel as a derived demand (Vythoulkas, 1990). The dynamic nature of interactions between transportation system performance and our activity-travel behaviour warrants us to investigate the rhythm of activity-behaviour that clearly varies across days. This is especially the case for the weekly rhythm in terms of interactions between weekday and weekend activity/travel that intuitively call for much more empirical investigation. However, there has always been a trade-off between modelling efforts to capture the maximum behavioural ingredients and the cost of modelling (in terms of data collection and computational requirements), which is called parsimony in modelling travel demand. But it is clear that the activity generation process is a multi-day phenomenon. The activity generation process can be better explained as a multi-layered process, involving decisions of multiple dynamic ranges (long-, medium- and short-term decisions). So the modelling framework for activity generation process should be flexible enough to accommodate single-day to multi-day activity generation processes, as data, model applications and computational resources permit. The conceptual framework explained in the previous section conforms to this requirement. When considering multiple ranges of decision-making processes, not all activities have the same level of flexibility to enter into a typical planning period. For example, work/school activities may be regular throughout weekdays compared to other type of 42

activities like a doctor’s appointment, which may be once a month or even more infrequent. Considering fixed commitments and habits, some activity types can be considered as regular or skeleton activities within short planning periods. The presence of skeleton activities is well accepted among researchers, and provides another degree of freedom for designing a modelling framework. Skeleton activities provide the temporal/spatial ‘pegs’ for the scheduling process to start with, (Lee and McNally, 2003, 2004; Doherty et al, 2001). Skeleton activities are ones that are planned over a longer period of time and that are regular in nature. The activity scheduler can take the skeleton activity attributes as defining the initial provisional schedule at the starting of the planning period being modelled. The data from the computerized activity-diary survey, CHASE, indicates that approximately 45 percent of weekday and 20 percent of weekend activities are part of long-range planning and thereby act as skeleton activities, (Doherty et al, 2001). Frusti et al (2003) argue that activities with fixed commitments (skeleton) define the correlations among activity types, policy sensitivity and spatio-temporal rhythm of activity-travel behaviour. The modelling structure proposed in Figure 3.2 can accommodate the presence of skeletal activity types within the planning period. The time period available within the planning period excluding the skeletal activities defines the time budget for modelling activity-agenda formation as described Figure 3.3.

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00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00

Optimum Agenda: Episode a Episode b Episode c Episode d Episode g Episode k ………. ………. ………. Episode z

00000000000000000000000000000 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00000000000000000000000000000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 00000000000000000000000000000 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 00000000000000000000000000000

00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 0000000000000000000000000000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 0000000000000000000000000000 0000000000000000000000000000 000 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000

00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00

Filled Time Block

Open Time Block

Modelling Span

Figure 3. 3 Defining Time Budget for Modelling Activity-Agenda Formation Figure 3.3 shows the schematic diagram of defining the time budget within the planning period with the presence of skeletal activities. Considering a hypothetical person with part of the total modelling span filled with some skeletal activities the gaps provide the time window for filling by the planned activities. Although different approaches exist for defining time budget for activity-agenda formation (e.g., each individual open time block might be considered as an individual time budget), it is consider here that the summation of all open time blocks gives the time budget for the daily activity-agenda that defines the starting point for the activity-agenda formation process. Considering this framework of modelling the activity generation process, the next section discusses the issue of the measuring unit for defining optimum activity-agenda.

3.4 Application of Activity Utility for Modelling Activity-Agenda It is strongly arguable that our activity-travel behaviour is often myopic or suboptimal, where we do not necessarily act as a global optimizer; especially in the case of 44

activity planning, given that it is clear that the activity generation process is a multi-day phenomenon. In the case of continuous and differential planning horizons of long-, medium- and short-term decisions, it is almost impossible to act as a global optimizer. So, many trade-offs between competing activity decisions are often supposed to be solved by ‘local adjustment’ due to various reasons such as limited information availability, limitations in absorbing and retaining information in memory, etc. But it is a reasonable proposition that people act in ways to gain benefit or utility. In practical life we do make different types of trade-offs in developing activity plans as well as in performing individual activities. Considering the multidimensional nature of interactions and trade-offs, it is virtually inevitable that a utility-based measure is necessary to build an operational activity-based travel demand model (Miller, 2005c; Joh, 2004). But the problem is that the definition of utility remains arbitrary. Avoidance of the assumption of global utility maximization warrants defining the utility of the fundamental activity unit that we refer as activity episode. In this thesis we use the term ‘activity utility’ to indicate the utility of an individual activity episode. The definition of activity utility is intricately related to the conceptualization of time at the stage of activity planning (generation) versus at the stage of executing (scheduling). The concept of activity utility is used by several authors for activity-based travel demand modelling (Ashiru et al., 2003; Bhat, 2005; Charypar and Nagel, 2003; Joh, 2004; Meister et al., 2005; Kockelman, 1998; Kraan, 1997; Timmermans et al., 2001). Consistent with microeconomic theory, the utility of activity in these studies is defined in general as the utility derived from the consumption of goods, where goods in this case includes the time spent on the activity. This implies that the utility of an activity episode is derived from the activity duration. As a rational being we would always like to gain more utility by spending more time for a particular activity. But this is not always so straightforward for all types of activities. In the case of some activities like a doctor’s appointment, serve-dependents etc. the duration of the activity episode does not always remain in our hand. The dual nature of time in case of activity decision is well understood. Sometimes time is considered as a resource (to be spent) and sometimes as a commodity (to be consumed). The conceptual framework of this thesis is based on dividing activity analysis in terms of an activity 45

generation process and an activity scheduling process. And it provides the opportunity to identify the role of time precisely. This thesis is specifically concerned with the activity generation process, which we also refer to as the activity planning process. It is conceivable that when we plan activities, we basically are allocating time to different activities. It is thus synonymous to allocating resources. On the other hand, when we execute an activity we basically are ‘consuming’ the activity, with one measure of the amount consumed being the episode duration. Thus, it is argued that time is treated as a resource during activity planning and a commodity in activity scheduling. As discussed in Chapter 2, Winston (1987) divides activity utility into two parts-goal and process utility, which is consistent with the above discussion. The process component of activity utility is derived during the execution process of the activity and the goal component is defined by the end state accomplished by the activity. The goal utility component may be a function of activity episode duration, but at the moment of episode generation during the planning process, duration need not be based on an explicit utility-based calculation (being consistent with the idea of myopic decision while planning). On the other hand process utility is a feature of the episode act itself, will generally depend upon duration, and the actual episode duration will depend on scheduling and rescheduling trade-offs for different candidate activities drawn from the activity-agenda under different situations. The concentration of this thesis is on activityagenda formation, which is prior to the activity scheduling process; hence the utility specification of the activity episodes here refers to the goal or direct utility of the activity episodes. It is conceivable that given the continuous nature of our activity planning process or differential dynamics of the planning and execution of different activity types, in many cases activity planning may be conditional to some already-planned/-scheduled activities along different temporal scales. In this respect, one can argue that the activity planning process may be influenced by the expected utility of different activities, where the expected utility of any activity might be composed of both goal and process utility. In this thesis, however, it is argued that expected utility plays the major role in tentative schedule formation, which is assumed to be the next stage of activity generation and the 46

starting stage of activity scheduling process. In fact, when a multiple-day activity generation process model is developed considering feedback from activity scheduler, some of the expected utility components do get into the goal utility based activity generation modelling structure. Still, it is preferred to consider this as goal utility per se. At some point the distinction between the two concepts is a question of semantics. It is possible to conceive alternative terminology as well as modelling strategies, but the main objective here is to isolate the behavioural processes of activity generation and scheduling, so that the interactions can be identified in a clear way. We believe clear separation of activity generation and scheduling process will allow us to define the dynamic and continuous interactions between these two behavioural processes. Given this focus, discussions on the process utility (associated with activity scheduling) and expected utility are out of the scope of this thesis.

3.5 Necessary Output of Activity Generation Model to the Activity Scheduling Model Other than the planning horizons and modelling techniques of activity generation processes, the other critical question is what should be the appropriate outputs of the activity generator. The output of the activity-generation model should be different for different types of activities as classified in the previous sections. Skeletal activities can be considered to be parts of medium- to long-term decision making processes; hence the modelling approach of this type of activities for a short-term travel demand model should not be utility-based. The logic behind this argument is that considering the utility-based framework requires benchmarking the appropriate temporal reference of activity planning. For the activity-based travel demand model, it is often beyond the scope of the modelling time frame. We can argue that the utility-based calculation of skeletal activities may be components of a larger Integrated Land Use and Transportation Modelling framework, but for a stand-alone travel demand model a non-utility-based modelling framework recognizes the temporal differentials of planning horizon of such activities with respect to all other activity types. So the appropriate modelling approach for such activities can be a process-based approach as described in Chapter 5. For a process-based modelling approach, the activity generation model should give the outputs of start times as well as durations of the component activity episodes. These outputs would be the 47

starting input to the parallel activity scheduling process model: tentative schedule formation model. On the other hand, for non-skeletal activities, though different individual activity types might have different planning horizons, by definition the planning horizons are much smaller compared to the skeletal activities. A utility-base framework for such activity types is more appropriate than the process-based modelling approach. For such activity types it demands investigating whether the planning horizon should be a single day, a week or some other time period. In terms of the output of non-skeletal activity generator, the obvious element is the time allocation. The allocated time to the nonskeletal activities can be modelled as the total time allocated to specific activities, or given the average duration the total frequencies of the activities. In the case of start time of such activities it is important to investigate, whether the start time should be the part of the output of activity generator or not. Chapter 6 is dedicated on this issue. Other than start time and duration attributes of activity episodes, other episode attributes of possible interest are the travel modes and locations of activities, which are required to fully specify trip chains. It is conceivable that the travel modes as well as possible locations of specific activities may have influence at the generation stage. It is argued that the whole processes of activity generator and scheduling are continuous over time. The decisions of travel mode as well as activity location do give feedback into the generation stage in terms of the perception of travel time or the number of possible activity location, etc. but these should not be considered as the output of the activity generator. Rather, these attributes should be considered as feedback elements from the activity scheduler to the activity generator and in practical sense, there must be an iterative process to establish such relationships between these two latent behavioural elements.

3.6 Integration within Integrated Land Use Transportation and Environment Modelling Framework The two-way interactions between activity-travel behaviour and urban systems are well recognized in the literature. There is an informal consensus that the travel demand module within an integrated urban model should be activity-based, (Salvini and Miller, 48

2005; Waddell et al 2002). Growing concerns regarding emissions, urban sprawl etc., which may not be viewed as solely transportation problems, provide compelling motivation to develop integrated models that can capture interactions among multiple components of the urban system as a whole (Strauch et al, 2003). The ILUTE framework developed at the University of Toronto is such an integrated full-feedback model that allows a multilevel decision framework, where longer-term decisions influence the shorter-term decisions with full-feedback opportunity (Salvini and Miller, 2005). The activity-based travel demand module is a critical part of the ILUTE structure. Considering the activity generation component as the first level of the activity-based travel demand module, it provides the interface between travel demand and other components of ILUTE. Medium- to long-term household decisions (e.g. housing location, auto-ownership, job location, etc.) all influence the activity generation process in terms of defining skeletal activity types as well as the needs and preconditions for all other activity types. Appropriate linkages between travel demand and other modules in ILUTE, need to be established. This meaningful linkage is necessary to define the trade-offs in decision dynamics between travel demand and other modules. In our life we always face alternative courses of actions, such as choice of housing location, automobile ownership, vehicle allocation among household members, selecting modes for travel, selecting activities to perform, the location of the activities etc. As we do not know the way people measure such alternative courses of actions, from a researcher’s point of view it is virtually inevitable to adopt a utility-theoretic structure to approximate decision trade-offs and to ‘communicate’ the impact of one decision on other choices (Miller, 2005d). The ILUTE framework is based on this conception, and the generic classification of activity utility as defined in this chapter is not only consistent with this framework but also removes much ambiguity in the definition of utility at different stages of the activity decision making process. The utility component, goal utility, used to define the activity-agenda formation process reflects the influence of medium- to long-term household life-style decisions in a meaningful way and thereby helps to ensure proper linkages within ILUTE framework.

3.7 Conclusions This chapter describes the conceptual background of this thesis. It identifies the 49

key area of focus for the thesis: the activity generation component of an activity-based model. It defines the concept of activity-agenda formation to model activity generation as a ‘process’ that explicitly recognizes the motivational or need (goal) directed approach of our activity demand. The concept of activity utility is used to define a meaningful way of measuring trade-offs in the activity decision making process. The classification of activity utility into goal and process components recognizes the different nature of time in activity planning and activity scheduling. The concept of activity generation as a ‘process’ and the concept of goal utility as the measuring unit for the activity planning stage help to maintain the continuity and consistency in decision dynamics within the overall ILUTE framework. The influences of long- to medium-term household decisions are recognized by introducing the concept of skeletal activities as well as the time budget for activity agenda formation. The proposed modelling framework is flexible enough to test different planning horizons and different types of activity-travel decisions. In the next chapter the data sources used to test some of the hypotheses sketched in this chapter are discussed in detail.

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CHAPTER 04: SOURCE OF DATA FOR EMPIRICAL INVESTIGATIONS 4.1 Introduction The paradigm shift from trip-based to activity-based modelling, especially the microsimulation approach, has also introduced the requirement for detailed data that can provide information on the decision processes underlying the spatio-temporal organization of activities. Such detailed information is in many cases missing in conventional travel diary surveys, and even activity-based surveys. Though trip-based surveys have for a long time served as the primary source of data for conventional travel demand modelling, such data pose some serious limitations in terms of activity behavioural analysis. Trip-based surveys collect information regarding executed trips only. Executed trips are parts of the executed schedules and these do not reveal information concerning a large number of decisions and trade-offs involved in reaching final scheduling decisions. The basic tenet of the activity-based approach is to model the travel behaviour per se and modelling behaviour using a trip-based survey, in this case poses considerable challenges and difficulties, (Doherty et al, 2003). Thus, it is evident that behavioural data collection is required for travel behaviour studies (Ashakura and Hato, 2006). Considerable progress has been achieved over the last decade by using new survey methods that record the evolution of planning and re-planning of activities over multi-day observations periods (Lee-Gosselin, 2005). The ‘think-aloud protocols’ approach proposed by Hayes-Roth and Hayes-Roth (1979) instigated the new trend of activity data collection methodology that can provide insights into the behaviour behind the actions and planning of activities (Ruiz, 2005). Ettema et al, (1994) developed a computer program, called MAGIC, for capturing activity scheduling, re-scheduling decisions. Doherty and Miller (2000) developed a computerized self-interview activity data collection procedures technique called CHASE (Computerized Household Activity Scheduling Elicitor) that can collect activity planning and scheduling information over a multi-day period. Following CHASE and MAGIC a number of data collection procedures has been developed using different types of survey instruments. iCHASE, (Lee et al, 51

2000), REACT! (McNally, 2001) and EX-ACT (Rindsfüser et al, 2003) are examples of new data collection techniques that use new technology e.g. internet, computers, GPS etc. In addition to the demand for new and detailed data collection tools, there has been a growing demand for collecting longitudinal information of peoples’ activity-travel behaviour, which is called panel survey data. The panel survey is designed to capture behavioural elements like temporal consistency, habit formation, regularity, etc. in a more deliberate way. The objective of such a survey is to capture the process of activity decision making process over an extended period of time, rather than within a snap shot of time only (Lee-Gosselin et al, 2006). Motivated by these objectives, a series of surveys have been undertaken in Toronto during 2002-2006 as part of PROCESSUS -- a large network research program on the behavioural foundations of Integrated Land Use Transportation and Environment (ILUTE) models. The panel survey conducted in Toronto is called Toronto Activity Panel Survey (TAPS). TAPS is a three-wave activity diary panel survey. Details of survey methods and preliminary statistics of TAPS are documented in Doherty et al (2004), Lee-Gosselin et al (2006), Roorda (2002), Roorda et al (2005), and Roorda and Miller (2004). Data from TAPS, especially the multi-day CHASE survey data provide a rare opportunity to test the hypotheses developed in this thesis. This chapter describes the data set and the data collection technique used for the development of this thesis.

4.2 TAPS: Toronto Activity Panel Survey The TAPS was conducted in order to understand a variety of aspects of activitytravel decision processes of the residents of the Greater Toronto Area (GTA). TAPS is a three-wave panel survey using multiple types of survey instruments. The use of multiple survey instruments is due to the difference in objectives of each individual wave. The Wave 1 is a 7-day CHASE survey preceded with an up-front face-to-face interview. The Wave 1 is a process driven approach that can capture the activity planning, scheduling and rescheduling process. Waves 2 and 3 both employed a 2-day paper-and-pencil “memory jogger” combined with a follow-up telephone interview. Both Wave 2 and Wave 3 incorporated stated adaptation exercises that explored various aspects of activity rescheduling and skeleton activity scheduling behaviour. Table 4.1 and Table 4.2 present the basic characteristics of the TAPS waves (the tables are derived from Roorda (2005)). 52

Table 4. 1 Summary of Methods and Instruments used for TAPS

Wave

Data and Methods Common to

Data and Methods

1. Interviews conducted in English

All Waves 2. Computer aids used on-line to speed data entry during interview

Wave 1 (Conducted between March

1. CHASE instrument 2. Computerized self-administered survey

2002 to May 2003) 3. In-depth end-of-week review concerning flexibility, frequency and durations of major activity classes. 4. An add-on pilot study on a subset of 12 individuals outfitted with portable GPS unit 5. An add-on study of 30 households to assess data quality of CHASE survey

Wave 2

1. Paper-pencil memory jogger followed by telephone interview

(Conducted between July 2003 to May 2004)

2. Stated adaptation to hypothetical perturbations to randomly selected activities 3. Qualitative scheduling responses to

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conflicts

Wave 3

1. Paper-pencil memory jogger followed by telephone interview

(Conducted between August 2004 to May 2005)

2. Assessment of routine weekly schedule 3. Route track throughout the survey period using a small GPS unit.

Table 4. 2 Core Survey Elements of TAPS Waves Data Category

Residence Information

Data Collected

Current address (Previous Address of Wave 1), Tenure, Dwelling duration, TV and internet availability

Household Structure

Changes in household structure over past 1 year, reasons that the household member joined or left

Person Information

Name, household role, age, marital status, driving license, transit pass, cell phone usage, level of education, children under regular care, child care arrangements for children, employment status, job type(s), employer(s), duration of employment, school status, type of degree/diploma/certificate and gross income

Modes of

Vehicle available to the household members, make,

Transportation

model, vintage, ownership, length of ownership, principle driver(s), people that ride in the vehicle, vehicle 54

disposed off between waves, date of disposal

Activity Schedules

The planned and executed activities, activity descriptions, start time, duration, location, mode(s) of transportation, estimated travel time, passengers in the vehicle, other people involved in activity, children under the respondent’s care at the time of the activity.

TAPS, Wave 1 was conducted on a sample of 271 households. The sample size is selected based on the consideration of resource limitations. Each wave was conducted over the period of approximately 1 year to prevent the need for assembling a large-scale survey centre, staff training etc. over a short period of time. However, the survey was arranged in a way that individual households were surveyed at about the same time of the year in each wave. Wave 1 was the most detailed survey compared to other two waves in terms of extensiveness and temporal span of the survey, but Wave 1 was also more burdensome for the respondents. In order to reduce the burden of the respondents the length of interview was shortened for Waves 2 and 3. However, the attrition rate across the waves was very low. 84 percent of the households that completed Wave 1 also completed Wave 2. Based on the responses obtained through a special post-interview of 30 Wave 1 households, however, if the CHASE survey had been conducted for all three waves, the attrition rates would have been much higher. In addition to the differences in survey length (2 days in Waves 2 and 3 compared to 7 days in Wave 1) various changes in survey instruments also makes is difficult to trace the instrument bias in the data across the three waves. Based on these considerations, the empirical investigations of this thesis used the Wave 1 CHASE survey data only. The next sections discuss the details of CHASE survey methods and Wave 1 data statistics.

4.3 CHASE: Computerized Household Activity Scheduling Elicitor The CHASE program was designed based on the theory of the ‘think-aloud protocol’ as proposed by Hayes-Roth and Hayes-Roth (1978), where the ‘think-aloud 55

protocol’ indicates that the activity decision process can be abstracted by providing the subject with a number of alternative scenarios in a hypothetical urban environment. Following the same theory Ettema et al (1994) first developed a computer program in order to investigate activity scheduling behaviour. Their survey was conducted in a laboratory setting. CHASE is the first computerized survey tool that was designed for use in real-world household settings so that the effects of intra-household interactions as well as social networks on activity planning-scheduling behaviour can be captured in situ. Dohery and Miller (2000) and Doherty (1998) give the detail description of the CHASE software design and theory. CHASE concentrates on three main areas: 1. Household activity-agenda generation 2. Activity scheduling process over time in a household settings 3. The decision rules for activity decisions The survey is designed as a computer program. The motivations to develop a computerized survey are: 1. Increased speed in data entry. 2. Improved data quality (all information is entered by the interviewer directly into database file). 3. Provide graphical display to the respondents for interactive discussions. 4. Automatically recording the activity decision making process by following the sequencing of inputs. The survey is designed for a multi-day period and information is collected by day of week. Figure 4.1 shows a data entry dialog box of CHASE program.

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Figure 4. 1 CHASE Program Main Screen with Example Entries Source: Doherty and Miller (2000) CHASE is designed to collect information under realistic task planning conditions capable of capturing routine behaviour as well as complex dynamic decision making processes. The survey requires an upfront interview to collect household socio-economic and socio-demographic information to define the generic activity types that form the household activity-agenda. Household activity-agenda indicates the full list of activities performed by the household members along with their attributes. CHASE provides the generic activity types to the respondents for inclusion in the agenda. The generic activity classification of CHASE is developed based on Portland Oregon Household Activity Survey, 1994 and Statistics Canada Time-Use Diary, 1986. Figure 4.2 shows the generic activity classification of CHASE.

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Figure 4. 2 Generic Activity Classification used in CHASE Source: Doherty and Miller (2000) For a week-long survey, CHASE requires the household members to begin recording their activity decisions from the evening prior to the beginning of the week. For example, for a Monday-to-Sunday survey, the respondents start entering information on the Sunday evening before Monday. The basic instructions are (Dohery and Miller, 2000): 1. Try to login to the program at least once a day for the entire week. 2. Starting tonight, add activities anywhere in your schedule that you have already thought about doing before logging on to the computer. These include even those activities that you think may change at a later date. 3. On subsequent days, continue to add new activities to your schedule, but review your previous and future entries and modify/delete them according to any changes that have occurred. This may include modifying/deleting past events to reflect what actually occurred, or modifying/deleting a future planned event because of further changes in your plans. 58

4. Include all activities that last longer than 10 minutes; the exception is for short activities involving travel – include these (e.g. quick stop at the dry cleaners etc.). 5. You may overlap activities that take place at the same time (e.g. eating and watching TV) or that intervene within a longer activity (e.g. going out for lunch at work). 6. Activities start when you leave for them and end when you leave from them. In this way, travel time to the activity is counted as part of the activity, where as travel time away from the activity is captured by the next activity. 7. Try to complete the schedule alone; do not access your partner’s schedule. Figure 4.3 shows an ‘add’ entry dialog box of CHASE

Figure 4. 3 CHASE Add Entry Dialog Box Source: Doherty and Miller (2000)

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In addition to basic activity planning and scheduling options the CHASE program also prompts the respondents for the reasons why modifications or deletions were made. Once the survey week is complete, respondents are asked to complete an “End of Week Review” (EWR), in which the respondents are asked a systematic set of automated questions about temporal, spatial and inter-personal flexibility; maximum and minimum duration; frequency etc. The purpose is to systematically query the attributes of each uniquely labelled activity that the respondent performed during the week. These queries concern only the activity types in general, not each individual occurrence of the same activity type. As a continuous advancement to this innovative data collection tool, CHASE is also integrated with a GPS location indicator tool in order to track the movement of the respondent over the space (Litwin, 2005) A CHASE survey was first conducted in Hamilton, Ontario. A total 42 households composed of total 70 adults and 20 children were recruited during April to December 1997. The results of the Hamilton survey are summarized in Doherty and Miller (2000). The second CHASE survey was conducted in Quebec City in the year 1998. In that survey a total of 36 households were surveyed, (Litwin and Miller, 2004). The third CHASE survey was conducted in the Waterloo, Ontario, where a total of 100 young drivers were interviewed in the year 2002. In 2002, the most extensive and comprehensive CHASE survey was conducted in Toronto as a part of TAPS. Wave 1 of TAPS is the most well documented and details activity diary data available to this time. This data set is the data source for all empirical analyses of this thesis paper. The next section concentrates on Wave 1 CHASE survey of TAPS.

4.4 Wave 1 CHASE Survey of TAPS Wave 1 CHASE survey was conducted in Toronto on 271 households randomly selected from the telephone directory from the study area shown in Figure 4.4 (Note that the resident locations have been randomly adjusted to preserve the respondent’s anonymity)

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Figure 4. 4 Geographic Distribution of Wave 1 CHASE Survey Respondents Source: Doherty et al (2004) The study area includes the entire City of Toronto and its surrounding municipalities. The surrounding municipalities are Vaughan, Richmond Hill, Markham, Mississauga and Pickering. This study area covers 74 percent of all households in the Toronto Census Metropolitan Area and represents a good diversity in urban form, population densities and levels of transportation accessibility (Roorda, 2005). The Wave 1 survey includes two face-to-face interviews before and after CHASE survey. Figure 4.5 shows the survey process of Wave 1 of the TAPS.

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Figure 4. 5 Wave 1 Survey Process Source: Roorda and Miller (2004) The survey starts with an up-front face-to-face interview in which a notebook computer with installed CHASE software (as given to each household to be used for the duration of the survey) was used to collect household socio-economics, demographic, transportation mode and residence information. As per the interview result, the CHASE software is customized with an “agenda” of activities that the respondents of the household might conduct over the week-long survey/planning period. At the beginning of the week (Sunday evening, prior the survey starting day, Monday) the respondents entered activities that have already been planned for the upcoming week in the CHASE scheduler resembling a day-timer, as shown in Figure 4.1. Over the course of the survey week, the responded logged in at least once a day to enter newly planned activities and activities that have been executed since the last login time. All changes in planned activities and the reasons of changes are collected by CHASE from the respondent during inputting respective changes. The completed survey week is followed by “End of Week Review” (EWR) questions to collect specific information about types of activities undertaken by the respondents. Once the survey week ended the notebook computer was retrieved and a 62

follow-up interview was conducted in which the data were checked by the interviewers for omissions or problematic information. In addition, each household was contacted by the interviewers at least once during the survey week in order to identify any problems or difficulties in filling out the survey and to continue to build rapport with the respondents. Doherty (2004) and Doherty et al (2004) provide detailed information and descriptive statistics of the survey data. In summary, out of total 524 members in 271 households, a total of 453 individuals participated in the survey, of which total 423 to 430 adults provide usable data (the number varies 423 to 430 based on the screening criteria of missing or ambiguous information) representing an effective response rate of 16.6 percent. Overall, around 25 percent of all of the adult members did not complete the CHASE survey completely or did not participate effectively. The age of the respondents varies from 14 to 82 with an average age of 42.4 years. The male / female split of the data is almost even. In terms of adding, modifying and deleting activity episodes in CHASE, per day statistics of average values are: 12.0 additions, 1.47 modifications and 0.25 deletions. These result in an average of 11.8 observed activities and 3.74 one-way trips per day per person. The key aspects of this survey related to investigation of the activity generation process are discussed in the next section.

4.5 Use of Wave 1 CHASE Survey Data as Prime Data Source in Activity Generation Process Investigation The Wave 1 CHASE survey is the only comprehensive data source available to date for investigation of different aspects of activity planning and scheduling behaviour. However, CHASE is primarily designed to capture the activity ‘scheduling process’ rather than the activity ‘generation process’ per se. It concentrates on how schedules are built up over the course of the week, and it also collects information about the planning horizon to investigate planning and execution dynamics. It identifies activities in terms of ‘pre-planned’, ‘routine’ and ‘impulsive’ activities in general. The pre-planned activities may be planned on the same day as their execution or on the days (or weeks/months/years) prior to their execution day. Routine activities are regular activities. Impulsive activities are ones that are undertaken without prior planning. Such identification helps investigation of planning and execution dynamics to some extent, but 63

does not necessarily reveal the reasons for putting specific activity episodes into a specific time agenda. Most importantly how an individual develops his/her activity agenda for a day or a week is difficult to identify from these data without supporting hypotheses. It is clear from the data that the day/weekly activity-agenda contains pre-planned, routine and impulsive activities. As discussed in Chapter 3, the pre-planned, routine and impulsive activities represent different levels of household decision making processes (long-, medium- and short-term), but what is most important from the activity agenda formation point of view is to identify the trade-offs in selecting these activity types for a specific time budget (day/week). This is the main concern of this thesis. However, one important feature of this survey that makes it the source of data for all investigations of this thesis is the sequential way it collects the information. Respondents first ‘added’ the activity episodes within the day’s agenda, then subsequently modified or deleted episodes, if necessary, before execution. Although we do not observe the trade-offs involved in consideration of a particular episode in the agenda, we can fairly assume that the first-time-added episodes are the output of the activity generation process. The modifications or deletions after the first-time-adding represent more of the scheduling process effect than the generation process effects. So, the fundamental assumption that only the first-time added episodes represent the outcome of the activity generation process is maintained in all empirical investigations of this thesis. It is true that the first time added data in CHASE may contain some unobserved scheduling element within it. In other words, the first time CHASE entry may be conditioned by some already-planned/scheduled activities. The point is that both activity generation and scheduling processes are continuous processes throughout the life span of the people. We, the modellers model a very partial portion of life (whatever it is, a singleday or a single-week) and for this very reason; it will always remain controversial to draw a firm border between activity planning and activity scheduling. The modelling approaches in this dissertation are designed to overcome this data limitation. As mentioned in Chapter 2, activities are classified into two major categories: skeletal and non-skeletal activities. For the skeletal activities, the process-based approach is taken that 64

indirectly considers the sequential interactions between successive planning events, as described in Chapter 5. The non-utility-based modelling approach for skeletal activities recognizes that such activities are part of medium- to long-term planning processes and hence a utility-based modelling approach for short-term activity planning is not appropriate. On the other hand, in the case of non-skeletal activities, the hypothesis is that the probability of having some already-planned/scheduled activities may give a finite number of possible agendas. Since we do not observe the mental simulation process of developing alternative agendas, the reasonable hypothesis is that the first time added nonskeletal activity-agenda is one of the many possible agendas and it is the optimum one chosen by the individual. This hypothesis influences consideration of an optimization model for non-skeletal activity-agenda formation, as described in Chapter 7, 8 and 9.

4.6 Conclusions This chapter discusses the data issue for empirical investigation of activity generation processes. It is identified that proper investigation of these processes requires appropriate, detailed behavioural data. Data collection procedures for activity-travel behaviour have seen significant advancement over the last 10 years. Application of computer program to trace the activity decision-making process over time (CHASE) gives a new opportunity to test behavioural hypotheses empirically. The Toronto Activity Panel Survey (TAPS) is a very rich data source for such investigation. TAPS is composed of 3 waves spread over the time period of 2002 to 2005. The Wave 1 of TAPS is the largest part and involved a 7-day CHASE survey. CHASE (Computerized Household Activity Elicitor) is a computerized data collection tool developed based on the ‘thinkaloud protocol’, where the respondents note down the information about the activity planning and decision making process in situ under realistic task planning conditions. Thus it is capable of capturing routine as well as dynamic activity decision making processes. But, the fundamental limitations of this data source are: 1. The information is not complete at the household level for all households because of non-participation of some household members in the survey. 2. It does not capture the trade-offs involved in adding specific activity episodes for 65

the first time into a specific time (day/week) activity agenda. However, this is the only data source available to date that has extensively detailed information over a week-long time period. So, this Wave 1 CHASE data set of TAPS is used for all empirical investigations of this thesis. The common assumption regarding the data for all investigations is that the first-time-added activity episodes (the planned activities) to an agenda are the outcome of the activity generation process. Household-level incomplete information also restricts investigations to the individual level, but, where feasible, household-level effects are incorporated into the analysis. This chapter describes the detailed nature of the data source in terms of survey method, survey area, preliminary statistics and general discussions. The detailed description of individual data elements are presented in subsequent chapters.

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CHAPTER 05: MODELLING SKELETAL ACTIVITY GENERATION 1 5.1 Introduction Getting input from the activity generator, the daily activity scheduling process can be started with some routine and pre-planned activities arranged within nominal, preplanned sequence (Doherty et al, 2001). Given the routine and pre-planned framework, event-driven activities can be accommodated dynamically with possible adjustments within the pre-planned schedule, Litwin and Miller (2004). In practice, the three major approaches to modelling activity-travel demand: utility-based, rule-based and hybrid processes, all either directly or indirectly recognize the existence of routine or preplanned activities. In all cases, the starting points are sets of fixed activities that create the nucleus for the scheduling process. As mentioned in Chapter 4, the CHASE survey identifies three general categories of activities: pre-planned, routine and impulsive activities. Here the routine activities are also one type of pre-planned activity, which is planned for longer time periods (longer than a day or a week before). From the activity generation point of view the routine and pre-planned activities represent the long- and medium-term planning decisions. Considering that the activity generation process provides the activity-agenda to the activity scheduler, it is necessary to identify which activity types of pre-planned or routine activities should represent the fixed component of the tentative sequences of the generated activities. Kitamura and Fujii (1998) refer to such “fixed” components as the skeleton schedule, (Kitamura and Fujii, 1998). Skeletal components of the activity schedules act as temporal pegs around which all other generated activity episodes are organized (Lee and McNally, 2003). The temporal pegs represent the temporally fixed commitments of the individuals (Frusti et al, 2003). In case of workers/students, considering activities that occupy considerable portions of a full-day cycle and are almost fixed or regular in nature, night sleep and work/school episodes can be considered the simplest and minimum form of the

1

This chapter is partially based on the paper Habib, K.M.N., and E.J. Miller, “Modelling Worker’s Activity Skeleton Schedule”, Transportation Research Record 1985, pp. 88-97.

67

activity skeleton. In case of non-workers it is difficult to identify the minimum number of activity types (except night sleep) as fixed activity types. And from the behavioural point of view it is important to keep the fixed part of the generated activities as minimal as possible, because the routine or fixed activity classification in many ways depends on the analysis time frame (Kitamura et al, 2006). In addition to identifying skeleton activity type, as the travel behaviour associated with the entire activity generation and scheduling process is very complex and multidimensional (Schlich and Axhausen, 2003), considerable care is also necessary to define the way to model the components of the skeleton schedule (start time, durations etc.). The uses of empirical distributions of start time-duration to generate random draws of the skeletal components (for example, Miller and Roorda, 2003) on one hand make this first stage of activity-travel scheduling models insensitive to testing different policy impacts. On the other hand, a utility-based calculation for these types of activities for daily or weekly generation processes may not be appropriate. As the skeletal activities represent long term planning (e.g. type of work) or habit (e.g. night sleep), the utilitybased calculation does not represent the daily or even weekly adjustment process. A dynamic, process-based approach is more appropriate in such cases. The term ‘process-based’ refers here to a modelling approach that follows the sequences of time chunks as sequences of events. To accommodate these issues this chapter presents a modelling system for workers’ daily skeleton schedule generation (Skeleton for Workers Daily Activity Schedule: SWDAS) considering the full-day cycle. The design criteria of SWDAS are to support both single-day and weeklong modelling time frames. For a single-day modelling span it provides the nucleus for scheduling capturing the within-day dynamics and trade-offs in activity behaviour. For a weeklong modelling span it also accommodates the day-to-day dynamics of activity behaviour including learning and adaptation. Other than using a utility-based modelling approach the components of SWDAS are modelled using dynamic and sequential approaches. Figure 5.1 describes the components of SWDAS graphically. SWDAS divides workers’ daily activity skeletons into four components: 1. Duration between the time the worker wakes up and the time he/she goes to work 68

(“before work gap”). Given the time the worker wakes up, this duration defines work start time. 2. Work duration. 3. Duration between the end of the worker’s workday and the time he/she goes to sleep (“after work gap”). Given the time the worker stops working, this duration defines night sleep start time. 4. Night sleep duration. This chapter presents the mathematical details and empirical estimation results of the four sub-models of SWDAS. However, it should be mentioned that SWDAS deals with time use decisions only: start time and duration of the skeleton components. Activity episode location and mode choice decisions are modelled separately and are out of the scope of this model. SWDAS components take the perception (prior belief) of travel times and other locational attributes as input covariates. For single-day activity scheduling prior beliefs would be derived from the base year observed distributions, while for multi-day activity scheduling the previous day attributes could be carried forward as experience and belief for subsequent days. The objective of this approach to modelling is to accommodate within its scope day-to-day learning and adaptation in activity behaviour. Another starting input is the before-work gap start time. For singleday scheduling this would be simulated from base year observed distributions but for multi-day scheduling the end time of night sleep from the previous evening would be the start time of the next day before the work gap start time.

69

Figure 5. 1 Graphical Presentation of the SWDAS Components The rest of the chapter is organized as follows: the next section gives a brief literature review on skeleton schedule modelling and then describes the approaches taken in SWDAS, followed by the sections describing the mathematical formulations of the sub-models and empirical results using Wave 1 CHASE survey data of TAPS. The 70

chapter concludes with a summary of important results.

5.2 Modelling Workers’ Skeletal Component of Daily Activity-Agenda The operational activity-based modelling system ALBATROSS models the skeleton schedule explicitly (Arentze and Timmermans, 2004a). It uses a decision-tree algorithm to derive skeletons from observed activity diary data and considers only the work episodes as the skeletal components of workers’ daily activity skeleton. The decision-tree algorithm used in ALBATROSS is a data-driven approach that defines exhaustive sets of possible condition variables and selects the variables relevant for the homogeneous condition states and corresponding decision tree for work episode start times and durations. Such a data-driven approach can lead to inaccurate relationships or relationships by chance, if the conditioning variables do not have clear relationship with the decision variable (Speybroeck et al, 2004). This is a serious problem in the case of modelling human decision-making processes (Zorman et al 1997). The econometric modelling system CEMDEP also uses only work episodes as the pegs to define the workers’ skeleton pattern, (Bhat et al, 2004). It models the start timeduration of this skeletal component considering different socioeconomic variables within a discrete time representation. The discrete time representation of the skeleton components causes temporal aggregation, which might be exaggerated farther at the end of the scheduling process. FAMOS (Florida Activity Mobility Simulator) also considers the work episode of the workers as the only skeleton component of their daily activity schedule, (Pendyala et al, 2005). It uses observed distributions to simulate the start time-durations of the skeletal components randomly. Use of observed distributions always requires some index variables to identify different market segmentations. The relationships between index variable (e.g. age, sex, income etc.) and the objective variable of concern (e.g. start time, duration etc.) are not defined econometrically. Apparently intuitive index variables may not have significant relationships with the objective variable of concern. Use of such methods reduces sensitivities of the models to different policy measures and may lead to spurious conclusions. None of the above-mentioned models deals with the full-day cycle. Considerable adjustments, however, take place throughout the week between night sleep and other 71

activities. So considering night sleep together with work episodes to develop workers’ skeleton schedule helps to capture both day-to-day and within-day dynamics of activity scheduling. The current implementation of TASHA (Travel-Activity Scheduler for Household Agents) (for details see, Miller and Roorda, 2003) uses the same approach as in FAMOS to derive the fixed or less flexible components of the activity schedule. The SWDAS presented in this chapter is designed to replace the empirical distribution method in the next version of TASHA. To overcome all of the above-mentioned criticisms SWDAS considers time as a continuous variable over the entire full-day period. Two econometric methods are considered to develop the sub-models of SWDAS: multilevel linear models and continuous time hazard models. This chapter reports both of the approaches and compares the empirical results. In multilevel linear models three levels are considered: household level, personal level and temporal level of the person. In the continuous time hazard model individuals’ temporal variation of activity behaviour is modelled as a person-based shared frailty model with household level covariates. The best model for each component is selected based on the goodness-of-fit measure, the pseudo R2 value.

5.3 Mathematical Formulations of the Component Models Individuals’ time allocations to different activities are influenced by the households within which they reside (Miller, 2005b). Modelling household-based time allocation behaviour is not always possible due to data deficiencies. Person-based activity diaries often do not include all household members (Doherty et al, 2004). So, the challenge is to model person-level time allocation behaviour considering household-level effects. The multilevel linear modelling technique is a promising tool to consider household-based effects (fixed and random) on an individual’s time allocation behaviour (Goulias, 2002). In our case, the consideration of a multilevel modelling approach is justified because persons are nested in a household and the same person has multi-day observations within the dataset. So, the skeletal components are designed in a three-level structure: the household level, the person level within household and the temporal level of individual persons. On the other hand, hazard-based event history analysis can also incorporate individual-level unobserved heterogeneity (Habib and Miller, 2006). The distinction of 72

hazard-based analysis over multilevel linear models is the nonlinear approach and consideration of a hazard rate to determine the duration of the event. The following sections describe both multi-level linear models and hazard-based duration models developed in this chapter.

5.3.1 Multilevel Linear Model for Episode Duration The multilevel models considered in this chapter are hierarchical linear models for continuous dependent variables. The lowest level is the temporal level (day of week), i of the individual and the highest is the household of the individual, k. The second level is the individual him/herself, j. In this chapter, in addition to fixed effects, the influences of higher levels are modelled as random intercepts. Higher-level random effects may also be considered in terms of random coefficients of some variables in addition to the levelspecific random intercepts (for details see Bryk and Raudenbush, 1991 and McCullagh and Nelder, 1989). However, in our case, it is seen that the incorporation of random coefficients for personal and household level variables does not improve the model significantly and no random coefficient becomes statistically significant. So, only levelspecific random intercepts are considered. For a particular event, the duration D at day i for individual j in household k is: N

D = β 0ijk + ∑ β ijkn X ijkn + ε ijk + u jk + v k

(5.1)

n =1

where,

β oijk reprensents fixed Intercept X ijkn represents fixed effect Variables

ε ijk is the Level − 1 random effect u jk is the Level − 2 random effect v k is the Level − 3 random effect All of the three random effects are assumed multivariate normal with 0 mean and corresponding constant variances, σ2. So,

73

εijk ~ N (0, σ ijk2 ) u jk ~ N (0, σ 2jk ) vk ~ N (0, σ k2 ) These random effects represent the corresponding level-specific effects that have not been measured by fixed-effect variables. Here Level-1 units are nested within Level-2 units and Level-2 units are nested within the Level-3 units. The random terms are assumed to be uncorrelated with each other and with the covariates to yield a compound symmetrical structure of the residual matrix within households, with all household members having the same variance. This also gives the same correlation for all pairs of members of the same household conditional on the fixed covariates (for details see RabeHesketh et al, 2001 and Skrondal and Rabe-Hesketh, 2004). Given these random and fixed effects, the parameters are estimated by full information maximum likelihood. As opposed to this, the restricted likelihood approach estimates the variance components by maximum likelihood and then the fixed effects are estimated by the generalized least square method given those variance estimates. However both methods give similar estimation results (for example, see Goulias, 2002). The likelihood function to be estimated is based on the probability density of the highest-level observation (level-3). So, the log-likelihood to be estimated is log L = ∑ log Pk ( Dk ) , Pk ( DK ) represents probability density of duration D for household k k

Where, Pk ( Dk ) = ∫ Pk ( Dk | v k ) f (v k )dv k vk

  = ∫ ∏ Pjk ( D jk | v k ) f (v k )dv k vk  j  and , Pjk ( D jk | v k ) =

∫P

jk

( D jk | u jk , v k ) f (u jk )d (u jk )

u jk

=



∫ ∏ P

ijk

u jk

i

 ( Dijk | u jk , v k ) f (u jk )d (u jk ) 

Here the responses of individual persons within household, k are independent to 74

one another given the random effect vk and the responses of individuals of household, k at the temporal level (Level-1) are independent to one another given the random effects ujk and vk . The observed dependent variable is of the lowest level response variable representing the conditional expectation given the covariates and upper level random effects. For the normal distribution assumption of the sampling data at first level, the inverse of the conditional expectation (known as link function that maps the mean values of the responses to the linear predictors) is an identity function.

The Conditional Expectation of Duration E ( Dijk | Ψijk ) = Ψijk

and

Var ( Dijk | Ψijk ) = σ ijk2

The Identity Link Funtion is

η ijk = Ψijk Where the Ψijk = β 0 + ∑ βX ijkn n

Another important point, which is common in all multilevel models, is that the Level-2 and Level-3 effects are mutually independent (Vermunt, 2004). The likelihood functions described above can be solved by the Gaussian-Hermit quadrature numerical integration method. However, adaptive quadrature is more efficient and reduces the number of total integral points required (for details see, Rabe-Hesketh et al, 2002). This chapter uses the adaptive quadrature method with the Newton-Raphson algorithm to solve the parameters iteratively (for details see Skrondal and Rabe-Hesketh, 2004; STATA, 2003; Gould and Scribney, 1999). The significance of the estimated covariate parameters and the variances of the random effects are evaluated by t-tests (considering 95% confidence levels the standard value is 1.64). The overall significance of the model against

the

null

model

is

tested

by

the

− 2(Loglikehood Null Model − Loglikehood Full Model )

is

likelihood Chi-squared

ratio

test,

distributed.

where, The

goodness-of-fit is measured by the pseudo R2 value, which is

Pseudo R 2 = 1 −

Loglikehood Full Model Loglikehood Null Model

, It Varies 0 to 1

75

5.3.2 Event History Analysis Models Event history analysis models are widely known as hazard models. Hazard models recognize the dynamics of activity episode duration by considering the conditional probability of termination of the episode influenced by different covariates. The basic details of hazard models are available in a variety of references (for example see, Habib and Miller, 2005a). In this chapter we consider the continuous time hazard model that can be divided into two basic types: semiparametric and parametric hazard models. The basic assumption of semiparametric models is that the proportional hazard rate covariates have a multiplicative effect on the nonparametric baseline hazard rate. The unobserved heterogeneity across the specified groups can be accommodated as a multiplicative function. The form of the semiparametric model used in this chapter is (for details see Habib and Miller, 2006 and Gould and Scribney, 1999) hij (t ) = h0 (t )α j exp( xij β )

(5.2)

where, h0 (t) is the baseline hazard rate α j is the unobserved heterogeneity function for individual i in household j xij is a set of fixed effect variables of individual i in household j β

is the set of coefficients for xij

t

represents time

The corresponding survival function  T  S ij (t ) = exp − ∫ hij (t )dt  (5.3)  t =0  The unobserved heterogeneity is considered to have a Gamma distribution with mean value 1 and variance θ. This assumption gives a closed form of the likelihood function used to estimate the parameter of the covariates as well as θ. The variance of the random distribution, θ, measures the degree of within-household correlation. If the αj of equation (5. 2) is expressed as a logarithmic function (let log(αj) = ν) then it becomes,

hij = h0 (t ) exp( xij β + ν )

76

(5.4) This model does not contain any constant term because it is homogeneous to degree 0 in the number of covariates and the parameters are estimated by partial likelihood method. The partial likelihood method is based on the assumption that the time interval between the events does not contribute any information about the relationship between the covariates and baseline hazard rate. For details of the estimation process see (STATA, 2003 and Cox, 1976). Unlike semiparametric models, parametric hazard models parameterize the baseline hazard rate. If the survival time of the event is expressed as a function of covariates:

ln tij = xij β + κ ij , where κ ij is the error term (5.5) then this is called an accelerated time hazard model, while if the baseline distribution is expressed as parametric function multiplied with covariate function then it is called a proportional parametric hazard model, (this is same as equation 5.1 but unlike the semiparametric model, the h0(t) is a parametric function). In this chapter both proportional and accelerated time parametric hazard models are developed. For accelerated time models, the distributional assumption of the error tern in equation 5.5 yields different types of models. In this chapter Weibull, log-logistic and lognormal distributions are considered. The survival functions of the corresponding models are: Weibull ,

S = exp(− exp(− pxij β ))t p ij )

(5.6)

Logistic ,

S = {1 + (exp(− xij β )t ij )1 / γ }−1

(5.7)

Lognormal , S = 1 − Φ{

ln(t ij ) − xij β

σ

}

(5.8)

Here p, γ and σ are ancillary parameters of the corresponding distribution functions. For the proportional parametric hazard model, the Gompertz distribution is

77

considered. The survival function of the Gompertz proportional parametric hazard model is

{

}

S = exp − exp( xij β )γ −1 (exp(γ t ij ) − 1)

(5.9)

Here γ is the ancillary parameter of the Gompertz distribution. The positive value of γ indicates an increasing hazard rate with time, while a negative value indicates decreasing hazard rate with time. When the value of γ is zero then the Gompertz model reduces to the exponential model. The consideration of unobserved heterogeneity in these parametric models is also multiplicative, as in the semiparametric hazard model.

hij = α j hij (t ) (5.10) Here hij(t) is the individual hazard model given the covariates xij, h(t|xij). The αj is any positive distribution. Similar to the semiparametric model, it is considered as Gamma distributed with mean value 1 and variance θ. The parameters of all parametric hazard models are estimated by the Full Information Likelihood method. Here θ measures the degree of unobserved heterogeneity of an individual’s activity behaviour in different temporal settings. A value of zero indicates no heterogeneity, while the greater the value of θ the greater the effect of unobserved heterogeneity. For all hazard models statistical tests are the same as those for Multilevel Linear Models. In this chapter, all of the above-described models are developed for each component of SWDAS. However, for brevity, corresponding tables report multilevel linear models and two hazard models for each component. Two hazard models for each component are selected based on higher AIC values, (for details of the AIC measure, see Akaike, 1974)

AIC = −2( Log likelihood ) + 2( Number of Variables + Number of Ancillary Parameters + 1)

The best model for each component is then determined based on the highest pseudo R2 value among the three candidate models. 78

5.4 Empirical Estimation Results of SWDAS Components This section describes the estimation results of four sub-models of SWDAS based on Wave 1 CHASE survey data of TAPS. After cleaning the original sample data for missing information, a subset of the sample was selected for estimation of the individual component models. The sub-sample selected consists of 916 complete daily observations of 259 individuals in 198 households. This sub-sample was selected considering the complete whole-day information. The individuals are either full-time or part-time workers having complete activity information of the whole day as well as other socioeconomic information of concern. The sample data covers an entire week, but not all individuals have observations for the entire week. The variables considered are related to activity, person and household. The details of individual variables incorporated in the models are discussed in the following sections. It should be mentioned that although some variables show statistical insignificance, they are kept in the model based on importance of the variables and considering the small sample size used in this analysis (i.e., with a larger sample size these variables might be significant). All durations are expressed in minutes, all start times are expressed as fractions of 24 hours starting from 12 midnight, and weekly frequency indicates the number of working days per week. The weekly frequency information is collected from EWR (End Week Review) questions. In terms of job sectors: service industry, manufacturing, business service-administration and food service enter into the work duration model as dummy variables.

79

Table 5. 1 Models for ‘Gap Duration before Work’ Multilevel Linear Model

Gompertz Proportional Hazard Model

Covariates

Coefficient (t stat)

Coefficient (t stat)

Start Time (Fraction of 24 hour) Tuesday (Dummy) Wednesday (Dummy) Number of Work Episodes Total Work Durations of the Previous Day Travel Time from Home to Work Mode of Work Trip: Auto Mode of Work Trip: Transit No. of Work Locations Weekly Work Frequency Temporal Flexibility of Work Duration (Dummy) Male (Dummy) Adult with Partner at Home (Dummy) At Home Job (Dummy) Full Time Job (Dummy) Income (CAD/Year) Household Size Household children CONSTANTS Ancillary Parameters Γ P Θ Level-1 Variance Level-2 Variance Level-3 Variance Loglikelihood Likelihood Ratio Probability > Chi-Square Value Pseudo R2 H0 : θ =0

369.60 (9.95) 23.89 (1.45) -9.01 (-0.52) 105.04 (4.99)

-2.21 (-7.85) 0.23 (2.21) -0.94 (-5.73)

-0.08 (-3.73)

Weibull Accelerated Time Model Coefficient (t stat) 0.99 (6.61) 0.05 (0.96) -0.11 (-1.83) 0.49 (5.54) 0.0005 (-0.59)

0.36 (2.52) -87.07 (-5.56) -131.67 (-5.91) 5.55 (2.04) 11.14 (1.54)

0.003 (-2.89) 0.81 (6.86) 1.10 (6.46) -0.06 (-2.46) -0.12 (-2.26)

0.001 (2.29) -0.45 (-6.72) -0.63 (-6.64) 0.03 (2.43) 0.06 (1.82)

-3.88 (-0.28)

0.17 (1.61)

-0.12 (-1.82)

-23.95 (-1.76) 2.64 (0.14) 53.75 (1.64) -35.79 (-1.83) 7.02E-05 (0.37) 16.14 (2.04) -31.36 (-2.61) 62.99 (1.44)

-0.07 (-1.12) 0.25 (1.75) 0.40 (2.381) -0.06 (-1.579) -4.7 (-14.00)

-0.16 (-2.04) 0.20 (1.33) -0.27 (-3.11) 1.23E-06 (1.44) 0.07 (2.06) -0.04 (-1.09) 4.72 (25.25)

0.0045 0.64 33740.00 (20.91) 2493.30 (2.06) 0.002 (0.003) -6089.87 317.30 0.00 0.03

-1058.3 312 0.00 0.13 Rejected Selected Model

1.84 0.628

-1054.6276 297.98 0.00 0.12 Rejected

5.4.1 ‘Gap Duration before Work’: The Work Start Time Table 5.1 summarizes three models for this component. In the multilevel linear model the household level random effect is not significant. The significance of the variance in personal and temporal level in multilevel model justifies the unobserved heterogeneity assumption in the other two hazard models in the table. Also the null hypothesis regarding the unobserved heterogeneity in these two models is rejected. This 80

indicates the day-to-day dynamics in work start time of the same individual. The value of

θ higher than 0 indicates that a considerable amount of an individual’s behaviour is unobserved. Likelihood ratio tests justify all three models described in this table, but the pseudo R2 value is the highest for Gompertz proportional parametric hazard mode and so this model is selected. The positive value of γ of the selected model indicates increasing hazard rate of the before work gap duration with time. In terms of the covariates of the selected model, start time is the most significant variable after the constant term. Start time of the before work gap duration, i.e. the end time of night sleep has positive influence on the duration. A higher number of work episodes in the day results in longer gaps before starting the first work episode. The total time spent for work in the previous day negatively influences the current day beforework gap duration. Both auto and transit commuters have shorter gaps before work compared to those who walk or use bikes to go to work. However, transit users have less before work duration than auto users. Higher number of possible work locations and higher weekly work frequency increase before-work gap duration. Temporal flexibility of work duration results in earlier work start times. Males start work earlier than females. Single adults at home, adult children and other adults in household start work earlier than adults with partners in the household. Full-time employees start work earlier than parttime employees. People with job locations other than home start earlier then people with at-home jobs. Household size influences the before work-gap duration positively, but a greater number of children in household has a negative effect.

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Table 5. 2 Models for ‘Work Duration’

Coefficient (t stat) 13.76 (1.00) 31.02 (2.56) -0.13 (-2.53)

Gompertz Proportional Hazard Model Coefficient (t stat) -0.10 (-0.84) -0.25 (-2.24) 0.0001 (0.91)

Log logistic Accelerated Time Model Coefficient (t stat) 0.16 (2.56) 0.03 (0.54) -0.0001 (-0.66)

-826.11 (-10.73)

7.10 (9.50)

-3.14 (-9.75)

-35.99 (-2.18)

-0.58 (-3.75)

0.11 (1.66)

0.02 (1.16)

-0.0002 (-1.14)

0.0003 (4.24)

-0.02 (-0.16) 48.88 (3.56) 55.48 (2.83) -7.60 (-2.95) -16.29 (-2.40)

0.002 (1.69) -0.57 (-4.35) -0.50 (-2.74) 0.06 (2.67) 0.22 (3.49)

-0.0008 (-1.61) 0.17 (3.01) 0.23 (3.08) -0.03 (-2.80) -0.14 (-5.58)

54.71 (4.23)

-0.57 (-4.78)

0.08 (1.71)

22.93 (1.88) -99.54 (-3.65)

-0.17 (-1.48) 0.75 (3.00)

0.02 (0.47) -0.15 (-1.60)

-64.40 (-2.56)

0.33 (1.50)

-0.05 (-0.54)

-18.76 (-0.60) 22.42 (1.23) 39.24 (1.88) 3.32 (0.12)

0.59 (2.08) -0.60 (-3.45) -0.39 (-2.07) -0.43 (-1.80)

-0.26 (-2.34) 0.15 (2.24) 0.12 (1.63) 0.02 (0.24)

28.92 (2.07)

-0.17 (-1.31)

0.06 (1.27)

103.28 (2.49) 1.03E-4 (-0.58) 6.77 (1.02) -23.42 (-2.90) 810.89 (15.01)

-0.97 (-2.40) 2.31E-6 (1.50) -0.02 (-0.33) 0.11 (1.56) -10.69 (-20.39)

0.21 (1.28) -5.14E-07 (-0.82) 0.04 (1.69) -0.08 (-2.92) 7.09 (35.11)

Multilevel Linear Model Covariates Monday (Dummy) Friday (Dummy) Duration of Gap Before Work Work Start Time (Fraction of 24 hour ) Number of Work Episode Total Work Duration of the Previous Day Travel Time from Home to Work Mode of Work Trip: Auto Mode of Work Trip: Transit No. of Work Locations Weekly Work Frequency Temporal Flexibility of Work Duration (Dummy) Male (Dummy) Single Adult in Home (Dummy) Adult with Partner at Home (Dummy) At Home Job (Dummy) Full Time Job (Dummy) Service industry Job Manufacturing Specific Business Service and Dummy Administration Variables Food Service Income (CAD/Year) Household Size No. of Household children CONSTANTS Ancillary Parameters γ θ Level-1 Variance Level-2 Variance Level-3 Variance Loglikelihood Likelihood Ratio Probability > Chi-Square Value Pseudo R2 H0 : θ =0

15275.68 (17.70) 8635.72 (6.61) 3.2E-13 (9.7E-09) -5849.58 660.22 0.00 0.05

0.0092 0.537

0.36 7.87E-08

-587.50 526.86 0.00 0.31 Rejected Selected Model

-948.33 550.20 0.00 0.22 Accepted

5.4.2 Work Duration Table 5.2 summarizes three models for work duration. As for the previous 82

component, the household level random effect is not statistically significant in the multilevel model. The temporal and personal level random effects in the multilevel model are significant and justify the higher value of θ in the Gompertz proportional parametric hazard model (although the log-logistic distributional assumption of baseline hazard rate gives a very low θ value). A likelihood ratio test justifies all of the three models described in this table, but the pseudo R2 value is the highest for Gompertz proportional parametric hazard model, which is, therefore, the selected model. The positive value of γ of the selected model indicates an increasing hazard rate of work duration with time. In terms of the covariates of the selected model, the day-specific dummy variables indicates people work longer on Monday and Friday, which are assumed to be the first and last day of the working week. The total gap-duration before work negatively influences the work duration. The start time of work is the most significant variable after the constant term. It indicates people starting work late have shorter total daily work durations. In the case of multiple work episodes per day, a higher number of work episodes reduces the total time allocation to work for that day. Total work duration of the previous day influences the present-day total work duration positively but the effect is small (very low coefficient value). Commuting time has a negative effect on the duration of work episode and both auto and transit users tend to work shorter durations compared to those who walk or use bikes to go to work. However, transit users work longer than auto users. Higher number of possible work locations and higher weekly work frequency both reduce total work duration. Temporal flexibility of work duration influences people to work longer time. Males work longer than females. Single adults at home and adults with a partner at home work shorter durations compared to adult children and other adults in the household. Fulltime employees work longer durations than part-time employees and people having an athome job work shorter durations than the people having out-of-home job locations. According to job classification, people in the service industry, manufacturing sectors, food service sector (hotels, bars and restaurants), and business service-administration work longer durations than people in other sectors. Within these 4 job sectors, people in food service sectors work longer than the people in the other 3 sectors. Income has a positive influence on work duration. Household size influences the 83

work duration positively but a greater number of children in the household has a negative effect. Table 5. 3 Models for ‘Gap Duration after Work before Night Sleep’ Lognormal Accelerated Life Model Coefficient (t stat) -0.01 (-0.15) 0.06 (1.36)

Log Logistic Accelerated Time Model Coefficient (t stat) -0.01 (-0.20) 0.05 (1.37)

-0.24 (-18.44)

5.50 (41.37)

5.29 (46.40)

-0.25 (-17.57)

0.0001 (-1.04)

-0.0001 (-0.95)

5.37 (1.22) 0.29 (1.65) 4.54 (1.39) -10.77 (-1.32)

-0.15 (-3.36) -0.001 (-0.79) -0.04 (-1.28) -0.02 (-0.30)

-0.06 (-1.63)

-4.79 (-0.62)

-0.04 (-0.49)

-0.04 (-0.77)

4.83 (0.96) -1.4E-05 (-0.32) -5.21 (-0.85) -1.10 (-0.62) 2.04 (0.97) 0.78 (0.31) 1331.55 (82.62)

-0.14 (-2.79) 7.69E-07 (1.70) 0.08 (1.32) 0.04 (2.08) -0.06 (-2.82)

-0.08 (-2.19) 4.25E-07 (1.22) 0.06 (1.30) 0.03 (2.10) -0.04 (-2.12)

4.43 (34.20)

4.37 (42.98)

Multilevel Linear Model Covariates Tuesday (Dummy) Thursday (Dummy) Start Time (Fraction of 24 Hours) Gap Before Work Duration (Minutes) Total Work Durations of the Day (Minutes) Number of Work Episodes Age (Years) Male (Dummy) Single Adult in Home (Dummy) Adult with Partner at Home (Dummy) Full Time Job (Dummy) Income (CAD/Year) Driving License (Dummy) Household Size No. of Household children No. of Household Autos CONSTANTS Ancillary Parameters σ γ θ Level-1 Variance Level-2 Variance Level-3 Variance Loglikelihood Likelihood Ratio Probability > Chi-Square Value Pseudo R2 H0 : θ =0

Coefficient (t stat) 4.01 (1.32) 5.38 (1.62) -1069.38 (-50.07)

-0.02 (-0.79)

0.46 1.04E-8 1067.82 (17.98) 638.76 (7.07) 5.59E-6 (1.3E-4) -4635.73 2648.14 0.00 0.22

-583.23 1379.93 0.00 0.54 Accepted

0.21 8.85E-9

-454.94 1637.62 0.00 0.64 Accepted Selected Model

5.4.3 ‘Gap Duration after Work before Night Sleep’: The Night Sleep Start Time Table 5.3 summarizes three models for this component. In the multilevel linear model the household level random effect is not significant. Although the variances in personal and temporal level in the multilevel linear model are significant, the unobserved 84

heterogeneity assumption in terms of θ values in the two hazard models in the table are not significant (the null hypothesis is accepted). The reason for this may be accommodation of heterogeneity by the distributional assumption in the hazard models. This is justified by the pseudo R2 of the hazard models. The pseudo R2 of Log-logistic accelerated time hazard model is the highest, 0.64 and it is the selected model for this skeleton component. In terms of the covariates of the selected model, the before work gap duration is the most significant covariate. It seems that people who start work late go to sleep late. On the other hand, total work duration of the day and the total number of work episodes influences the after-work gap duration negatively. Full time employees have longer gaps after work in comparison to part time employees. High-income people have longer after-work gaps than low-income people; having a driving license increases the opportunity to be involved in other activities and thereby increases the after-work gap duration, but the number of autos per household shows a negative influence on it. Both household size and the number of children influence the after work gap duration positively.

85

Table 5. 4 Models for ‘Night Sleep Duration’

Covariates Start Time (Fraction of 24 Hours) Total Work Durations of the Day (Minutes) Gap After Work Duration (Minutes) Age (Years) Male (Dummy) Single Adult in Home (Dummy) At Home Job (Dummy) No. of Household children CONSTANTS Ancillary Parameters σ θ Level-1 Variance Level-2 Variance Level-3 Variance Loglikelihood Likelihood Ratio Probability > Chi-Square Value Pseudo R2 H0 : θ =0

Lognormal Accelerated Time Model Coefficient (t stat)

Multilevel Linear Model

Semiparametric Hazard Model

Coefficient (t stat)

Coefficient (t stat)

-329.70 (-58.93)

8.68 (14.36)

-0.03 (-3.80)

0.0008 (2.97)

0.0001 (0.57)

-0.06 (-6.36)

0.0013 (4.00)

-0.0002 (-1.82)

-0.01 (-0.99) 0.03 (0.28)

0.0007 (0.42) -0.05 (-1.40)

-0.31 (-2.23)

-0.0011 (-0.03)

0.20 (0.62) -0.03 (-0.51)

-0.05 (-0.59) -0.04 (-2.06) 5.90 (56.56)

9.13 (2.26)

423.47 (55.08)

1.56

0.55 1.7400E-08

1055.39 (58.78) 2275.65 (423) 761.03 (407.3) -4789.1 1370.41

-5017.67 220.67

-757.04 14.08

0.00

0.00

0.10

0.13

0.02 Rejected

0.01 Accepted

Selected Model

5.4.4 Night Sleep Duration Table 4 summarizes three models for this component. Two types of hazard models are investigated: semiparametric and lognormal accelerated time hazard model. The performance of the parametric hazard model is the poorest. In this model, the assumption of unobserved heterogeneity is not statistically justified and the pseudo R2 value is also very low. This may be due to the inappropriate assumption of the baseline hazard rate (although the lognormal distribution shows the best result among all other distributions considered during this analysis). On the other hand the semiparametric hazard model does not assume any baseline hazard distribution, so it performs better than the parametric hazard model in terms of pseudo R2 value. Also the very high value of θ 86

(higher than 1) and its statistical justification indicates the reason of the poor performance of the parametric hazard model: a larger portion of the behavioural factors are unexplainable by the observed covariates data and hence makes the baseline hazard rate too unstable to fit into a particular distributional assumption. But the goodness-of-fit of the semiparametric hazard model is still very low (0.02). In this case, the multilevel linear model performs best. The assumed random effects of all of the three levels considered in this model are statistically significant and the pseudo R2 value is reasonable (0.13) compared to other models. This implies that night sleep duration is very much influenced by personal and household level factors that are not explained by the covariates available from activity diary data set. So the multilevel linear model is the selected model for this component. In terms of the covariates of the selected model, the start time is the most significant variable. The interpretation of this start-time coefficient needs some care. The starting time is assumed on a continuous scale as fractions of 24 hours. The value of start time is 1 at midnight and at that time this variable has the maximum effect. Start times before midnight have lower effects in decreasing order farther from midnight and the start times after midnight also have lower effect than midnight, but with increasing order farther from the midnight. The gap after work before the starting of the night sleep and total work duration also have high, negative influence on night sleep duration. Of course there must be balancing effects of these two variables with night sleep start time. The variable indicating the individual’s age and sex are not significant statistically at all. Single adults at home sleep longer than adults with partners at home, adult children and other adults. Also, no household-related variables show statistical significance.

The overall comments on all four component models should include: the night sleep model contains the least number of fixed covariates, but only this component model captures the unobserved random effects of all three levels considered in the modelling system (temporal level of individual, person specific level and the household level). For all other components, the household-based random effect is not statistically significant. In terms of goodness-of-fit, the model for gap duration after work shows the best fit of 87

observed data followed by work duration component. Remarkably, however, it incorporates no unobserved heterogeneity. The night sleep duration model and gap before work duration model show similar fit to the observed data. Other than the night sleep duration model, the other three component models are hazard models (nonlinear). The application of the Gompertz distribution for parametric hazard models shows promising results. The Gompertz distribution is a very flexible growth model, which is basically the truncated Type-I extreme value distribution, and its flexible nature enables it to fit the complete range of sigmoid curves (Gumbel) (for details see Sanchez-Choliz, 2005). The application of the Gompertz distribution in this chapter yields higher fits to observed activity data, especially for fixed commitment type of activities, where the conventional distributional assumptions often fail to give desired result (Habib and Miller, 2005a). In terms of covariates, the start time of the episode of concern show negative influence on the duration of the events except for the gap before work duration. In all models, the competition between motorized (auto and transit) and nonmotorized (walk and bike) mode for commuting is clearer rather than competition between autos and transit. Within auto versus transit competition, transit has higher absolute coefficient values. Total work duration of the previous day influences workers to start later but work longer. One important finding is that the personal attribute ‘age’ does not enter in any model significantly. This contrasts with models in the literature in which age is the most commonly used index variable in operational activity-travel scheduling models to derive start time-duration of the skeleton activities from the observed distributions.

5.5 Conclusions This chapter describes empirical models to generate skeletal components of workers’ daily life. The approach considers the full-day cycle to capture day-to-day dynamics of workers daily activity behaviour. The modelling system divides the workers’ daily life into four components: Gap before work, Work, Gap after work and Night sleep. The component models consider previous day’s total work duration as a covariate. In order to model the individual components of the system, two econometric methods are considered: multilevel linear models and hazard-based event history analysis models. The multilevel linear models consider individual observations nested in three levels: the temporal level, the personal level and the household level. The hazard models adopt the 88

individual-based shared frailty approach. The chapter reports the three best models for each component selected according to the goodness-of-fit to observed data. The model having the highest goodness-of-fit among the three candidate models is then selected for inclusion in SWDAS. Thus, for the gap before work and work duration components the Gompertz proportional parametric hazard models are selected; for the gap after work duration the log-logistic accelerated time model is selected. Finally, for the night sleep duration the multilevel linear model is selected. In terms of fitting the observed data, the gap after work duration model gives the best fit, followed by the work duration component. The goodness-of-fit for gap before work duration and night sleep duration are the same. In terms of overall features of the selected component models, the night sleep duration models have the least number of covariates and a higher number of random effects. In terms of covariate effects, the age of the person does not show any significant effect in any model. Variables representing the commuting modes show that the motorized modes compete with nonmotorized modes as a whole. A notable contribution of this chapter to the existing literature of activity-based travel demand analysis is the application of the Gompertz distribution in modelling duration of the events. This distribution shows greater flexibility in fitting the observed activity diary date better, especially for the activities with fixed commitments (work)

89

CHAPTER 06: INVESTIGATING SEQUENCING OF NON-SKELETAL ACTIVITIES IN ACTIVITY-AGENDA FORMATION 6.1 Introduction Understanding the processes of activity needs and engagements is critical to activity-based travel demand models (Axhausen 1997). Understanding time use decision making is critical to understand the mechanisms of activity needs and engagements (Kitamura et al 1997). The key time use decisions regarding an activity are: deciding when to start the activity and how long to continue it. Activities with at least these two basic attributes are termed activity episodes. Gärling et al (1999) argues that the activity participation rates (frequency) and corresponding durations create time pressure to undertake short-medium-long term activity planning and sequencing. The previous chapters discussed the clear division between activity generation (planning) and activity scheduling in activity-based travel demand modelling. This thesis deals solely with the activity generation component. Activity generation or planning is defined as the process of activity-agenda formation. Chapter 5 presents models for the fixed or skeletal components of the activity-agenda for a specific time period (time budget). Given the skeletal component, the total time budget provides time windows to be filled with other activity types called non-skeletal activities. So the next step is to model the activity generation of the non-skeletal activities. Prior to modelling the generation of the non-skeletal activities the concern is whether the generation process should be concerned with the arrangement of the activity episodes along the time scale. More specifically, whether the activity generation component of non-skeletal activities should consider both start time and duration relationships. Given the activity-agenda, the scheduler arranges / rearranges the episodes in order to accommodate interactions within the real-time environment, more specifically, the interactions between travel and activity needs (Levinson 1999). In activity-based modelling, activity scheduling is the final stage of generating trip chains or travel demands. The timing (start time) and duration relationship during the generation of activity-agenda is a critical issue. RUM-based models consider complete activity patterns 90

as input. Considering the whole activity pattern as input, however, assumes strong relationships between start times and durations of different activity types during the activity planning process or activity-agenda formation. It is not clear whether the sequencing of activity episodes in an activity-agenda in terms of the time of day together with the relationship between start time and duration of different activity types should be the job of the generation component or the scheduling component of the activity-based model. For skeletal activities (e.g. work / school), the timing and duration are often fixed by external factors, for example employment type, long-term household decisions, etc. But for non-skeletal activity types, timing and duration depends on various factors. So from the activity-based travel demand modelling perspective, the investigation of start time and duration relationship of different nonskeletal activity types in the generated activity-agenda is of considerable importance. In addition to the interest of model building, understanding the start time and duration relationships of different activities in the activity planning process (the generation stage) are also critical to understand the impacts of different policies that affect interactions of activity demand and transportation network performance, such as Travel Demand Management (TDM), Transportation System Management (TSM), Congestion Management etc. The effectiveness of different transportation policy measures depends on peoples’ activity-travel behaviour. For example, congestion pricing in peak periods to reduce peak-period travel demand may be effective if people change their peak period out-of-home activity participations. Changes in activity-travel patterns in response to different policies depend on the flexibility of the start time of the activities with respect to time of day as well as their duration. Different types of activities may have different types of start time and duration relationships and thereby different types of response to transportation policy measures. So, understanding the start time and duration relationships of different activity types also helps to predict the impacts of different urban transportation policy measures. However, this critical issue has not been investigated adequately to date, in particular in terms of the use of appropriate econometric specifications to understand the causal relationships underlying observed behaviour. So far, only Pendyala and Bhat (2004) have investigated this issue using econometric techniques. They consider two 91

causal relationships: ‘start time selection is conditional on duration’ and ‘duration is conditional on start time selection’. They use trip diary data (data of the executed schedules) to investigate these causal relationships for maintenance type activities by using a simultaneous equation approach. The analysis of this chapter is inspired by Pendyala and Bhat (2004) and is intended to further investigate this critical issue in terms of using more detailed activity data and through the use of sequential (i.e., nonsimultaneous) econometric frameworks complying with the assumed causal structures. According to Pendyala and Bhat (2004): “Activity scheduling surveys that involve the collection of data on underlying behavioural process make it possible to study timing decisions in a robust framework” and such a data set “would greatly help further explore the causal linkages between timing and other activity-travel variables”. The TAPS Wave 1 CHASE dataset is such a “process oriented” database and is used in this investigation. The investigation is detailed with respect to identifying unique causal relationships between two decisions (start time selection and duration determination) for different time periods within a day. The investigation is disaggregated with respect to individual activity types. The unique causal relationships refer to whether these two decisions are correlated or not, and, if they are correlated, then what are the exact relationship. Strong and well defined correlations between start time selection and duration determination at the stage of activity planning will warrant consideration of activity sequencing in activity-agenda formation modelling, on the other hand, poor or less well defined relationships will justify the assumption that the activity sequencing is more the job of the activity scheduling/rescheduling process than the activity generation process. The finding of this chapter influences the methods and investigations of the next chapters of this thesis. The chapter is arranged in the following way: the second section discusses the causal relationships between activity start time and duration, the third section describes the mathematical formulations of the econometric specifications, the fourth section describes the data, the fifth section provides results of the empirical estimations and the last section gives concluding remarks 92

6.2 Causal Structures for Start Time and Duration Relationship of NonSkeletal Activities Both start time and duration are time-related attributes of activity episodes. The start time of an activity is a discrete point on the time scale and the duration follows to the end of activity. Considering individual activity episodes as units of analysis, the generated attributes of the activity episodes: start time, duration, mode etc., are adjusted during the scheduling process to cope with the time-space constraints/opportunities. The generated activities in the planning stage may have some sequence, precedence and priorities in implementation that are derived from the importance and prerequisites of the corresponding activity needs. It is important to know the relationship between start time and duration of the activities in the activity-agenda because it ultimately defines the scheduling process. In order to investigate the relationship between start time and duration of non-skeletal activities in the activity-agenda, two possible options can be considered: 1. Start time of the activity is selected first and then duration is conditional on the start time. 2. Duration of the activity is selected first and start time depends on the duration. So, two separate causal structures are hypothesized in this chapter as described in detail in the following subsections. Based on findings from the literature review it is hypothesized that during the activity generation/planning stage people consider the tentative start time of activity episodes according to discrete time periods within the day. This means the activity generator devises the sequence of non-skeletal activities tentatively and fixing the exact start time is the job of activity scheduling. Based on preliminary investigation of TAPS Wave 1 CHASE survey data we consider 5 divisions of a day for start time selection, such as: Early Morning (EM), Morning (M), Mid-Day (MD), Afternoon (AF) and Evening (EV). Based on these divisions and the continuous time duration assumption, two causal structures are devised.

6.2.1 Start Time of the Activity Episode is Planned First This causal structure assumes that the start time of the activity is selected first and 93

then the duration is estimated based on the selected start time. The duration is conditional to the start time. Figure 6.1 shows this causal structure graphically: Start Time Selection

Duration for Start Time in EM

Duration for Start Time in M

Duration for Start Time in MD

Duration for Start Time in AF

Duration for Start Time in EV

Figure 6. 1 Causal Structure: Start Time is Conditional to Duration Selection

This is a conditional/sequential causal structure where selection of episode duration is conditional to its start time. As the day is divided into 5 discrete parts, this causal structure means selecting the starting time period using a discrete choice framework. Once the start time is selected then the duration is planned. For each possible individual start time segment, a separate duration decision is to be modelled. Thus the econometric formulation of this causal structure stands as a sample selection modelling specification. It is a sequential two-step causal structure. The selection of start time is to be modelled as a function of socio-economic characteristics, activity characteristics and any policy variables of concern (e.g. congestion pricing for the time of the day, frequency of the public transit etc.). Given the selected time of the day, the duration of activity is to be modelled as a function of socio-economic variables and activity characteristics.

6.2.2 Duration of the Activity Episode is Planned First This causal structure assumes that the start time selection is conditional on the planned duration for the activity episode. Figure 6.2 shows this causal structure graphically:

94

EM Duration

Start Time Selection

M MD AF EV

Figure 6. 2 Causal Structure: Duration is Conditional to Start Time Selection

This structure gives priority to episode duration and then, given the duration, the start time of the activity episode is selected. This structure is also a sequential two-step causal structure. The duration is modelled as a continuous variable and as a function of socio-economic and activity characteristics. Given the duration, the start time selection model is a time-of-day choice model considering duration as an endogenous variable together with other socio-economic variables, activity characteristics and any policy variables of concern (e.g. congestion pricing for the time of the day, frequency of public transit at that the time of day, etc.)

The use of appropriate causal structures is very important and critical for both policy analyses as well as for understanding behaviour. The importance of an appropriate causal structure for different TDM impact assessment is well discussed in Pendyala and Bhat (2004). In the case of the activity-based travel demand model, understanding the proper causal relationship for different types of activities is crucial, especially for hybrid activity-travel demand models, where the activity generation process uses the concept of activity utility to form the activity-agenda for a particular time period. If a well defined relationship is justified through statistical and econometric investigation, it should be taken into consideration in model applications. Understanding the relationship between start time and duration can also help to devise rules for the activity rescheduling process as well. For example, consider a 95

hypothetical conflict in activity scheduling of a person between two activity episodes in the afternoon: one is a Household Obligation type activity and the other is a Service type activity. Now if the Household Obligation type activity is sensitive to starting in afternoon and the Service type activity is not, then the former one should get priority in scheduling and the later one can be shifted to a different part of the day. The main objective of this chapter is to investigate the existence of such causal relationships between these two key attributes within the activity planning stage for different non-skeletal activities.

6.3 Modelling Techniques and Estimation Procedures Devising an appropriate econometric framework to investigate the proposed causal relationships is not an easy task. Pendyala and Bhat (2004) used a similar causal structure but assumed that both start time and duration are simultaneously determined. They used trip diary data to investigate the relationships. The trip diary data contains only the observed trips. Activity attributes are calculated using estimated travel time. Such data do not contain the necessary ingredients to understand the trade-offs involved in deciding start time and durations of different activities in the planning stage prior to scheduling/implementation. To understand the detailed behavioural relationships between start time and duration, we need detailed micro data representing the activity planning stage. Such a data set is used in this chapter, and, given the availability of such data, it is feasible and more appropriate to consider sequential decision structures complying with the

proposed

causal

relationships.

In

this

chapter

we

consider

sequential

discrete/continuous econometric frameworks so that logical consistency is maintained throughout the modelling structures, permitting exploration of behavioural relationships. The following sub-sections describe the econometric specifications of the models and corresponding estimation procedures in detail.

6.3.1 Causal Structure: Start Time
Duration This causal structure is a two-step Discrete-Continuous structure. The first step decision is a discrete-choice start time selection model. Given the selected start time the second step decision is a continuous model of episode duration. So, this structure 96

becomes a sample selection model. The sample for estimating duration is selected based on the selected start time. Heckman (1979) first proposed the sample selection model for binary discrete-continuous decision, i.e., a binary selectivity model. Lee (1983) extended the binary selectivity model of Heckman to the multinomial selectivity model. Dubin and McFadden (1984) also proposed a similar multinomial selectivity model. The basic differences between the Lee and Dubin-McFadden procedures are the assumption of the correlation between error terms of two models (multinomial choice model and continuous choice model) and the assumption regarding the selectivity correction in the continuous model. Bourguignon et al (2004) combine these two methods to overcome individual criticisms. In this chapter, the Bourguignon et al (2004) method of multinomial sample selection model is used. A brief description of the model is given below. Let: D = xβ + α S j = yγ j + θ j

(6.1)

Here, D is the continuous duration; x is a vector of covariates and α is the error term of the continuous duration model component. Sj indicates the utility of selecting start time j, y is a vector of covariates and θ is the error term of the start time selection model. For the duration model component, the basic assumption is that α is normally distributed with expected value E(α|x, y)=0 and variance V(α|x, y)= σ2. For the start time selection model component the error term θ is IID Type I Extreme value distributed. So, the model described in equation (6.1) is basically a latent discrete-continuous model, where the duration in a specific part of the day is observed only when the start time corresponding to that part is chosen. For simplicity of description, let us assume the duration D is observed for start time category 1. The selection of category 1 start time from a set of probable categories j indicates:

S1 >

max (S j ) j ≠1

(6.2)

Now for the sake of description, we can define 97

ε1 =

max max ( S j − S1 ) = ( yγ j + θ j − yγ 1 − θ1 ) j ≠1 j ≠1

(6.3)

For the IID Type I Extreme value assumption of θ, the probability of choosing the start time category 1 takes the well-known multinomial logit form (McFadden, 1973) P ( S1 ) = P (ε 1 < 0 | y ) =

exp( yγ 1 ) ∑ exp( yγ j )

(6.4)

j

The parameters of the above model can be estimated using maximum likelihood estimation but a problem arises while estimating the parameters of the duration model component. The duration D is observed for the specific category of the selected start time. So the estimation of the parameters β needs to account the fact that the error term of duration model component, α is not independent of all corresponding error terms of the start time selection model, θj. Note that this will also introduce a correlation between x and α. As a result, the least square estimate of the duration model will not be consistent. To overcome this problem the start time selectivity bias correction is necessary. For clarity of description, let us define: Λ = { yγ 1 , yγ 2 , yγ 3 ,......... yγ n } , For n category of start times.

(6.5)

According to Heckman (1979), the bias correction in the duration model for the start time selection can be based on the conditional mean of the error term of the duration model component:

E (α | γ 1 < 0, Λ ) = ∫

0

α f (α , ε 1 | Λ )

∫ P(ε

−∞

1

< 0 | Λ)

dε 1 dα = ∆ ( Ω )

(6.6)

Here f (α , ε 1 | Λ ) is the conditional density of α and ε1. The expression of P(ε1) as mentioned in equation (6.4) can be replaced in the above equation. Now for the invertible relationship between N components of Λ and the corresponding N probabilities in equation (6.4), there is a unique function Ψ that can be substituted for Ω:

98

E (α | γ 1 < 0, Λ ) = Ψ(P1, P2, P3, …………, PN)

(6.7)

Thus, the consistent estimation of the continuous duration model can be based on the regression

D = xβ + Ψ ( P1 , P2 , P3 ,...........PN ) + α / = xβ + ∆(Ω) + α /

, α / is the residual that is mean − independent of the regressors

(6.8)

Here the main problem is to define ∆(Ω) in the duration model. The specifications of ∆(Ω) make the difference between different methods as described earlier in this section. Comparisons of different methods based on simulated data are available in Bourguignon et al (2004). Here the target is the consistent estimation of the duration model component considering the start time selectivity bias. We know that any completely specified marginal distribution can be transformed into a standard normal distribution. So, in order to consider the error conditionality of the duration model component, the error term of the start time component can be transformed as follows:

θ *j = J (θ j ) = Φ −1 ( F (θ j )) , j =1, 2, 3, ...........N

(6.9)

The assumption is that the values of α in equation (6.1) and θj* are linearly correlated. If ρj is the correlation between α and θj*, α can be expressed as a linear combination of θj*.

α = σ ∑ ρ jθ *j + η j

(6.10)

η is the residual that is orthogonal to all θj* and E(η ) = 0. For the estimation of the duration model, it is necessary to know the expected value of α conditional on the specific start time selection because for each selected start time a separate duration model will be derived. For example, for the selection of start time 1, we can write that 99

E (α | S1 >

max j ≠1

( S j )) = σ ∑ ρ j E (θ *j |S1 > j

max j ≠1

( S j ))

(6.11) and

E (θ *j | S1 >

max j ≠1

( S j )) = ∫ J (θ j ) f (θ j | S1 >

max j ≠1

( S j ))dθ j

(6.12) The conditional density f (θ j | S1 >

max ( S j )) can be derived to yield: (see j ≠1

Bourguignon et al, 2004)

E (θ1* | S1 >

max j ≠1

( S j )) = ∫ J (θ1 ) g (θ1 + log P1 )dθ1

Where, P1 is the probability as per equation (6.4). Now, assuming δ = θ1+logP1

E (θ1* | S1 >

max j ≠1

( S j )) = ∫ J (δ − log P1 ) g (δ )d (δ )

(6.13) For θj*, when j ≠ 1 −θ 1  e j  −θ j E (θ | S1 > ( S j )) = ∫ J (θ j ) )dθ j  g (θ j ) − e exp(− j ≠1 1 − Pj  Pj  * j

max

−θ

1 1 e j −θ j = J ( θ ) g ( θ ) d θ − J ( θ ) e exp( − ) dθ j j j j j 1 − Pj ∫ 1 − Pj ∫ Pj Again considering δ = θj+ logPj and the fact that

E (θ *j | S1 >

∫ J (θ

j

) g (θ j )dθ j = E (θ *j ) = 0

Pj max ( S j )) = J (δ − log Pj ) g (δ )dδ j ≠1 Pj − 1 ∫ 100

(6.14) For convenience, assume m( Pj ) = ∫ J (δ − log Pj ) g (δ )dδ , ∀ j Replacing the error term of the duration model component in equation (6.1) by its conditional expected value derived from equation (6.11) and a residual α / , for a particular start time category j/ we can write

  Pj D = xα + σ /  ρ j / m( Pj / ) + ∑ ρ j m( Pj ) + α / Pj − 1 j≠ j/   = xβ + ∆(Ω) + α / (6.15) This is the multinomial sample selection model. This is a sequential discretecontinuous model in two steps: the first step involves estimation of the multinomial logit model for start time selection including the estimation of the fitted probabilities and other components that incorporate all information influencing the multinomial logit model, and then the duration equation is estimated by the least squares method. This approach incorporates all correlation coefficients between the error term of the duration equation and the error term of the start time selection equation. The coefficients and statistical significance of the corresponding ∆(Ω) of equation (6.15) indicate the influence of the start time selection on the duration estimation. A statistically significant ∆(Ω) in the duration model indicates the dependence of the duration to the corresponding start time selection. Bourguignon et al (2004) prove that although this method may violate the IID assumption, it provides the best way to correct the selectivity bias.

6.3.2 Causal Structure: Duration
Start Time This causal structure assumes that duration is planned before the start time selection. So the hypothesis is: duration of the activity episode is endogenous to the start time selection process. Without treating this endogeneity, the consistent estimation of the start time selection is not possible. The endogeneity correction needs treatment of the endogenous variable. If the treatment model shows the statistical significance of the endogenous variables in the start time selection model, the causal structure can be 101

considered to be justified. Acceptance of the assumed causal structure proves the duration of the activity is planned before the start time. There are several techniques available for modelling endogeneity. The most widely used one are instrumental variable (IV) techniques. Greene (2003) discusses the IV techniques for different types of models. The main idea of the IV technique is to use a projected variable (instrument) in place of the endogenous variable ensuring that the instrument is not correlated with the error term of the main equation. However, the selection of the appropriate instrument is not an easy task and often is controversial (Petrin and Train, 2004). A second approach is proposed by Berry et al (1995) and known as the product-market fixed effect approach. For discrete choice models, this approach proposes the correction of the alternate specific constant (the fixed effect). The constant is replaced by a regression of the predicted endogenous variable and its other characteristics. The problem with this approach is the homogenous market assumption. It assumes that all individuals belong to the same group, which means that it cannot handle individual level endogeneity. A third approach is known as the control function approach (Heckman, 1978 and Hausman, 1978). The control function approach is capable of handling individual level endogeneity and provides a two-step correction procedure that is consistent with our proposed causal structure. This method is used in this chapter to determine the influence of the duration on the start time selection. A brief description of this method is given below. Let duration and start time utility now be given by D = xβ + α S j = V ( yγ j , D) + θ j where V ( ) indicates the indirect utility (6.16) This model is also composed of two components. The notation is the same as in the previous section. In this case, however, the duration D is now assumed to be endogenous to the start time selection. The endogeneity assumption indicates that duration is not totally independent of the error term θj of the start time selection model. So, correction is needed for the endogeneity because, for the multinomial logit start time selection model, the mean value of the error term θj should be independent of the 102

covariates. A possible remedy for this problem is to introduce a control function. The objective is that the control function squeezes out the correlation between unobserved parts of duration with the error term θj by introducing a new variable termed the ‘control variable’. To do this, the duration is regressed on covariates x, from which a residual can be computed: D = xβ + α D = E(D | x) + α

α = D − D = the fitted residual, Where, D is observed value and D is the predicted value Here, the fitted residual of the duration equation incorporates the unexplainable part of the duration that may be correlated with the θj. The fitted residual α also indicates the portion of duration not explainable by the covariates x. This fitted residual

α is the ‘control variable’ needed to correct the endogeneity of the duration in the start time selection model (Petrin and Train 2004). As a result, the start time selection model becomes:

S j = V ( yγ j , D, f (α )) + θ j (6.17) Where f (α ) is the control function and

f (α ) = E (θ j | α ) = πα (6.18) Where π is the function of covariance between θj and α . So the model stands as: D = xβ + α S j = yγ j + κ D + πα + θ j = yγ j + κ D + ∆ (Ω) + θ j (6.19) Thus, the control function approach uses the duration residuals by entering them

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directly into the choice model. The two-step estimation procedure is straightforward: First, the duration is estimated as a function of covariates (known as instruments) and the residual is calculated. Second, the start time selection model is estimated using all covariates and the estimated residual (control variable) enters as a separate variable to provide the duration endogeneity correction. The statistical significance of the control variable thus determines whether the duration is endogenous to the start time or not. An application of this method for residential location choice model considering the price as endogenous variable is also available in Guevara (2005).

6.4 Description of Data for Empirical Investigation TAPS Wave 1 CHASE survey data are used to investigate start time and duration relationships of non-skeletal activities (all general activity types except work/school and night sleep). The CHASE program tracks the activity episodes added by each participant of the household sequentially. The modifications or deletion of the first added episodes are also recorded that gives the implementation status of the episode. The survey results thus show the addition, modification and deletion of different activity episodes over the period of the survey week. At the end of the survey, it is seen that not all first-time-added activity episodes are implemented. Some are modified and implemented, some are modified and at last deleted from the list without implementation, and some are deleted after adding without any modifications. These features of the data help to unveil many minor details in activity planning and scheduling process. As mentioned in Chapter 4, the episode attributes of the first-time-added episodes are assumed to correspond to the activity planning/generation stage. So the activity episodes that are added first are used in this analysis. As shown in Figure 4.2 of Chapter 4, CHASE divides activities into nine generic types: Basic Needs, Work/School, Household Obligations, Drop off/Pick up, Shopping, Service, Recreation, Social and ‘Only for Children’. Within these nine groups, the Night Sleep and Work/School type activities are considered skeleton activities and have been dealt with in Chapter 5. The remaining generic CHASE activity types are used in this investigation except for the Recreation category. Considering the basic difference between At-home and Out-of-home Recreation we further divide this category into two types: At-home Recreation and Out-of-home Recreation. So the types of activities 104

considered in this chapter are: Household Obligations, Drop off/Pick up, Shopping, Service, At-home Recreation, Out-of-home Recreation and Social activities. Basic Needs include at home meals and sleeping which are regular and routine type activities. In this chapter we are interested in non-skeletal activity types that are planned as activity-agenda for a specific time period (day or week) and so Basic Needs are not included in this analysis. Although the Basic Needs category includes At-home activities other than Night Sleep which were not accounted for in the skeleton schedule analysis in the previous chapter, these are dealt with in the next chapter in which all non-Night Sleep at home activities are considered as residual activities within a ‘Hicksian composite activity type’. The data set for investigation includes 271 households and 426 individuals. Not all individual and households have all activities of concern during the survey period. So, different activity types have different number of activity episodes and corresponding individuals and households. For the start time selection model we divide the day into five time periods. These time periods are: Early Morning (EM) : After midnight to 7:00 am Morning (M)

: 7:01 am to 10:00 am

Mid-Day (MD)

: 10:01 am to 4:00 pm

Afternoon (AF)

: 4:01 pm to 7:00 pm

Evening (EV)

: After 7:01 pm to midnight

Preliminary investigation of the data shows the observations of different activity types are more or less clustered in terms of similar durations within these segments of the day. Figure 6.3 shows the sample distributions of each activity type. Each individual graph shows the cumulative distribution of observed number of activity episodes against the average duration according to the individual segments of the day. It is clear that the Household Obligation activities are more or less distributed across the day after early morning. The Drop off/Pick up activities are concentrated after early morning and before evening. Shopping, Service and Out-of-home Recreation activities are concentrated in the 105

mid-day. At-home Recreation activities are concentrated in the evening and the Social activities are more or less distributed after mid-day. In terms of duration Household Obligation, Service and At-home Recreation activities are of similar durations throughout the day with the average duration of 138, 131 and 163 minutes respectively. Early morning Drop off/Pick up activities are shorter in duration. Morning and mid-day Shopping activities are longer in duration. Longer duration Out-of-home activities are after morning and longer duration Social activities are after early morning.

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Figure 6. 3 Observed Duration Distribution According to Time of Day

In terms of covariates different socio-economic variables regarding the person and 107

his/her corresponding household and the activity specific attributes are considered. The activity specific attributes mainly include •

Travel time in minutes

•

Mode of travel to the activity location (dummy variable for auto, transit and other modes)

•

Weekly frequency of the activity,

•

Number of potential locations for the activity,

•

Dummy variable representing flexibility (1 for flexible and 0 otherwise) of the duration of activity,

•

Continuous start time (as a fraction of 24 hours of the day)

•

Number of children involved in the activity.

The socio-economic attributes include •

Age in years

•

Sex (dummy variable: 1 for Male, 0 otherwise)

•

Marital status (dummy variable: single, married and adult child)

•

Job type (dummy variable: at home job, out-of-home job, retired or unemployed, full time job and part time job)

•

Driving license (dummy variable: 1 for having driving license and 0 otherwise)

•

Household size

•

Household children (number)

•

Household automobile (number).

To guarantee the non-negativity of duration predictions, the logarithm of duration is used for the duration models.

6.5 Estimation Results of the Models This section discusses the details of the estimated individual models. For the first 108

causal relationship, the points of concern are to identify the influences of start time selection on the duration determinations. So, the duration models containing start time selection corrections are reported only. For the second causal relationship, the points of concern are to identify the effects of duration on the start time selections. So, the start time selection model is reported only. Since the two causal relations give two different types of models, the comparison of goodness of fit measures is not relevant. Rather, the assumed causal structures are evaluated in terms of statistical significance of the error correlation correction components. The relationship between two decisions regarding each activity type (start time selection and duration determination) is investigated by identifying four distinct relationships: 1. The duration is conditional upon the start time selection 2. The start time selection is conditional upon the duration determination 3. Both start time and duration of the activity are independent of each other or very loosely connected 4.

Both start time and duration of the activity are simultaneously decided. In the duration model for a particular part of the day, the error correlation

correction for start time selection enters corresponding to all parts of the day. The significance of the error correction between the same start time category and the corresponding duration indicates the extent to which duration is conditional on start time. The significances of the correction for the correlation between duration and choosing other start time categories also indicate the trade-offs between start time and duration selection processes and unveil important behavioural elements. However, for simplicity of discussion and concerning the main objective of this chapter, only the endogeneity correction of the corresponding time of day selection is shown in the tables. On the other hand, the significance of the control variable in the start time selection model indicates that the duration is endogenous to the start time selection process and hence we can infer that duration comes before the start time selection in 109

activity planning. For a particular time period, the significance of the error correlation correction in the duration model as well as the control variable in the start time selection model indicates the simultaneous decision for start time and duration. Similarly, for a particular time period the insignificance of both the error correlation correction in duration model as well as the control variable in the start time selection model indicates that the start time and duration are loosely related or simultaneously decided. In addition to discussing the start time and duration relationships of the concerned activity types, the effects of different covariates on duration and start time selection are also discussed. However, as the main concern of this chapter is to identify the relationships between the decisions regarding start time selection and duration determination of the specific activity types, the investigations of the covariate effects are restricted to the explanation of the effects only without additional efforts to investigate the probable reasons of the specific effects. Since the sign of the covariates and especially the error correction components are not always known a priori, the two-tailed ‘t’ test is used to measure the statistical significance of the parameters. The standard criterion for a 95 percent confidence interval of for the two-tailed ‘t’ value is 1.96. Although some of the variables in the models reported in this chapter are not significant by this criterion, they provide significant insight into the behavioural process and so are retained for the purpose of discussion. The following sub-sections discuss the models for the individual activity types under consideration.

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Table 6. 1 Activity Type: Household Obligations Variable Name EM M Coeff (t) Coeff (t) Log-Linear Duration Model: Start time →Duration Start Time -2.09(-3.74) 8.02(9.81) Male Household children Frequency Duration Flexibility ∆EM-Dur ∆M-Dur ∆MD-Dur ∆AF-Dur ∆EV-Dur Constant

0.12(0.98) 0.00(0.04) 0.22(4.51) 0.01(0.04) 0.08(0.13)

0.14(1.72) 0.00(0.13) 0.16(5.74) -0.07(-0.84)

Time of Day MD Coeff (t)

AF Coeff (t)

EV Coeff (t)

0.53(1.55)

-2.26(-3.93)

-3.45(-6.64)

0.22(3.16) -0.01(-0.24) 0.10(3.78) -0.03(-0.48)

0.22(4.60) 0.02(0.89) 0.07(3.41) 0.10(1.94)

0.10(1.56) 0.08(3.22) 0.04(1.80) 0.11(1.56)

0.12(0.18) -1.03(-1.19) 3.80(5.15) 1.32(0.36)

0.91(0.49)

1.11(0.81)

5.77(9.23)

Time of Day EM M MD AF Coeff (t) Coeff (t) Coeff (t) Multinomial Logit Start Time Selection Model: Duration → Start Time Travel Time -0.03(-2.10) -0.07(-5.45) -0.01(-3.40) Auto -0.14(-0.61) 0.02(0.13) -2.98(-4.04) Age -0.01(-1.42) 0.00(-0.22) 0.01(1.34) Male 0.31(1.92) -0.43(-4.04) -0.49(-5.01) Single 2.47(3.21) 0.79(2.04) -0.58(-2.14) Married -0.25(-0.99) 1.95(2.58) 0.99(2.68) Driving License -0.12(-0.53) 0.82(4.51) 0.38(2.54) Base Out of home Job -0.02(-0.07) 0.31(1.58) 0.55(2.93) Household Size -0.01(-0.24) 0.04(0.93) 0.27(3.94) Household children 0.11(1.91) 0.02(0.36) -0.29(-3.34) Household Autos -0.02(-0.19) -0.09(-1.16) -0.14(-2.02) Log of Duration 1.44(2.97) 2.35(7.46) 1.82(6.42) ∆duration -2.07(-4.20) -2.26(-7.07) -1.58(-5.47) Constants -9.20(-4.52) -10.89(-8.41) -7.57(-6.64)

0.66(1.25) 7.93(5.20)

Variable Name

EV Coeff (t) -0.01(-1.66) -0.37(-2.41) -0.02(-3.62) -0.22(-2.02) -0.08(-0.27) -0.33(-1.31) 0.18(1.09) -0.17(-0.99) 0.02(0.31) 0.11(1.89) 0.05(0.59) 1.42(4.52) -1.72(-5.40) -4.99(-4.01)

6.5.1 Household Obligation Activities Household Obligation activities include cleaning and maintenance of the household dwelling unit, preparation of meals, attending children and pets, etc. Table 6.1 summarizes two models corresponding to the two causal relationships between start time and duration of Household Obligation activities. The log-linear duration models indicate that the start time selection is endogenous to the duration determination only for the afternoon time period. The start time selection models indicate that duration is

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endogenous to the start time selection process for all parts of the day compared to the afternoon. So, it is clear that for Household Obligation activities duration decision is conditional upon start time selection only for the afternoon but for the rest of the day the duration decision conditions the start time selection process. The negative values of the alternate specific constant of the start time selection models compared to the afternoon indicate people normally prefer afternoon for the Household Obligation type of activities. The effect of actual start time within the time period under consideration indicates that for the morning and mid-day activities the duration is longer for late starts, but the duration is shorter for late starts in the early morning, afternoon and evening activities. Males engage in longer duration activities in the mid-day and afternoon compared to females. A greater number of household children results in longer durations in the evening and afternoon. On the other hand, larger household size increases early morning activities. It is interesting to note that people having a higher weekly frequency of Household Obligation activities are engaged in longer duration activities too. The effects of travel time and the use of automobile to travel in the start time selection model indicates that people normally choose afternoons if they need to travel to perform these activities and also people with out-of-home jobs prefer mid-day and afternoon. Higher number of household automobiles increases the availability of auto to the individual members of the household and increases the selection of the afternoon for Household Obligation activities. On the other hand, having a driving license increases the freedom to choose mornings, mid-days and afternoons compared to the other parts of the day. Older people prefer afternoon to evening for these types of activities. Single heads or married couples prefer early morning and morning for this type of activities compared to the adult childs at home.

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Table 6. 2 Activity Type: Drop off / Pick Up Variable Name EM M Coeff (t) Coeff (t) Log-Linear Duration Model: Start time →Duration Start Time 1.74(0.97) 0.54(0.32) Male -0.29(-1.30) 0.10(0.89) Household children 0.10(0.41) -0.04(-0.60) Frequency -0.04(-0.54) 0.07(1.80) Duration Flexibility 2.04(4.98) 0.60(4.12) ∆EM-Dur 2.03(2.39) ∆M-Dur 2.88(3.59) ∆MD-Dur ∆AF-Dur ∆EV-Dur Constant 14.27(3.14) 5.63(3.20)

Time of Day MD AF Coeff (t) Coeff (t)

EV Coeff (t)

-0.63(-1.09) 0.07(0.67) -0.15(-2.83) 0.16(4.40) 0.34(2.15)

-2.17(-1.53) -0.30(-1.69) -0.10(-1.24) -0.05(-0.77) 0.31(1.14)

-0.03(-0.02) -0.06(-0.60) 0.02(0.31) 0.08(1.85) 0.47(3.31)

0.70(1.07) 0.83(1.02) 5.95(6.35)

3.62(2.48)

Time of Day EM M MD AF Coeff (t) Coeff (t) Coeff (t) Multinomial Logit Start Time Selection Model: Duration → Start Time Travel Time -0.12(4.8) -0.04(4.97) -0.02(3.03) Auto 0.67(1.34) -0.40(2.0) -0.50(2.75) Age -0.03(1.8) -0.01(0.7) 0.001(0.19) Male -0.31(1.89) -0.70(2.01) -0.45(2.91) Single 1.08(1.06) 0.001(0.00) 1.57(2.33) Married 0.61(0.61) -0.22(0.51) 1.49(2.31) Driving License 0.37(0.57) -0.02(0.04) 17.67(5.61) Base Out of home Job 1.51(1.32) -0.16(0.62) 0.10(0.42) Household Size 0.24(1.14) 0.32(2.94) 0.39(3.94) Household children -0.19(1.61) -0.19(1.8) -1.09(4.11) Household Autos -0.23(0.77) 0.21(1.38) 0.06(0.44) Log of Duration -0.62(1.43) -0.01(0.03) -3.76(3.82) 0.19(0.43) 0.16(0.4) ∆duration 2.67(2.75) Constants -9.70(0.001) -0.22(0.14) -0.16(0.12)

2.03(1.99) 2.62(0.83)

Variable Name

EV Coeff (t) -0.01(1.5) 0.66(2.42) 0.001(0.26) -0.33(1.72) -0.90(1.79) -1.06(2.25) 1.01(1.4) 0.05(0.15) 0.40(3.34) -0.30(2.38) -0.17(0.97) 0.62(1.28) -0.50(1.02) -3.45(2.1)

6.5.2 Drop off / Pick up Type Activities Drop off/Pick up activities include chauffeuring household members or others, buying foods/snacks/drink etc. on the way to somewhere else, picking up or dropping off dry cleaning, video rentals, mail, etc. Table 6.2 summarizes two models corresponding to the two causal relationships between start time and duration for Drop off/Pick up activities. The log-linear duration models for each part of the day indicate that start time selection is endogenous to the duration determination for early morning, morning and evening activities. The start time selection models indicate that duration is endogenous to 113

the start time selection only for early morning activities. The significance of both start time selection effect on the duration and the endogeneity of the duration to start time selection indicate that both start time and duration are endogenous to each other for this time of day. So, it can be inferred that for Drop off/Pick up type activities the duration decision is conditional upon the start time selection for morning and evening activities only. For early morning the start time and duration decisions are simultaneous but for the rest of the day the duration and start time decisions are independent of each other or loosely connected. The negative values of the alternate specific constant of the start time selection models compared to the afternoon indicate people normally prefer afternoon for the Drop off/Pick up activities. The duration models for each time period also indicate the duration of Drop off/Pick up type activities are not influenced by the actual start time within the period (all parameters are statistically insignificant). The start time selection model shows that episode duration does not affect the start time selection except in early morning. Higher weekly frequency influences longer mid-day episodes but higher numbers of household children result in shorter mid-day episodes. It is interesting to note that the duration flexibility of the activity influences decisions for longer duration episodes. Longer travel time requirement for the activity influences to choose afternoon compared to other parts of the day. Auto users prefer afternoon and evening compared to the other parts of the day. However, the early morning is preferable to the all other parts of the day if the person has a driving license. Single heads or married couples prefer morning to the other parts of the day. Larger household size influences to choose morning, mid-day and evening. Higher number of household children reduces the probability of choosing early morning.

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Table 6. 3 Activity Type: Shopping Variable Name

Time of Day M MD AF Coeff (t) Coeff (t) Coeff (t) Log-Linear Duration Model: Start time →Duration Start Time -0.60(-1.11) -1.71(-1.13) 13.15(3.60) Male 0.25(0.97) -0.03(-0.25) -0.19(-2.51) Children Involved -0.09(-0.72) 0.52(2.14) 0.24(3.37) Frequency 0.04(0.44) -0.03(-0.99) -0.01(-0.26) Available Locations -0.04(-0.40) -0.05(-2.65) -0.05(-2.01) Duration Flexibility 0.16(0.71) -0.08(-0.63) 0.28(3.75) Out of home Job -1.50(-1.27) -0.51(-1.34) -0.59(-0.84) 1.70(1.30) ∆M-Dur 0.28(0.12) ∆MD-Dur -1.97(-0.85) ∆AF-Dur ∆EV-Dur Constant -3.06(-0.76) 7.79(1.65) 3.52(4.19)

EV Coeff (t) -1.64(-0.71) 0.08(0.60) -0.15(-1.39) 0.08(1.33) -0.01(-0.21) -0.02(-0.12) 1.11(1.80)

-1.29(-0.96) 3.69(1.11)

Variable Name

Time of Day M MD AF Coeff (t) Coeff (t) Multinomial Logit Start Time Selection Model: Duration → Start Time

EV Coeff (t)

Travel Time

-0.01(1.01)

0.001(0.12)

-0.02(1.62)

Auto Age Male Single Married Driving License Out of home Job Household Size Household children Household Autos Log of Duration ∆duration Constants

0.39(0.9) 0.02(1.21) -0.40(1.35) 17.51(0.01) 17.94(0.01) 17.08(0.01) -1.33(2.86) -0.12(0.63) 0.36(1.77) -0.16(0.59) 0.26(0.33) 0.28(0.36) -36.39(0.001)

0.10(0.49) 0.02(2.23) -0.09(0.59) -0.33(0.83) -0.02(0.06) 0.02(0.05) 0.31(0.82) -0.01(0.09) -0.04(0.41) -0.24(1.78) 0.29(0.7) 0.01(0.03) -0.78(0.47)

0.56(1.72) 0.00(0.1) 0.28(1.24) -0.48(0.87) -0.51(1.03) -0.65(1.16) -0.97(2.24) 0.11(0.84) -0.29(1.83) -0.20(0.98) 1.70(2.78) -1.76(2.82) -5.12(2.11)

Base

6.5.3 Shopping Activity Shopping activities include all types of shopping. Table 6.3 summarizes two models corresponding to two causal relationships between start time and duration of Shopping activities. It is to be noted that no observation was found for early morning, so the part of the day selection options do not include EM. The log-linear duration models of any part of the day do not show any significance of the endogeneity of start time selection as a part of the day. The start time selection models indicate that the duration is 115

endogenous to the start time selection for evening Shopping activities only. So it can be inferred that only for the evening Shopping activities the start time selection is conditional upon the duration decision but for the rest of the day the start time and duration decisions of Shopping activities are independent to each other or loosely connected. The duration models also indicate that people start the longer duration activities in the later part of the morning. Females engage in longer duration activities in the mid-day compared to males. Higher number of household children influences longer duration episode in the morning and mid-day. Higher number of potential Shopping locations influences shorter duration mid-day and afternoon episodes. On the other hand travel time does not show any significant effect on time of day selection for Shopping activity. People prefer evening for the longer duration Shopping episodes. But the people with out-of-home jobs do not prefer morning and evening for Shopping activity. However, the constant term of the start time selection model indicates that people prefer afternoon to evening for Shopping activities in general. It is to be noted that both the duration determination and start time selection models of Shopping activities show a very low number of statistically significant covariates. The evidence also supports that for Shopping activities the start time and duration decisions have insignificant relationships within activity-agenda formation.

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Table 6. 4 Activity Type: Services Variable Name EM M Coeff (t) Coeff (t) Log-Linear Duration Model: Start time →Duration Start Time 0.00(0.00) 4.09(1.04) Male 0.15(0.57) 2.93(7.45) Household 0.00(0.01) -0.14(-1.28) children Frequency -0.42(-1.05) -0.04(-0.34) Duration -1.31(-1.03) 0.58(2.35) Flexibility ∆EM-Dur -3.84(-9.37) -1.81(-1.44) ∆M-Dur ∆MD-Dur ∆AF-Dur ∆EV-Dur Constant 3.67(1.63) 15.84(5.81)

Time of Day MD Coeff (t)

AF Coeff (t)

EV Coeff (t)

-2.09(-2.29) -0.01(-0.06) -0.15(-2.07)

1.75(0.77) -0.23(-0.97) -0.13(-1.38)

-3.21(-1.01) 0.35(0.54) 0.43(1.74)

0.07(1.03) 0.25(1.64)

0.04(0.40) 0.93(4.46)

0.24(1.30) 1.57(3.02)

1.67(1.43) 0.15(0.16) 4.64(5.81)

1.98(0.92)

Time of Day EM M MD AF Coeff (t) Coeff (t) Coeff (t) Multinomial Logit Start Time Selection Model: Duration → Start Time Travel Time 0.001(0.02) -0.15(3.11) 0.02(2.36) Auto 0.36(0.53) -0.22(0.61) -0.51(1.78) Age 0.02(0.79) 0.02(1.63) 0.04(3.36) Male 2.22(3.5) 0.24(0.77) 0.22(0.86) Single 19.94(0.001) 0.09(0.12) -0.61(1.17) Married 19.11(0.001) 0.66(0.96) -0.35(0.73) Driving License -0.98(1.05) 0.40(0.6) 0.61(1.09) Base Out of home Job 17.06(0.001) -0.13(0.17) -1.38(2.36) Household Size 0.16(0.54) -0.22(1.4) -0.16(1.29) Household -0.03(0.08) 0.21(1.1) -0.03(0.17) children Household Autos -0.90(1.68) -0.54(2.14) -0.47(2.43) Log of Duration 1.57(3.23) 2.28(2.4) 0.97(2.54) -1.61(1.6) -0.65(1.63) ∆duration -1.12(2.21) Constants -45.67(0.001) -1.97(1.13) -6.69(2.94)

1.60(1.32) 4.18(0.95)

Variable Name

EV Coeff (t) -0.03(2.09) -0.16(0.41) 0.02(0.9) 1.24(3.42) -0.23(0.35) -0.92(1.4) 0.24(0.31) -0.30(0.32) -0.09(0.52) 0.04(0.17) -0.59(2.09) 0.001(0.001) 0.34(0.62) 0.30(0.13)

6.5.4 Service Type Activity Service activities include banking activities, barber/saloon/beautification, servicing vehicles, religious services, doctor’s appointment, medical services etc. Table 6.4 summarizes two models corresponding to two causal relationships between start time and duration of Service activities. The log-linear duration models for each part of the day show that the start time selection is endogenous to the duration determination for early 117

morning activities only. The start time selection models indicate that only the morning activity durations are endogenous to the start time selections. So, it can be inferred that for the early morning Service type activities the duration decision is conditional upon the start time selection and for the morning activities the start time selection is conditional upon the duration decision. For the rest of the day the start time selection and duration decisions are independent of each other or loosely connected. Other than the start time and duration relationship, males undertake in longer duration Service type activities in the early morning compared to females. Higher number of household children reduces the duration of mid-day Service type activities. Higher flexibility in the duration of Service activities encourages longer duration morning, afternoon and evening episodes. Older people prefer mid-day to any other parts of the day. Longer travel time requirements reduce the probability of choosing early morning and evening and increase the probability of choosing morning. People with an out-ofhome job have lower probability of choosing mid-day. Higher number of household automobiles influences to choose afternoon for the Service activities.

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Table 6. 5 Activity Type: At-Home Recreation Variable Name EM M Coeff (t) Coeff (t) Log-Linear Duration Model: Start time →Duration Start Time -3.53(-7.69) -7.95(-10.43) Age -0.01(-0.64) 0.01(0.91) Male -0.03(-0.17) 0.49(5.24) Household Size 0.14(0.67) -0.26(-1.05) Frequency 0.00(-0.08) 0.13(2.50) Duration -0.34(-2.19) -0.05(-0.58) Flexibility Out of home -0.03(-0.04) -1.42(-1.31) Job Income 0.0001(0.36) 0.0001(-2.03) -0.53(-0.33) ∆EM-Dur 2.76(1.16) ∆M-Dur ∆MD-Dur ∆AF-Dur ∆EV-Dur Constant 4.04(0.57) 7.91(2.40)

Time of Day MD Coeff (t)

AF Coeff (t)

EV Coeff (t)

-3.83(-13.96) 0.00(-0.01) -0.13(-1.78) 0.16(1.52) 0.03(1.66) -0.08(-1.21)

-9.45(-34.70) 0.01(1.67) 0.08(1.39) 0.09(1.29) -0.01(-0.45) -0.04(-0.85)

-5.36(-33.48) 0.01(5.05) 0.01(0.24) 0.02(0.45) 0.01(0.58) 0.08(2.74)

0.47(1.00)

0.38(1.20)

-0.17(-0.72)

0.0001(1.05)

0.0001(-2.47)

0.0001(2.07)

1.03(1.06) 1.44(1.75) -1.65(-0.28)

14.27(5.05)

Time of Day EM M MD AF Coeff (t) Coeff (t) Coeff (t) Coeff (t) Multinomial Logit Start Time Selection Model: Duration → Start Time Age 0.01(1.84) 0.01(2.33) 0.02(3.28) Male -0.02(0.13) -0.08(0.63) 0.60(2.97) Single -0.52(1.41) 0.13(0.29) 0.24(0.8) Married 0.10(0.24) 0.19(0.67) -1.33(3.76) Driving License 0.16(0.73) 0.24(1.46) 0.56(2.39) Out of Home Job -0.53(1.59) 0.08(0.27) -1.06(3.87) Base Household Size -0.04(0.65) -0.12(1.97) 0.09(2.17) Household -0.07(0.19) 0.05(0.11) 0.27(0.88) children Household Autos -0.33(2.9) -0.02(0.2) -0.20(2.52) Log of Duration 0.40(0.33) -0.96(0.89) 1.65(2.0) -0.88(0.72) 0.04(0.04) ∆duration -1.72(2.08) Constants -2.40(0.46) 3.37(0.74) -7.84(2.24)

3.01(1.89) 10.05(12.91)

Variable Name

EV

-0.01(2.17) -0.53(4.9) 0.48(2.09) 0.28(1.31) 0.50(3.7) -0.08(0.38) 0.02(0.51) -0.05(0.21) -0.15(2.38) 7.17(10.74) -7.01(10.51) -29.18(10.3)

6.5.5 At-Home Recreation Type Activity At-home Recreation activities include all types of entertainment and recreational activities at home and that do not require to travel. Table 6.5 summarizes two models corresponding to two causal relationships between start time and duration of At-home Recreation activities. The log-linear duration models for each part of the day show that

119

start time selection is not endogenous to the duration determination of the At-home Recreational activities. The start time selection models indicate that duration is endogenous to the start time selection process for mid-day and evening. So, it can be inferred that for At-home Recreational activities the start time selection is conditional on duration only for mid-day and evening activities. But for the rest of the day these two decisions are independent on each other or loosely connected. Other than the start time and duration relationship, for each part of the day it is seen that people engage in longer duration activities if they start earlier in that part of the day. It is clear that the evening episodes are longer in duration for older people but older people prefer the other parts of the day to the evening. Males involve in longer duration morning episodes but they prefer early morning compared to other parts of the day. Higher number of household size influences choosing mid-day for At-home Recreational activities. Higher weekly frequency influences longer duration early morning episodes. Higher duration flexibility and higher income influences longer duration evening episodes. Higher number of household automobile influences to choose mid-day but having a driving license influences to choose early morning and evening for At-home Recreational activities. The longer the duration of the activity, the higher the probability of selecting mid-day and evening for At-home Recreational activities.

120

Table 6. 6 Activity Type: Out-of-Home Recreation Variable Name EM M Coeff (t) Coeff (t) Log-Linear Duration Model: Start time →Duration Start Time 0.56(1.25) 1.61(0.61) Age 0.01(0.47) -0.21(-3.37) Male -0.51(-0.48) 5.88(4.82) Household Size 0.21(1.32) 0.59(3.34) Frequency -0.06(-1.28) 0.33(4.12) Available Locations 0.02(1.03) -0.08(-1.90) Duration Flexibility 0.09(0.96) 0.34(1.80) Out of home Job -0.07(-0.13) -3.56(-4.32) Income 0.00(1.83) 0.00(0.84) ∆EM-Dur 5.29(2.69) 1.32(1.15) ∆M-Dur ∆MD-Dur ∆AF-Dur ∆EV-Dur Constant 8.04(1.61) 15.75(5.19)

Time of Day MD Coeff (t)

AF Coeff (t)

EV Coeff (t)

-0.09(-0.10) 0.04(2.83) -1.92(-2.49) -0.19(-1.98) 0.10(2.34) -0.04(-1.31) 0.17(1.30) 0.23(0.57) 0.00(-0.60)

-2.0 (-1.11) -0.02(-1.26) 1.27(1.35) 0.28(2.36) 0.24(5.15) -0.04(-1.67) 0.04(0.28) -1.18(-2.22) 0.00(-1.17)

-1.11(-0.57) 0.02(1.02) 0.08(0.10) -0.08(-0.73) 0.08(1.13) 0.01(0.32) 0.23(1.36) 1.43(2.61) 0.00(-1.71)

-3.44(-1.77) -0.31(-0.11) 13.76(3.72)

9.17(2.22)

Time of Day EM M MD AF Coeff (t) Coeff (t) Coeff (t) Multinomial Logit Start Time Selection Model: Duration → Start Time Travel Time -0.03(1.85) 0.0003(0.09) -0.02(2.36) Auto 0.38(1.33) -0.03(0.14) 3.03(3.68) Age 0.02(1.67) -0.01(0.77) -0.06(3.2) Male -0.56(1.36) -0.12(0.43) 0.35(1.63) Single 0.59(0.57) -0.38(0.65) -0.42(0.86) Married 1.49(1.65) -0.65(1.28) -0.46(1.08) Driving License 1.08(1.8) 0.12(0.33) 17.18(5.06) Base Out of home Job -0.37(0.58) -0.02(0.04) -1.62(2.22) Household Size 0.19(1.52) -0.20(1.57) -0.92(2.44) Household children 0.43(1.11) 0.28(1.93) -0.35(2.11) Household Autos 0.33(1.08) -0.09(0.49) 0.14(0.94) Log of Duration -0.99(1.33) 0.24(0.54) 0.86(2.31) ∆duration 0.58(0.79) -0.66(1.43) -1.10(2.85) Constants -11.54(0.01) -2.59(1.21) -2.74(1.53)

-0.33(-0.15) -3.17(-0.90)

Variable Name

EV Coeff (t) 0.0034(1.25) 0.15(0.55) 0.0001(0.01) -0.13(0.53) -0.43(0.84) -0.65(1.44) 0.29(0.67) -0.20(0.31) -0.15(1.1) -0.37(2.05) 0.22(1.36) 0.07(0.16) -0.31(0.71) 0.18(0.09)

6.5.6 Out-of-Home Recreation Type Activity Out-of-home recreation type activities include all types of entertainment and recreational activities outside home that requires travel. Table 6.6 summarizes two models corresponding to two causal relationships between start time and duration of Outof-home Recreation type activities. The log-linear duration models for each part of the 121

day show that the start time selection is endogenous to the duration determination for early morning activities only. The start time selection models indicate that duration determination is endogenous to the start time selection only for mid-day. So, for Out-ofhome Recreational activities, the duration is conditional upon the start time selection for the mid-day activities and the start time is conditional upon the duration determination for early morning activities. For the rest of the day, the duration determination and start time selection decisions are independent of each other or loosely connected. Other than the start time and duration relationship, longer travel time discourages starting Out-of-home Recreational activities before mid-day, but people with a driving license and using automobile prefer early morning to start. Older people do not prefer early morning and have shorter early morning episodes but longer mid-day episodes. Males prefer longer duration early morning and shorter duration mid-day activities compared to females. Larger household size influences longer duration early morning and afternoon activities but shorter duration mid-day activities. People with out-of-home job prefer longer duration evening episodes, shorter duration afternoon episodes but to start the activity they prefer afternoon compared to early morning. Higher weekly frequency influences longer duration morning, mid-day and afternoon Out-of-home Recreation activities.

122

Table 6. 7 Activity Type: Social Variable Name EM M Coeff (t) Coeff (t) Log-Linear Duration Model: Start time →Duration Start Time -0.80(-0.39) -0.44(-0.12) Male 0.72(1.92) -0.60(-1.91) Children Involved 0.11(0.41) 0.09(0.57) Frequency -1.27(-2.37) 0.76(2.54) Available Locations 0.06(1.43) 0.02(0.52) Duration Flexibility 0.60(1.67) -0.15(-0.67) -0.12(-0.16) ∆EM-Dur ∆M-Dur 1.89(2.96) ∆MD-Dur ∆AF-Dur ∆EV-Dur Constant -1.46(-0.34) 7.56(3.35)

Variable Name

Time of Day MD Coeff (t) 0.63(0.96) 0.20(1.39) 0.18(2.55) 0.52(3.13) 0.04(2.36) -0.08(-0.72)

AF Coeff (t)

EV Coeff (t)

2.33(1.88) 0.42(3.38) 0.11(1.92) 0.44(2.99) 0.06(3.50) -0.17(-1.68)

-4.30(-5.13) 0.01(0.05) -0.13(-1.74) -0.04(-0.28) 0.06(3.91) -0.06(-0.58)

1.27(0.96) 0.50(0.47) 5.54(5.66)

2.44(1.05)

EM M MD AF Coeff (t) Coeff (t) Coeff (t) Multinomial Logit Start Time Selection Model: Duration → Start Time Travel Time -0.001(0.16) 0.004(1.42) -0.10(3.85) Auto -0.53(1.17) 0.30(1.04) 0.16(1.03) Age 0.01(1.55) 0.003(0.56) -0.04(3.47) Male 0.45(1.53) -0.30(1.06) -0.31(1.95) Single 0.70(1.41) 0.24(0.39) -0.11(0.36) Married -0.14(0.32) 0.90(1.63) 0.23(0.87) Driving License 0.24(0.59) -0.15(0.39) 0.09(0.36) Base Out of home Job -0.30(0.58) 0.01(0.03) 0.11(0.44) Household Size -0.02(0.15) -0.02(0.18) 0.35(2.49) Household children 0.02(0.11) 0.06(0.64) -0.50(2.79) Household Autos -0.33(1.64) -0.39(1.89) -0.02(0.14) Log of Duration -0.45(1.89) 1.26(2.79) -0.96(2.37) ∆duration 0.77(1.86) 0.43(1.78) -0.92(2.01) Constants 1.98(1.03) 1.66(1.49) -5.70(2.89)

-0.21(-0.23) 6.69(5.12)

EV Coeff (t) -0.004(1.1) -0.12(0.73) -0.02(3.18) 0.26(1.65) -0.01(0.04) -0.15(0.6) 0.14(0.59) -0.08(0.31) 0.19(2.24) -0.24(2.38) -0.10(0.88) -0.65(2.64) 0.35(1.4) 3.38(2.98)

6.5.7 Social Activity Social activities include visiting, hosting, religious/cultural activities, bar/clubs, planned social events etc. Table 6.7 summarizes two models corresponding to two causal relationships between start time and duration of social activities. The log-linear duration models for each part of the day show that the start time selection is endogenous to the duration determination of morning social activities only. The start time selection models indicate that the duration determination is endogenous to the start time selection for the early morning activities only. So it can be inferred that for early morning Social activities 123

start time selection is conditional upon the duration determination and for morning Social activities the duration determination is conditional upon the start time selection. For the rest of the day the start time selection and duration determination decisions are independent of each other or loosely connected. Other than the start time and duration relationship, males engage in longer duration afternoon social activities compared to females. Involving children in social activities increases the durations of mid-day social activities. Higher number of household children increases the preference for afternoon to start social activities. Afternoon is also preferable for people to start the activity if the travel time is longer and older people prefer afternoon to the other parts of the day relative to younger people. The alternate specific constants in the start time selection model also indicate that people are more likely to be involved in afternoon and evening Social activities than during other parts of the day.

6.5.8 Summary Sub-sections 6.5.1 to 6.5.7 discussed the estimated parameters of the models by activity type. A summary of the relationships between start time selection and duration determination of all activity types corresponding to each part of the day under consideration is presented in Table 6.8. The table presents 7 activity types and 5 parts of a day, so the total number of cells in this table is 35. Each cell of this table represents the corresponding relationship between start time selection and duration determination during the planning stage of activities. Out of the 35 cells a majority of cells (a total of 18 or 51%) contains cases in which start time selection and duration determination is independent to each other during activity planning; 10 cells indicate that duration determination is endogenous of the start time selection during the activity planning; 6 cells represent the relationship that start time selection is endogenous to the duration determination and only 1 cell represents the relationship that both start time and duration are decided simultaneously.

124

Table 6. 8 Summary of Start Time and Duration Relationships Activity Types

Early Morning

Morning

MidDay

Afternoon

Evening

Household Y Y Y X Y Obligations Drop off/Pick-up XY X O O X Shopping O O O O Y Service X Y O O O At-home Recreation O O Y O Y Out-of-home X O Y O O Recreation Social Y X O O O Notation: X
Start Time Selection is Endogenous to the Duration Determination Y
Duration Determination is Endogenous to the Start Time Selection XY
Duration Determination and Start Time Selection are Simultaneous O
Duration Determination and Start Time Selection are Independent

Regarding the question of whether activity sequencing decisions should be a major concern in the activity generation model, the above table presents an answer based on empirical evidence from activity diary survey data (CHASE). It is evident that a strong relationship between start time selection and duration determination at the stage of activity planning (agenda formation) is not well supported. More than 50 percent (18 out of 35) cells in this table show no significant relationship, while a further 28 percent (10 cells) indicates that duration is prior to (conditions) start time. Individually, some activity types show significant relationships, but only for some specific parts of the day. Only the Household Obligation type activities show specific relationships across the day but the relationships are not consistent across the day. The relationship in the afternoon is opposite to those of the other parts of the day. This evidence supports the hypothesis that for the non-skeletal activities the start time and duration relationship is not very important at the stage of activity-agenda formation

6.6 Conclusions This chapter presents the results of a detailed investigation into the relationship between start time and duration of different activities. The activities considered for investigation are non-skeletal type activities: Household Obligations, Drop off/Pick up, Shopping, Services, At-home Recreation, Out-of-home Recreation and Social activities. TAPS Wave 1 CHASE survey data are used in the analysis. The CHASE survey provides 125

details of activity generation-scheduling steps for different types of activities throughout the survey week. The data set used for this chapter represents the planned activity episodes with their attributes: start time, duration etc. The aim is to investigate the relationship between activity episode start time and duration that may exists during the activity planning stage prior to scheduling and thereby obtain insights into how activityagendas are generated. Two causal relationships are hypothesized: start time is conditional upon duration, and, conversely, duration is conditional upon start time. Start time is represented by five discrete time periods within the day: early morning, morning, mid-day, afternoon and evening. The analyses involve sequential estimations for each causal structure under investigation. The first causal structure is modelled as a multinomial sample selection model corresponding to the start times for a log-linear duration model, while the second causal structure is modelled as multinomial logit start time selection model with duration as an endogenous variable. Statistical significance of the correction for sample selection and the control function for the endogenous variables are used to judge the existence of different relationships between the start time and the duration of activities. Among different types of activities considered in this chapter, only Household Obligation activities show the existence of relationships between start time and duration across the day. But the relationship is not consistent across the day. One possible reason may be the activity type itself. Household Obligation activities may be the part of skeletal activities and defined by intra-household task allocation process. However, the incomplete observations at the household level of TAPS Wave 1 survey data restricts us further investigation on this issues. Other than the start time and duration relationship, the individual models give insight into the factors influencing duration or start time individually. However, it is difficult to find a large number of statistically significant variables. This is also an indication of insufficient evidence regarding start time and duration relationship of the non-skeletal activities at the stage of activity-agenda formation. The evidence found in this chapter strongly infers that activity sequencing is more the job of the activity scheduling/rescheduling process than the activity generation process. Based on this hypothesis and supported by the findings of this chapter, the next 126

chapters present models of activity generation of non-skeletal activities, with emphasis on modelling frequency / time allocation to individual activities without determining start times. That is, the sequencing of activity episodes within the time gaps of skeletal activities is not taken into consideration.

127

CHAPTER 07: MODELLING ACTIVITY-AGENDA FORMATION 7.1 Introduction This chapter presents an econometric modelling framework for activity-agenda formation. The activity-agenda here means the collection of different types of activities that are to be scheduled within the time gap of the skeleton agenda as modelled in Chapter 5. The proposed framework uses the concept of activity utility. As described in Chapter 3, activity utility is divided into two parts: Goal and Process utility. The concept of Goal utility is used to model the frequency of individual activity types within the time budget constraint. The specification of the model ensures the scope for unplanned (or not defined a priori) activities through the assumption of a composite activity. Thus, it can accommodate two types of time trade-offs: between the composite activity and all specific activities and among the specific activities. The Kuhn-Tucker optimality condition is used to ensure that a finite probability exists for any given activity to have a zero frequency within a given planning period. The individual activity-specific utility is assumed to haves two components: baseline utility and additional utility. The adoption of a logarithmic function for additional utility ensures that a satiation effect occurs with increasing frequency. Heterogeneity in activity behaviour is also considered by incorporating error correlation in the baseline utility. The proposed model assumes that people optimize the total utility of the activities in the selection of an activity-agenda, but this optimality is not deterministic. Rather it is a stochastic optimality with endogenous and unobserved random variables within the objective function. The model is tested using TAPS Wave 1 CHASE survey data considering a week-long agenda formation time frame. The chapter is organized as follows: the next section describes the concept of activity utility in agenda modelling followed by sections describing the econometric specification of agenda formation, the estimation procedure of the large scale demand system necessary for agenda modelling, the description of data used for empirical estimation of the models and discussion of the estimated models. The chapter ends with some conclusions

7.2 Utility Theory and Large Scale Demand System Modelling 128

The application of utility theory to model activity generation, especially in terms of activity-agenda formation, is a large-scale demand system modelling problem. In terms of microeconomic theory the activities in the activity-agenda represent numerous qualitydifferentiated goods to be chosen given a time budget and other constraints. Examples of empirical application of large-scale demand system models are rare in the activity-based travel demand modelling literature. Kraan (1997) uses a utility-based approach for modelling time and money allocation. But the econometric formulation in this paper does not address the issues of non-participation in specific activities, undecided activities within time budget, etc. Kockelman (1998, 2001) presents a utility-based large-scale activity generation model. Her approach is a system of demand equations for a number of activity/trips under consideration. She used a modified translog cost function as the specification of indirect utility of the activities; given time and income constraints. The assumption of multivariate Poisson distribution with Gamma heterogeneity is used to derive the system of demand equations using Roy’s identity for each individual activity type. Ettema (2005) develops a similar system of demand equations for activity demand generation. He used the Seemingly Unrelated Regression Equation (SURE) technique to model the demand of a number of activities modelled individually using the Nested Tobit approach proposed by Melony et al. (2004). Their econometric approach of using an activity utility concept as proposed by Kitamura et al. (1996) is more of a statistical stitching of individual univariate elements rather than a robust and comprehensive model of time allocation to different activity types. Although these techniques are promising, they do not necessarily ensure corner solutions that are key characteristics of activity-travel behaviour (i.e. not all activities to be engaged in during a given planning period). Bhat (2005) extended the model proposed by Kim et al. (2002) to develop the multiple discrete-continuous extreme value model (MDCEV) and uses the Kuhn-Tucker condition to ensure the possibility of corner (zero-frequency) solutions. Bhat (2006) and Bhat et al (2006) further extended the previously proposed MDCEV modelling structure to consider nested decisions and alternatives outside the system of demand. Chen and Mokhtarian (2006) investigate the time allocation trade-offs between maintenance and discretionary activities using an Almost Ideal Demand System (AIDS) model, which does 129

not use the utility maximization approach and hence the concept of activity utility is not clear. On the other hand, modelling large-scale demand systems has received considerable attention in environmental economics. Although the application of KuhnTucker optimality conditions to model the combined extensive (discrete) and intensive (quantity) dimensions of activity choice decisions has recently emerged in the activitybased travel demand literature (Bhat, 2005, 2006), this method was applied decades ago (Wales and Woodland, 1983) in environment and resource economics. But estimation difficulties have restricted the widespread use of such models in practical applications (von Haefen et al., 2004). Recently considerable advancement has been achieved in terms of developing specifications that give closed form likelihood structures and application of simulation techniques for complex specifications (von Haefen and Phaneuf, 2004). von Haefen et al. (2004) and von Haefen and Phaneuf (2004) propose a utility structure that utilizes the Kuhn-Tucker optimality condition to ensure corner solutions and at the same time gives a closed form likelihood function. The important feature of this specification with respect to applicability of modelling agenda is that it allows consideration of an unplanned composite activity (not decided a priori but highly flexible) within the time budget that is very relevant to activity-agenda formation. The specification allows representation of the two stage trade-off in activity behaviour: firstly between all specific activities and composite activity (the slack time within the time budget) and then among different activity types. von Haefen et al.’s (2004) and von Haefen and Phaneuf’s (2004) proposed utility structure remains at the core of the current research efforts. Although the MDCEV model proposed by Bhat appears to have similar features, there is a significant difference between our approach and the modelling approach proposed by Bhat (2006). The major difference is the consideration of left-over time after spending into specific activity types given a specific time budget. This left-over time is defined in our approach as ‘composite activity’ and Bhat (2006) defines it as ‘outside good’. According to Hicks’s theory of composite good this item can be a bundle of similar types of undefined alternatives, (Hicks, 1946). It represents the time left over in the time budget after time spent on the specific alternatives under consideration is 130

accounted for. Given a fixed time budget, if the time spent on specific alternatives under consideration is assumed to be random, the composite item function becomes implicitly random too (deduction of the sum of random variables from a fixed variable is also random). For this reason our modelling approach does not consider any explicit random element in this composite element. Whereas the similar element in MDCEV model specified by Bhat (2006) referred to as the ‘outside good’ contains an explicit random term as well. However, this explicit inclusion of a random term in the outside good imposes certain restrictions on the model estimation process to ensure identification. As per Bhat (2006), the outside good cannot be composed of more than one good. In the MDCEV modelling framework, considering more than one good as a one common outside good (the left over component within the total budget after allocating to the specific goods) requires either explicitly distinguishing each of the outside goods separately and considering only one as the outside good or considering an individual error term with each outside good item. Considering separate error terms for each outside good item would not lead to the same formulations as described in Bhat (2006) because the IID error term assumption would not hold in that case (sum of more than one IID error term would not result in a single IID error term) and the obvious option would be to consider the normal error term assumption and in that case the likelihood function will not be of closed form. Mathematically Bhat’s (2006) formulation is tempting, but the economic interpretation in terms of practical application in demand system modelling that it leads to results in the need to adopt ambiguous or unnecessary assumptions. Thus, the von Haefen approach is adopted in this thesis given the view that it deals with the composite good issue in a more attractive way.

7.3 The Specification of Utility Function of Activity-Agenda The proposed specification divides the total utility of an activity-agenda into two parts: the total utility derived from all activities under consideration and the total utility derived from all other, unmodelled activities called the composite activity (similar to the concept of Hicksian Composite goods). The total time budget for the activity-agenda, T is then divided into the total time for the J activities of concern plus the total time for the composite activity: 131

J

∑t

j

+z = T

(7.1)

j =1

Here tj represents the time allocated to individual activity, j, and z represents the time allocated to the composite activity. We can write the total utility function as: N

U total = ∑ U j + U z

( 7 .2 )

j =1

Here, the Uj indicates the utility derived from jth activity and Uz represents the utility derived from the composite activity. The utility derived from jth activity is then assumed as a multiplicative form of three functions: the baseline utility, κ(); an unknown idiosyncratic error term, ε~ and an additional utility for increasing activity frequency, χ(). The baseline utility refers to the baseline preference for the activity. It is assumed to be a linear in parameter function of socio-economic and activity-specific variables. The exponential functional form can ensure the positivity of this baseline utility. The additional utility for individual activity j defines the quantitative consumption. We define it as a function of the variables that attracts/discourages participation in the specific activities. The logarithmic functional form of this component can ensure the decreasing rate of satisfaction with increasing consumption and incorporation of a constant term (the translating parameter) ensures the possibility of a corner solution in the Kuhn-Tucker optimality condition (i.e. no participation in the activity). So the first component of equation (7.2) becomes:

(

)

U j = κ () ε ~ χ ()

(

= eβ =e

p

X

p

e

eδ ε j

)ln(α()Y + θ )

(( β p X p ) + e δ ε j )

~

j

(βaX j ) a

ln(e

Y j + eθ )

(7.3)

Where, Xp is the vector of variables defining the person’s tastes and preferences

132

βp is the parameter corresponding to Xp δ is the scale parameter Xa is the vector of variables corresponding to the attraction/aversion to activity j

βa is the parameter corresponding to Xa Yj is the frequency of the activity j (the quantitative consumption)

θ is the translating parameter that defines the slope of the indifference curve and ensures the feasibility of corner solutions. On the other hand, the utility derived from the composite activity is simply defined as a function of the total time spent, z, on the composite activity: U z = f (z )

( 7 .4 )

Considering that f(z) is a strictly increasing function with z we use the general form as:

Uz =

1 z (1− exp( ρ )) 1 − exp( ρ)

(7.5)

Where,

ρ is a parameter to be estimated that defines the final shape of the f(z) function and the exponential function is used to ensure the positivity of utility. Now, combining the two parts the total utility we get:

U total =

N

∑U

j

+UZ

j =1

=

N

∑e j =1

(( β p X p ) + e δ ε j )

ln( e

(βaX

a j

Y j + eθ ) +

)

1 z (1 1 - exp( ρ )

exp( ρ ))

( 7 .6 )

133

The above specification ensures several key properties required for a large-scale demand system model. These are described below: This specification ensures the overall utility function of the activity-agenda is a strictly increasing function of each individual activity type and the composite activity enters as additive to the collective sub-function of individual activities. It ensures the scope of modelling the trade-off between planned and unplanned (composite) activities at the first stage. The logarithmic form of the additional utility function accommodates the satiation effect of increasing frequency of any specific activity type. This specification also ensures that if an activity is not chosen (Yj =0) the changes of the corresponding Xa variables do not have any influence on the total utility. This means the derivative of the total utility function with respect to any attractor variable Xa of any particular activity is zero if the corresponding frequency Yj is zero. This property indicates that the addition of any activity type in the choice set of activity-agenda does not have any effect on agenda utility unless that specific activity is chosen. This property allows considering very large choice sets in the demand system. This functional form is a direct utility function with an endogenous idiosyncratic error component that gives rise to an endogenous regime switching type of model under time budget and non-negativity of activity frequency constraints. The functional form is a strictly differentiable, strictly increasing and quasi-concave function that can give 2J combinations of possible activity-agenda sets, where J is the total number of activities in the choice set (2 represents 1 for interior and 1 for corner solution).

7.3.1 Estimation Procedure Considering a specific time budget, the proposed utility maximization model for activity-agenda formation becomes:

134

Maximize: N

U ( X p , X a , ε) = ∑ e

(( β p X p ) + eδ ε j )

ln(e

( βa X ja )

j =1 N

Y j + eθ ) +

1 z (1 exp(ρ)) 1 - exp(ρ)

= ∑ f p ( X p , ε j ). f a ( X j ,Y j , θ ) + f z ( z) a

j =1

Subjected to :

∑d

T j

.Y j + z = T ,

d j indicatesthe average duration of activity j

j

Yj ≥ 0,

T indicatesthe total time budget j =1, 2,............................,N

z ≥0 To ensure the possibility of corner solutions in the activity-agenda we can exploit the Kuhn-Tucker optimality condition in the above mathematical formulation. For this optimization problem the Kuhn-Tucker first order optimality conditions are: (Kuhn and Tucker, 1951, LEMMA 1) ∂U −dj *λ ≤ 0 ∂Y j &

( 7 .7 )

∂U −λ≥0 ∂z

Where

λ is the Lagrange Multiplier. The equality condition of equation (7.7) holds when the Yj is non-zero. Considering the equality for z, the constant λ can be expressed as:

λ=

∂U ∂Z

135

Substituting the value of λ, we get:

∂U ∂U ≤ dj * ∂z ∂Y j

j = 1, 2, 3,.............N

(7.8)

Mathematically, the econometric specifications of the utility function as described in the previous section defines a specific region Ř in the universal choice set of different activity types that contains the error term εj compatible with the observed choice set. If the functional specification of the Utotal can give the non-singular ∂ U / ∂Y j ∂ε j and zero 2

∂ 2U / ∂z∂ε j value, the implicit function theorem tells us that the unknown error term εj should have a functional form of known quantities (Krantz and Park, 1951). This means:

ε j = f j ( X p , β p , δ , X a , β a , Y j , θ , ρ) Being consistent with this we can exploit the first order Kuhn-Tucker condition derived in equation (7.8) to get:

ε j ≤ f j ( X p , β p , δ , X a , β a , Y j , θ , ρ) :

( 7 .9 )

ε j = f j ( X p , β p , δ , X a , β a , Y j , θ , ρ)

if Y j > 0

ε j < f j ( X p , β p , δ , X a , β a , Y j , θ , ρ)

if Y j = 0

Intuitively the above conditions indicate that for positive-frequency activities the marginal utilities are the same across the optimal allocation. Assuming a distributional assumption of εj, we can easily derive the likelihood function for estimating the structural parameters of the proposed model. Putting the exact expressions of the total utility function in equation (7.8) and (7.9), we get:

136

  dj  − exp(( β + β P X P ) + ln  0   exp( β a X a )  1  εj ≤ + ln(exp( β a X a ) * Y j + exp(θ )) , ∀j  exp(δ )      +  − exp( ρ) ln(T − ∑ d jY j )    j   

(

)

(7.10)

Now, let us consider an individual, i with the activity frequencies Yj>0 for j ≤ K and Yj = 0 for j > K (where j= 1, 2, 3… N and K is the total number of non-zero activity frequencies). Using the transformation of variable theorem, the contribution of this person i to the overall likelihood function of the sample is:

l= ∫

f K +1

−∞

fN

...............∫ G ( f1 , f 2 ,....... f K , εK +1 ,.....ε N ) | J | dεK +1 ,.....dε N

(7.11)

−∞

Where, G( . ) indicates a generating function. |J| is the determinant of the Jacobian of transformation from (ε1, ε 2, ε3,…….. ε N) to (Y1, Y2, Y3,…………… YK, εK+1, … ε N). Here the Jacobian, J = ∂ε j / ∂S j , where Sj =YK if j ≤ K otherwise Sj = εK. This gives the Jacobian a partitioned structure whose lower right component is identity and the upper right component is zero. So, the determinant of the Jacobian becomes just the determinant of a K X K matrix of ∂ε j / ∂Y j . Considering that the εj has a normalized type I extreme value (IID) distribution, we get the likelihood function:

(

l (Y | β0 , β a , δ , β p , θ , ρ) = ∏ [exp(− f j (.)) / exp(δ )] j

1Y j > 0

)

| J | exp[− exp(− f j (.))]

Where 137

1Yj>0 is the indicator function for the chosen activity

So, if the total number of individual observations is P in the sample, the total likelihood function becomes

(

)

1   L(Y | β0 , β a , δ , β p , θ , ρ) = ∏  ∏ [exp(− f (.)) / exp(δ )] . | J |. exp[− exp(− f (.))]  P  j  Y j >0

This is a closed form likelihood function. For a fixed parameter model, the structural parameters of the above likelihood function can be estimated by using a numerical gradient-based search method for a fairly large number of activities without any difficulties. Once the structural parameters of the model are estimated the model becomes simply a constrained optimization problem. To obtain the optimum activity-agenda of an individual, the objective function should be integrated over the possible values of unknown error terms (a similar approach is taken by Bhat, 2005). In other words, being consistent with the behavioural assumption that people are not always global optimizers, one can generate a set of random numbers as a candidate vector for the unknown error terms in the model and substitute those values in the objective function to generate a random activity-agenda for that person.

7.3.2 Accommodating Heteroskedascity The major assumption of the above formulation is that the error term, εj, is IID Type-I extreme value distributed across the alternatives and a homogeneous population. However, this assumption is restrictive and can be overcome considering an error correlation procedure. The error term εj can be divided into two components ξj and z’ ζj. The component ξj is IID type-I extreme value distributed across the alternatives. In the component z’ζj, however ζj may have any multivariate distribution, where z’ represents the covariates whose parameter coefficients have this distribution. Several covariates may be assumed to have such random coefficients. Having the random parameters, the likelihood function should be integrated over all possible values of the random components. So the likelihood function becomes a multidimensional integral:

138

L(Y | β0 , β a , δ , β p , θ , ρ)

(

)

1   = ∫ ∫ ∫ .... ∫ ∏  ∏ [exp(− f (.)) / exp(δ )] . | J |. exp[− exp(− f (.))] dζ 1dζ 2 dζ 3 ..dζ n ζ ζ ζ ζ P  j  1

2

3

Y j >0

n

This likelihood function can be estimated using a quasi-Monte Carlo simulation technique to approximate multidimensional integral and maximize the logarithm of the simulated likelihood function across the individual parameters to be estimated (Gourieroux and Monfort, 1996). Halton sequences can be used to draw realization of the random components. Detailed descriptions of the quasi-Monte Carlo method and Halton sequences are available in Train (2002) and Bhat (2003). As discussed in later sections, four socio-economic variables are considered to have random parameters in this chapter. The distributions of the parameters that become part of the error component are assumed to be multivariate normal distributed. Having a large number of alternative activities considered in this study, the off-diagonal elements are restricted to zero so as to reduce the total number of parameters to be estimated using a relatively small data set. This assumption simplifies the estimation procedure but still allows for heteroskedasticity as well as positive correlation in the unobserved determinants of the choice across the alternatives (von Haefen, 2004 and Train, 2002).

7.4 Data for Empirical Estimation TAPS Wave 1 CHASE survey data are used for estimating empirical specifications. Thus, the assumptions concerning the extent to which these data capture activity-agenda formation discussed in Chapter 4 are applicable here. Important points are that all specifications in this chapter consider a 7-day planning period and model the weekly frequency of the activities. This chapter is dedicated to investigating appropriate specifications for agenda formation. The insights developed in this chapter are then used in the next chapters to investigate other issues of the activity generation process: daily versus weekly cycle of agenda formation and appropriateness of activity type classifications. After cleaning for missing information, the total 7-day agenda information for 405 individuals out of 426 was selected for the study. The activity choice set for the activity139

agenda is defined by the set of individual activity types. The generic activity classification is devised to ensure the homogeneity of individual activities within the group. Table 7.1 summarizes the activity classification, the sample average duration and observed frequencies of each activity type. This classification excludes work/school, night sleep and at home basic need activities. These activities, especially work/school and night sleep, generate the skeleton of daily activity schedule and are fundamentally different from other activity types. Again, the work/school activity duration and frequency are often defined by other factors. Hence, the activity-agenda defined by this chapter excludes these two types of activities, and, for time budget calculations, the observed duration of work/school is excluded from the total time budget. In Chapter 5, we consider work and night sleep as part of skeleton activities. However, here we include night sleep and at-home basic need type activities combined as a composite activity. The activity-agenda formation model does not assume any sequencing of the activities under consideration, hence the modelled time allocation to composite activity can be used to provide the necessary input to the skeletal activity generation model.

140

Table 7. 1 The Disaggregate Generic Activity Classification

Activity Group Type Act 01 Act 02 Act 03 Act 04 Act 05 Act 06 Act 07 Act 08 Act 09 Act 10 Act 11 Act 12 Act 13

Act 14

Individual Activity Items

Basic needs like lunch, coffee etc. but not at home Household obligation: cleaning, maintenance, meal preparation, attending kids, attending pets etc. Drop off / Pick up things like: video rental, dry cleaning, postal mails etc. Shopping: major grocery (at least 10 items) Shopping: convenience store, minor grocery (less than 10 items), drug stores etc. Shopping: personal clothing, houseware etc. Services: doctors / medical appointment etc. Services: saloon/barber/beauty, banking, auto servicing etc. Recreation: hobbies, workout, sports, theatre, other outdoor recreational activities Recreation: at home TV program, video, napping, relaxing etc. Social : visiting/hosting, planned social events, bars/special clubs etc. Social: religious and cultural activities Other type of activities that fall as both social as well as recreational type activities ICT use: telephone (more than 10 minutes), internet shopping, browsing etc. Volunteer activities

Average Duration (Minutes)

‘0’ Frequency (%)

Maximum Frequency (Number)

82

43.5

11

107

5.7

20

40

70.4

10

70

52.3

5

43

61.5

7

102

35.1

7

83

76.5

5

76

53.8

7

131

19.8

15

134

1.2

17

206

20.7

10

124

61.7

13

53

60

12

93

44.4

13

7 91.6 The total time budget for the activity-agenda defined in this chapter includes the

Act 15

180

time for these 15 activity types shown in Table 7.1 with night sleep and other at-home basic need type activities. The night sleep and at-home basic need activities are modelled as a composite activity in this model. Litwin (2005) finds that these two activity types undergo most frequent modification in activity planning. The encapsulation of these two 141

activity types within the composite activity type in activity-agenda formation allows us to model this behavioural dimension. People know that they have to participate in these activities. So they keep a rough allocation of time to these basic activities. This approach also provides the slackness in time allocation among other activities of the agenda required by the model. Activities in Table 7.1 are differentiated if the two types are fundamentally different in nature and/or they have very different average durations. For example: Act 04, Act 05 and Act 06 all are shopping activities in general but these are fundamentally different types and average duration of these three types are also significantly different. In the case of Act 07 and Act 08, both are service type activities but Act 07 (doctor’s / medical appointment) is more constrained by the service supplier than the by the person receiving the service. Act 09 and Act 10 are both recreational activities but Act 10 represents strictly at-home activity whereas Act 09 can be both at-home and out-of-home. Act 11 and Act 12 are both in general social activities but they are fundamentally different and their average durations are also significantly different. These 15 activity types are considered to be the choice set for activity-agenda formation. Considering a full week as the planning period the observed weekly activityagenda is the set of these activity types with corresponding frequencies given the average durations. The activity participation rates (frequencies) are identified as the number of times per week a given activity type is planned. Frequencies vary from 0 to any positive number. The 4th column of Table 7.1 presents the percentage of observations with 0 frequencies per week for each activity type. The 5th column of Table 7.1 presents the maximum observed frequency for each activity type. Act 10 has the lowest percentage of 0 frequencies and Act 15 has the highest percentage of 0 frequencies. Act 02 has the highest observed frequency but the percentage of 0 frequencies is higher than that of Act 10. The 405 individuals define the observations for the model estimation process. Each individual is assumed to have the same choice set (15 activity types) for agenda formation. For each individual, the total weekly duration (24 times 7 days) minus his/her total weekly work/school duration is considered to be the time budget for agenda 142

formation. The average duration of any activity for any individual is considered to be the observed weekly average duration of that activity of that particular individual person. Several socio-economic variables are considered in the model specifications. These are individual’s age, gender, total yearly income in Canadian Dollars, indicator of having a driving license, total work/school hours in the week, size of the household of the person and total number of autos in the house. Two activity-specific variables are considered; these are ‘number of possible activity locations’ and ‘travel ratio’. The ‘number of possible locations’ represents the spatial distribution of activity space for the person. This variable is collected during the survey by the EWR (End of Week Review) questions. The variable ‘travel ratio’ is calculated to encapsulate the trip information within activity generation model. The concept of ‘travel ratio’ was used in several studies (Ettema, 2005; Schwanen and Dijst, 2002). Ettema (2005) defines the travel ratio as the ratio of the summation of activity duration and round trip travel time to the activity duration. Thus it refers to the price of activity time in terms of travel time. By definition it is greater than or equal to 1. The longer the travel time to the place of an activity, the greater the value of ‘travel ratio’ exceeds 1 in value. This variable brings trip information inside the model of activity-agenda in a normalized way other than using simple travel times. We calculated ‘travel ratio’ according to Ettema’s definition. The next section discusses the estimated results of several proposed specifications and interpretation of the results.

7.5 Estimation Results of Empirical Models Several specifications of the proposed model were tested. Tables 7.2, 7.3 and 7.4 summarize the result of three selected specifications. Table 7.2 and Table 7.3 consider a homogeneous population, while Table 7.4 introduces heteroskedasticity into the model. For the heteroskedastic model, four variables are finally selected to have random coefficients. A Standard Halton sequence is used to draw random variables. Stable parameter values are achieved after 500 random draws. The choice set for the activity-agenda is defined by 15 generic activity types defined in Table 7.1. As the number of activity types is large, the socio-economic variables in the baseline utility component are considered generic for all activity types. The alternate specific baseline and additional utility are derived by introducing activity 143

specific dummy variables. One can argue for an alternative baseline utility function for each individual activity type. But in this case the number of parameters to be estimated would become excessive. For the same reason the translating parameter, θ, that allows for the possibility of corner solutions is assumed to be the same for all activity types. The logarithmic form of the additional utility function component also helps to avoid separate satiation effects for individual activities. So here the socio-economic variables in the baseline utility function in general indicate the activity participation tendencies and the activity-specific dummy variables indicate relative importance of individual activities in agenda formation. All specifications pass the likelihood ratio test, so to assess goodness of fit we report the pseudo R2 value, which is 1 minus the ratio of the log-likelihood value of the proposed specification and the loglikelihood value of the null model. The null model represents the constants-only model. The Log-likelihood value of null model is 12773.538. The statistical significance of the parameters are considered significant for 95 percent confidence limit for which the‘t’-statistics should be greater than or equal to 1.64. However, the variables with statistically insignificant parameters are also retained in the model because they provide significant insight into behavioural process and we also believe that if a larger data set were available these parameters might show statistical significance. The translating parameter θ gives the reference additional utility for zero frequency activities and the composite activity parameter (ρ) indicates the effects of the time budget in agenda formation. For a coherent preference specification the value of 1exp(ρ) should be less than 1. A lower value of 1-exp(ρ) indicates lower effect of time budget or the composite activity on agenda formation.

144

Table 7. 2 Model with Activity Specific Dummy in Additional Utility Component

The Log-Likelihood Value: -11433.636 The Pseudo R2 Value: 0.105 Parameter -0.125

t-Statistics

Scale Parameter, δ 4.39 Baseline Utility Component: Constant -9.146 -2.07 Age in10 years -0.010 -0.59 Male (Dummy) -0.020 -0.41 Income in 1000 CAD / Year 0.001 2.34 Driving License (Dummy) 0.103 1.12 Household Size -0.012 -0.84 Household Autos ≥ 2 (Dummy) -0.028 -0.60 Total Working Hours -0.0001 -0.05 Number of Possible Activity Locations -0.007 -0.63 Translating Parameter: θ 0.075 0.15 Additional Utility Component: -2.95 -0.416 Travel Ratio 0.040 Dummy Variable for Act 01 0.12 1.013 Dummy Variable for Act 02 7.47 -1.163 Dummy Variable for Act 03 -3.82 -0.396 Dummy Variable for Act 04 -1.22 -0.829 Dummy Variable for Act 05 -2.64 0.300 Dummy Variable for Act 06 0.90 -0.883 Dummy Variable for Act 07 -2.48 -0.578 Dummy Variable for Act 08 -1.77 0.906 Dummy Variable for Act 09 2.77 2.173 Dummy Variable for Act 10 5.47 1.306 Dummy Variable for Act 11 4.20 -0.211 Dummy Variable for Act 12 -0.56 0.272 Dummy Variable for Act 13 0.89 -0.282 Dummy Variable for Act 14 -0.76 -1.133 Dummy Variable for Act 15 -3.06 Composite Activity Parameter: ρ 0.479 1.54 Table 7.2 presents the first specification where the activity-specific dummy variables are placed in the additional utility component with the activity cost indicator variable, ‘travel ratio’. The baseline utility components of the activities are composed of person and household specific socio-economic variables and one activity-specific 145

variable, ‘number of possible activity locations’. However, except for ‘annual income’, the parameters of the other variables in the baseline utility component failed to show statistical significance. But in the additional utility component the main variable, ‘travel ratio’ has a significant parameter, and also in case of the activity specific dummy variables, 9 out of 15 have statistically significant parameters. The pseudo R2 value of this specification is 0.105. Table 7. 3 Model with Activity Specific Dummy Variable in Baseline Utility Component The Log-Likelihood Value: -10515.663 The Pseudo R2 Value: 0.177

Scale Parameter, δ Baseline Utility Component: Constant Age in10 years Male (Dummy) Income in 1000 CAD / Year Driving License (Dummy) Household Size Household Autos ≥ 2 (Dummy) Total Working Hours Dummy Variable for Act 01 Dummy Variable for Act 02 Dummy Variable for Act 03 Dummy Variable for Act 04 Dummy Variable for Act 05 Dummy Variable for Act 06 Dummy Variable for Act 07 Dummy Variable for Act 08 Dummy Variable for Act 09 Dummy Variable for Act 10 Dummy Variable for Act 11 Dummy Variable for Act 12 Dummy Variable for Act 13 Dummy Variable for Act 14 Dummy Variable for Act 15 Translating Parameter: θ Additional Utility Component: Travel Ratio Number of Possible Activity Locations Composite Activity Parameter: ρ

Parameter

t-Statistics

-0.161

-5.07

-11.810 0.003 -0.070 0.001 0.139 -0.025 0.024 -0.002 1.146 2.502 -0.235 0.617 0.142 1.246 0.082 0.426 2.063 3.193 2.332 2.332 1.198 1.039 -0.069 -0.323

-7.45 1.58 -1.42 1.22 1.68 -0.35 0.28 -1.35 3.17 6.53 -0.70 1.61 0.41 3.40 0.21 1.21 5.40 8.35 6.60 2.43 3.68 2.65 -0.15 -2.15

-0.339 -0.011 0.553

-3.67 -0.86 5.26 146

Table 7.3 presents the second specification where the activity-specific dummy variables are introduced into the baseline utility component together with other socioeconomic variables. The additional utility component is composed of two activityspecific variables: ‘travel ratio’ and ‘number of possible activity location’. This specification is better than the previous one as the number of statistically significant parameters is higher. In addition, the pseudo R2 value is 0.177, which is much higher than that of the first specification. The Table 7.4 presents the heteroskedastic model. Other than the random coefficients, this specification is similar to the second specification. Four variables are selected for random coefficients. This specification gives the highest pseudo R2 value among all specifications. Also relative to the other specifications, this specification is better because it considers the random taste variation across the population and correlations in the unobserved determinants of the choice. As all of the three specifications presented in this chapter show the same signs for the corresponding parameters, the following discussion concentrates mainly on the heteroskedastic model. In the heteroskedastic model the random coefficients of the variables ‘age’, the dummy variable representing ‘male’ and the variable ‘household size’ in the baseline utility have mean value lower than the standard deviation. This indicates considerable variations of effects (the effects change from positive to negative values) of these variables across the population. But the other random coefficients of the variable ‘annual income’ have mean value much higher than the standard deviation so the sign of this parameter is the same across the population. This indicates higher income people tend to have larger activity agendas, with smaller time allocated to the composite activity. This finding is consistent with another study conducted on the same study area. Carrasco and Miller (2006) found that the higher income people have comparatively larger activity spaces, having more opportunity to engage in activities.

147

Table 7. 4 Heteroskedastic Model with Activity Specific Dummy in Baseline Utility Component The Log-Likelihood Value: -10332.441 The Pseudo R2 Value: 0.191 Parameter

t-Statistics

-10.061 -0.2685 Scale Parameter, δ Baseline Utility Component: Constant -48.257 -4.54 Age in10 years 0.006 1.28 Standard Deviation of Age Coefficient 0.016 4.28 Male (Dummy) 0.074 0.68 Standard Deviation of Male Coefficient 0.221 1.68 Income in 1000 CAD / Year 0.001 0.71 Standard Deviation of Income Coefficient 0.0001 0.40 Driving License (Dummy) 0.218 1.00 Household Size -0.057 -1.72 Standard Deviation of Household Size 0.149 3.79 Coefficient Household Autos ≥ 2 (Dummy) -0.017 -0.09 Total Working Hours -0.026 -3.88 -10.81 Dummy Variable for Act 01 -1.316 0.80 Dummy Variable for Act 02 0.038 -18.69 Dummy Variable for Act 03 -2.733 -17.50 Dummy Variable for Act 04 -1.856 -18.05 Dummy Variable for Act 05 -2.390 -10.93 Dummy Variable for Act 06 -1.254 -18.45 Dummy Variable for Act 07 -2.343 -16.46 Dummy Variable for Act 08 -2.151 -2.98 Dummy Variable for Act 09 -0.339 6.58 Dummy Variable for Act 10 0.622 -0.71 Dummy Variable for Act 11 -0.082 -12.54 Dummy Variable for Act 12 -1.466 -6.33 Dummy Variable for Act 13 -1.337 -12.37 Dummy Variable for Act 14 -1.452 -13.57 Dummy Variable for Act 15 -2.389 Translating Parameter: θ -0.254 -1.70 Additional Utility Component: Travel Ratio -0.299 -2.73 Number of Possible Activity Locations -0.026 -2.27 Composite Activity Parameter: ρ 1.892 9.53 In this model the variables in the additional utility functional component is a very

interesting element to investigate activity behaviour. The utility-theoretic structure

148

proposed for the modelling of activity-agenda formation is mathematically a primal form of a constrained optimization model. The Kuhn-Tucker optimality condition described in equation 7.8 can be interpreted as the virtual price of any activity (Yj) that is an endogenous function of activity frequency and the composite activity (Yj and z). As indicated by equation 7.8, the relationship of this function with the corresponding duration (dj) provides the conceptual link between the observed activity demand and the structure of preference in activity-agenda formation. The individual decides to consider including any activity in activity-agenda when the virtual price of the activity and the average duration (dj) are equal. On the other hand if the virtual price of the activity is lower than the average duration of the activity, the average duration acts as the reservation price for that activity, duration below which allows the activity to be considered in the activity-agenda. Now, once the activity is considered to be in the activity-agenda the amount of participation, the frequency of that activity (Yj) is influenced by the effects of covariates included in the additional utility function component. In all specifications presented in this chapter, the effect of ‘travel ratio’ is negative, indicating that the activities with higher cost of travel (as percentage of activity duration) will have lower frequency in the activity-agenda. The variable ‘number of possible activity location’ also shows negative effect. It indicates that the higher the number of possible locations the person needs to travel for any activity; the lower the frequency of that activity will be in the activity-agenda. This negative sign also indicates that the activity classification we used in this study is sufficiently disaggregated, for example if we considered all shopping activities as a single activity type, then this sign would be positive indicating that a higher number of locations for shopping for different goods would definitely increase the frequency of shopping activity as a whole. Whereas, when individual shopping types are specified, it is intuitive that for a particular type of shopping activity if the shopping locations are dispersed in space, people tend to lower the frequency of that shopping activity because of the higher travel cost involved. However, general interpretation of this variable must be made with care because the possible number of locations is obtained from the EWR question, not the actual observed number of locations visited by the respondent. 149

The values of 1-exp(ρ) are much lower than 1 in all of the three specifications. The heteroskedastic specification has the lowest value. The better the specification results, the lower the 1-exp(ρ) value. Lower 1-exp(ρ) values indicating that people care less about the composite activity or the slack time while thinking of activity-agenda, which may be true for relatively longer span (weekly) agenda compared to daily agenda. Investigation is necessary to compare daily versus weekly agenda formation processes. In addition, the activity specific dummy variables also have considerable behavioural interpretation. In this case the absolute values and signs of the coefficients do not have any practical significance, but the relative values indicate the corresponding importance of individual activities in agenda formation. Figure 7.1 shows the relative importance of different activity types in agenda formation.

Heteroskedastic Model with Activity Specific Dummy in Baseline Utility Function

01 5 A ct

01 4 A ct

01 3 A ct

01 2 A ct

01 1 A ct

09

01 0 A ct

A ct

08 A ct

07 A ct

06 A ct

05 A ct

04 A ct

03 A ct

02 A ct

A ct

01

Coefficient of Activity Specific Dummy Variables

Homoskedastic Model with Activity Specific Dummy in Additional Utility Function

Activity Type

Figure 7. 1 Relative Importance of Individual Activity Type in Agenda Formation

The individual values of corresponding dummy variable coefficients are different in the two specifications as plotted in Figure 7.1 because the components of the total utility function of the agenda considering the activity specific dummies are different in the two specifications. But interestingly, the shapes of the curves from both specifications 150

are almost same. So we can interpret the relative importance of different activity types in weeklong activity-agenda formation as relative direct utility gain or relative direct satisfaction or relative preference. In this figure it seems that the least preferred activity is Act 03, which is the drop off/pick up good activity. It is intuitive that the drop-off/pick-up goods type of activities may not give direct utility per se, but are necessary support for other activities. Act 15 (volunteer activities) is also seems to have less preference in weekly activity-agenda formation compared to other activities and the reason may be that people do not get direct utility from volunteer activities other than mental satisfaction. The most preferred activity is the Act 10, which is at-home recreation activities. This type of activity does not require travel and people enjoy the process of the activities too. So this type of activity has higher direct utility. Act 02 activities also have higher relative weight. Act 02 is the household obligation activity type; as a social being we place considerable weight on completing household responsibilities. Among the three shopping activities (Act 04, Act 05 and Act 06), personal clothing and other type of shopping (Act 06) gives higher satisfaction relative to the other two shopping types, which is intuitively reasonable. Between the two types of social activities, Act 11 and Act 12, visiting and hosting type (Act 11) social activities show higher satisfaction then religious or cultural activities (Act 12), which is consistent with the findings of other studies (Carrasco, 2006). The relative direct utility from activities involving ICT (Information and Communication Technology), Act 14, shows lower direct utility than direct interactive social activities (Act 11 and Act 12) and recreation activities (Act 09 and Act 10), but online shopping (Act 14) has higher direct utility than major grocery type shopping activity (Act 04).

7.6 Summary and Conclusions This chapter presents a modelling framework for a large-scale activity-travel demand system and the results of empirical estimations of several specifications. The framework is designed to generate demands for non-skeletal activities within a specific time budget. This first level of an activity-travel model is econometric in nature and accommodates different socio-economic and policy variables. The specifications of the models conform to the Random Utility Maximization (RUM) approach with endogenous random error components. Given average durations per activity type, the model can 151

predict the frequency of individual activities in the agenda for a given time period. The framework can be used in another way too: considering the decision to participate in any particular type of activity (i.e., frequency is either 0 or 1) it can be used to predict the time allocation to different activity types under a time budget constraint. Hence, it falls in the general category of multiple discrete-continuous models. The basic specification of the model is designed to handle the trade-offs involved in time allocation among different activity types and to all other undecided activities defined here as a composite activity or Hicksian composite good or slack time, with a specific time budget and non-negativity of activity participation rate constraints. The application of Kuhn-Tucker optimality condition to solve for the structural parameters ensures the possibility of zero frequency for a given activity type (i.e. corner solutions). Thus, this framework allows us to investigate complex inter-activity participation and time-use trade-offs in a very tractable way. Once the structural parameters of the model are estimated, the model becomes a constrained optimization model to derive an agenda under a given time-budget, non-negativity of the frequency constraint, and the given average durations of the individual activity types. Although this is an optimization model it does not lead to global optimization of activity behaviour. Various specifications were tested. The heteroskedastic specification with activity specific dummy variables in the baseline utility component shows better results in terms of goodness of fit of the observed data. This model allows us to investigate different issues in activity-travel behaviour. The model reveals the negative effects of travel time on activity participation rates. The spatial dispersion of the potential locations of a particular activity type also influences the participation decision negatively. Various socio-economic variables are used to define the baseline utility to participate in specific activities as opposed to unplanned composite activity. The model reveals that higher income people have a larger activity set and the effect of income has the same sign across the population. On the other hand, the effects of the variables age, gender and household size may vary from positive to negative across the population. This chapter is dedicated to investigating the applicability of the utility-based large-scale demand system model in activity-agenda formation modelling. The models tested in this chapter consider the modelling span of 1 week, and with given average 152

duration predict the optimum frequencies of specific activity types and time allocation to the composite activity. The specifications of the models are flexible enough to consider shorter modelling spans. The models can also be used to investigate the time allocation to specific activities as well as composite activity, other than just frequency of participation. Based on the insights gained in this chapter, the next chapter investigates day-to-day dynamics in activity-agenda formation considering the day as the modelling span and compares the results of corresponding week-long model.

153

CHAPTER 08: INVESTIGATING THE RHYTHM OF ACTIVITY-AGENDA FORMATION 8.1 Introduction Considering a typical day as the modelling time-span has become a commonplace in activity-travel demand modelling. All operational models are for a typical weekday. A typical day assumption refers to a hypothetical day to overcome the day-specific features of a week. The argument is that this reduces the data requirements for model development and also simplifies computational issues. But our activity-travel behaviour shows significant variability across the week (Kitamura et al 2003; Schlich and Axhausen 2003; Doherty et al 2004). Neglecting these daily variations undermines the basic principle of the paradigm shift to the activity analysis: that travel is a derived demand. The derived demand concept indicates the evolution of activity-travel patterns over time (Doherty 2006). It is also obvious that day-to-day variations are intricately related to within-day variations of activity-travel behaviour. Modelling within-day variations in activity-travel behaviour in a typical day model thus becomes incomplete or adhoc if the day-to-day variations are not addressed properly. But for a multi-day modelling approach the unit of time for agenda formation needs to be verified. Considering a week as the modelling span, what should be the time budget for activity-agenda formation? Is this the whole week or individual days? This is the question of the rhythm of activity-agenda formation and this issue needs careful investigation. This chapter investigates this issue of the rhythm of activity-agenda formation. The previous chapter presents an econometric framework for modelling activity-agenda formation in general but the empirical specification of the models assumes a week-long planning period. This chapter uses the same econometric formulation of activity-agenda formation but considers individual days of the week as the time budget unit of analysis within week-long activity-agenda formation. The generation of non-skeletal activities is the focus of the model. The possibilities of repeated participation or non-participation in some specific activity types across the days and the week are inherent in the models that allow capturing the underlying weekly dynamics in time-use and the activity-travel 154

behaviour. For the explicit consideration of within-day dynamics in time-use behaviour, the worker’s total number of working hours (skeleton activity) is considered as a variable in the models and for the day-to-day dynamics of time-use and activity-travel behaviour, the previous day’s total executed activities are considered as variables in the models. The models exploit the concept of activity utility. The empirical estimation of the models uses the same TAPS Wave 1 CHASE survey data as in the previous chapter. The results of the day-specific agenda formation models are then compared with the corresponding weeklong model developed in the previous chapter. The rest of the chapter is organized as follows: the next section discusses the activity-agenda formation process in brief, followed by the sections discussing data and the interpretations of the estimated models. The chapter concludes with a summary of the key findings.

8.2 Econometric Formulation for Day-Specific Activity-Agenda The econometric specification of the day-specific agenda formation models is: Maximize :

 e (( β X ) + e ε1 ) ln(e ( β X 1 )Y1 + e θ )   (( β p X p ) + e ε2 )  a a ln(e ( β X 2 )Y2 + e θ )  e 1 a   p p a U ( X p , X a , ε ) =  e (( β X ) + e ε3 ) ln(e ( β X 3 )Y3 + e θ )  + z (1 ρ 1 exp( )   ....................................   .......... a p p a e (( β X ) + e ε15 ) ln(e ( β X15 )Y15 + e θ ) p

δ

p

a

a

δ

δ

exp( ρ ))

δ

Subject to :

∑d

T j

.Y j + z = T ,

d j indicates the average duration of activity j

j

T indicates the total time budget for the day Yj ≥ 0 , z ≥0

j = 1, 2, ............................, N ; and Y j is the corresponding frequency z is the time allocation to composite activities

The notation is the same as described in Chapter 7, except now T indicates the time budget for the day rather than the whole week. This specification ensures that the overall utility of the daily activity-agenda is a strictly increasing function of each individual activity type and the composite activity enters as additive to the collective sub155

functions of individual activities. It explicitly models the trade-off between planned and unplanned activities (composite activity) at the first stage of daily activity-agenda formation. This specification also ensures that if an activity is not chosen (i.e. Yj =0) for the day the changes in the corresponding Xa variables do not have any influence on the total utility of the daily activity-agenda. This means that the derivative of the total utility function with respect to any attractor variable Xa of any particular activity is zero if the corresponding frequency Yj is zero. This property indicates that the addition of any activity type in the choice set of activity-agenda does not have any effect on the agenda utility unless that specific activity is chosen. Thus it allows considering very large choice sets in the demand system, which is specifically advantageous for the daily activity-agenda modelling, where we can specify numerous types of activities for consideration.

8.3 Data for Empirical Estimation TAPS Wave 1 CHASE survey data are used to provide observations of daily activity-agenda formation. The generic activity classification as described in Table 7.1 is adopted to ensure homogeneity in terms of basic type and average duration of the activities within the same group. Monday (Day0) is considered as the starting day of the week. Saturday (Day5) and Sunday (Day6) are the weekends. A total of 405 individuals form the data set for model estimation. To give some idea of the composition of weekly activities by day, Figure 8.1 presents the maximum daily frequencies of the activities as observed in the data set. Considerable variations are clear across the week. For Act01 the maximum frequency is the highest at the middle of the week, for Act02 the maximum frequency is the highest for the first day of the week and the last day of the weekends. Act03, Act04 and Act07 show constant maximum frequency across the week. Considerable variations in nonmajor grocery shopping (Act05 and Act06) are also clear in the data. Other than the maximum frequency, the data reveal that people participate in some specific type of activities repeatedly throughout the week whereas lower participation rates are also clear for some activities (serial non-participation). For modelling the daily activity-agenda formation process, the modelling span for each day is considered as 24 hours, the average duration of the activities are considered to 156

be the weekly average values. Each individual is considered to have a choice set consisting of the 15 activity types described in Table 7.1.

Figure 8. 1 Observed Maximum Frequencies of the Activity Types

Several socio-economic variables are also considered as covariates. These are: the individual’s age, gender, total yearly income in Canadian Dollars, an indicator of having a driving license, total work/school hours in the week, size of the person’s household and total number of autos in the household. Two activity-specific variables are considered: the ‘number of possible activity locations’ and ‘travel ratio’. The travel ratio is the ratio of the summation of activity duration and travel time to the activity duration (Ettema, 2005). It refers to the price of activity time in terms of travel time. By definition it is 157

greater than or equal to 1. The longer the travel time required to reach an activity location, the higher the value of the ‘travel ratio’. This variable brings trip information inside the activity-agenda formation model in a normalized way, rather than simply using travel time. This variable makes the model sensitive to transportation system performance. The ‘number of possible locations’ variable represents the spatial distribution of activity spaces for the person. This variable is collected during the survey by the EWR (End of Week Review) questions. This is also a key variable that defines the spatial dispersion of activity places and its influence on activity/travel behaviour. A worker’s total number of daily working hours is considered as a variable for the baseline utility component. This variable accommodates the within-day activity scheduling dynamics because it is well understood that working time acts as a temporal peg around which other activities are scheduled. Considering this variable in the activityagenda formation model makes the model schedule sensitive. Assuming the weekly cycle as the rhythm of life, day-to-day variations and trade-offs are obvious in our activity/travel behaviour. The issues of repeated participation and serial non-participation in specific activities are also clear in the data. In order to accommodate these issues another variable is considered in the model: the previous day’s total number of executed activities. This variable is included in the additional utility component; so that the previous day’s total executed activities will influence the present day’s activity-agenda formation. This variable accommodates day-to-day variations in activity-agenda formation and it also introduces an activity scheduling element inside the activity generation process.

158

Parameters Scale Parameter Baseline Utility Component Constant Age in 10 years Male (Dummy) Income in 1000 CAD / Year Driving License (Dummy) Household Size Household Autos>2 (Dummy) Total Working Hours Activity Specific Dummy ActType01 ActType02 ActType03 ActType04 ActType05 ActType06 ActType07 ActType08 ActType09 ActType10 ActType11 ActType12 ActType13 ActType14 -0.06(2.23)

-0.03(1.22) -13.2(11.19) 0.007(2.52) 0.09(1.3) -3E-4(0.29) 0.13(1.04) -0.04(0.43) 0.08(0.58) -0.04(4.77) 1.07(5.27) 2.49(14.22) -0.18(0.91) 0.51(2.42) -0.06(0.52) 0.86(4.19) -0.19(0.87) 0.26(1.18) 2.22(12.22) 3.02(17.13) 2.34(12.09) 0.93(4.01) 1.20(5.96) 1.31(7.62)

-11.7(10.39) 0.005(2.08) -0.08(1.14) 6E-4(0.68) 0.10(0.80) 0.12(1.35) 0.03(0.21) -0.04(4.31) 1.44(6.97) 2.62(12.06) -0.32(1.29) 0.61(2.87) 0.37(1.69) 1.06(4.83) 0.19(0.87) 0.19(0.87) 2.27(10.34) 3.13(14.26) 2.10(10.01) 1.05(4.66) 1.08(5.13) 1.27(5.80)

1.00(5.42) 2.38(13.03) -0.10(0.54) 0.48(2.52) 0.29(1.79) 1.08(6.34) 0.30(1.37) 0.23(1.29) 1.96(10.96) 2.93(15.93) 2.04(11.53) 1.33(6.91) 1.12(7.87) 1.24(6.70)

-0.03(3.28)

0.34(2.55)

-12.3(10.4) 0.007(2.35) 0.08(1.11) 4E-4(0.44) 0.16(1.28) 0.05(0.52)

Values( |t| )

Values( |t| )

Values( |t| )

Values( |t| ) -0.08(2.79)

1.31(3.67) 2.53(7.07) -0.26(0.72) 0.21(0.53) -0.04(0.12) 1.02(2.77) -0.44(0.92) 0.25(0.62) 2.31(6.50) 3.08(8.44) 2.21(6.08) 1.18(3.16) 1.17(3.13) 1.47(3.99)

-0.04(3.77)

-0.02(0.10)

-12.44(10.7) 0.002(0.83) 0.06(0.92) 12E-3(1.17) 0.23(1.51) 0.08(0.80)

-0.04(1.60)

Thursday

Wednesday

Tuesday

Monday

Table 8. 1 Models for Daily and Weekly Activity-Agenda Formation

1.18(3.15) 2.43(6.68) -0.30(0.80) 0.46(1.13) -0.30(0.82) 0.77(2.01) 0.06(0.14) -0.08(0.43) 2.28(6.28) 2.93(8.08) 2.09(5.74) 1.09(2.85) 0.96(2.71) 1.37(3.78)

-0.03(2.73)

0.18(0.92)

-13.7(11.85) 0.007(2.44) 0.08(1.05) -17E3(1.72) 0.29(1.93) -0.04(0.31)

-0.02(0.66)

Values( |t| )

Friday

1.01(4.51) 2.50(11.54) -0.20(0.79) 0.19(0.72) -0.01(0.17) 0.95(4.24) -0.04(0.12) 0.27(1.25) 2.07(9.34) 2.95(13.82) 2.26(9.69) 1.07(4.31) 1.16(5.32) 1.34(6.17)

-0.02(2.33)

0.23(1.56)

-13.1(10.15) 0.005(1.89) 0.11(1.56) -11E-3(1.05) 0.27(2.24) -0.14(1.48)

-0.04(1.33)

Values( |t| )

Saturday

1.07(5.16) 2.46(13.28) -0.20(0.85) 0.34(1.41) -0.23(0.89) 0.80(3.70) 0.26(0.98) 0.01(0.28) 2.07(11.15) 3.05(17.13) 1.89(7.78) 0.89(3.86) 0.92(4.04) 1.37(7.06)

-0.03(2.60)

0.09(0.63)

-14.1(8.93) 0.003(0.81) -0.11(1.35) 1E-4(0.05) 0.08(0.58) 0.12(0.94)

0.002(0.06)

Values( |t| )

Sunday

1.15(3.17) 2.50(6.53) -0.24(0.70) 0.62(1.61) 0.14(0.41) 1.25(3.40) 0.08(0.21) 0.43(1.21) 2.06(5.40) 3.19(8.35) 2.33(6.60) 2.33(2.43) 1.20(3.68) 1.04(2.65)

0.002(1.35)

0.02(0.28)

159

-11.81(7.45) 0.003(1.58) -0.07(1.42) 8E-4(1.22) 0.14(1.68) -0.02(0.35)

-0.16(5.07)

Values( |t| )

Whole Week

ActType15 Translating Parameter Theta Additional Specific Utility Component Travel Ratio Number of Possible Locations For the Activity Previous Day Number of Executed Activities Composite Good Parameter Rho Pseudo-R square 0.69(10.64) 0.82(10.45) 0.220

0.88(12.98)

-0.02(1.55)

-0.03(1.84)

0.69(8.34) 0.177

-0.01(0.90)

-0.48(7.23)

-0.23(3.01)

0.74(8.17) 0.200

-0.22(1.96)

0.08(0.55)

-0.37(3.95)

-0.41(4.39)

0.37(1.29)

-0.08(0.23)

0.21(0.85)

0.75(8.69) 0.225

0.95(14.91)

-0.01(0.63)

-0.22(2.72)

0.10(0.92)

0.51(1.13)

0.82(10.75) 0.204

0.83(14.86)

0.00(0.44)

-0.20(3.34)

0.14(1.60)

0.33(0.69)

0.79(8.61) 0.217

0.81(13.24)

-0.03(2.59)

-0.33(4.79)

-0.14(1.46)

0.34(0.93)

0.87(8.39) 0.197

0.95(13.13)

-0.01(0.55)

-0.03(0.88)

0.31(4.72)

0.17(0.48)

0.55(5.26) 0.177

-0.01(0.86)

-0.34(3.67)

-0.32(2.15)

-0.07(0.15)

160

8.4 Interpretations and Comparisons of the Models Models are developed for each day of the week, considering Monday as the starting day. The models are presented in Table 8.1. As seen in the previous chapter, the specification with activity-specific dummy variables in the baseline utility component performs better than other possible specifications, so this specification is used for all dayspecific agenda formation models. For comparison of day-specific agenda formation modelling versus week-long agenda formation modelling, Table 8.1 also shows the weeklong agenda formation model of similar specification as developed in the previous chapter. The statistical significance of the parameters are considered significant for 95 percent confidence limit for which the‘t’-statistics should be greater than of equal to 1.64. However, the variables with statistically insignificant parameters are also retained in the model because they provide significant insight into behavioural process and also we believe that if a larger data set were available these parameters might show statistical significance. The goodness of fit of the overall model is measured by the pseudo-R2 value, which is 1 minus the ratio of log-likelihood value of the full model and the loglikelihood value of the null model (constant only model). The pseudo- R2 value closer to 1 represents better fit to the observed data. Individually, the goodness of fit values of the day-specific models are better than for the aggregate weekly model. This is because of the within-day and day-to-day variations in time-use and activity/travel behaviour. The aggregate weekly model suppresses these variations, whereas in the day-specific models these are addressed explicitly. Among the day-specific models, the Monday model, which represents the beginning of the week, gives lower goodness of fit value. This is because this model does not consider the variable ‘previous day’s total executed activities’. The CHASE survey data used in this chapter considered Monday as the beginning of the week and the data collection started on Monday. Hence the data are left censored for Monday per se and we lack the information of previous day’s executed activities. This raises the issues of rhythm of life. Although a multi-week travel diary survey reveals that travel behaviour is neither totally repetitious nor totally variable, (Schilich and Axhausen, 2003) a multi-year 161

panel survey of activity/travel behaviour reveals that at least a week is necessary to investigate the rhythm of life (Roorda and Ruiz 2006). In terms of the components of individual models, the socio-economic variables in the baseline utility components are considered generic because this reduces the number of parameters to be estimated and at the same time is justified in the way that the baseline utility component mainly defines the trade-offs in time allocation to specific activities and the composite activity but the activity specific dummy variables in the baseline utility component introduce the individual activities under consideration explicitly. So, the socio-economic variables in the baseline utility component in general indicate the activity participation tendencies and the activity-specific dummy variables indicate the baseline relative importance of individual activities in activity-agenda formation. The variables in the additional utility component indicate individual activity’s potential/attraction to derive the optimum set of activities. The specification of the models is in general a multiple discrete-continuous model specification, where under a given time budget constraint and the given average duration of the activities, the models determine whether to participate (discrete) in an activity and, if participating, then how many times (continuous) to participate. In such a discretecontinuous specification the scale parameter of the extreme value error plays a key role in linking the discrete and continuous part of the model (Arora et al, 1998) and also the higher the value of the scale parameter (exponential of the parameter), the higher the randomness in activity-agenda formation. According to Table 8.1, the randomness in activity-agenda formation is the highest for Sunday, which is consistent with our expectation that weekend activities are more random per se than weekday activities. Comparing the day-specific models and the weeklong model, the randomness reduces when the planning period is the whole week. Behaviourally this indicates that people become more definitive when thinking in the long term, while randomness/uncertainty increases with the reduction of the planning period (time budget). The constant term in the baseline utility component indicates the reference baseline utility (if all variables in the baseline utility component are considered to be zero). This component is the highest for Sunday compared to the other days of the week. 162

The high reference utility indicates the lack of sufficient information for Sunday compared to the other days. The translating parameter, θ, gives the non-zero reference for the additional utility component and ensures the possibility of zero participation in any activity type. The value of this parameter is the lowest for Monday and increases with the weekdays and again reduces at the end of the week (Sunday). The higher value of this parameter basically indicates the higher possibility of zero participation in some activities but a higher number of total activity participations. The higher value for the days at the middle of the week indicates that we usually participate in a higher number of activities midweek, but these tend to be concentrated in certain activity types, while other activities tend not to be engaged in at all mid-week. It also indicates serial non-participation in some activities during the middle of the week. Whereas, the lower values at the beginning or the end of the week indicate we tend to participate in variety of activities during these days. The ρ parameter indicates the sensitivity of the effect of the composite activity on activity-agenda formation. The value of 1-exp(ρ) is higher for the starting day of the week compared to the other days. It indicates that we are more cautious for allocating time to the composite activity at the beginning of the week, but eventually the time pressure increases and we become less concerned about it. This finding is very important and it also reinforces our argument in favour of multi-day modelling as opposed to typical-day modelling. This finding also ensures that our models comply with the behavioural psychology of time allocation and activity/travel behaviour (Gärling et al. 1999). In terms of the variables in the baseline utility component, age of the person is significant for earlier days of the week, indicating that older people plan for higher numbers of activities than younger people. Males plan for higher numbers of activities in the middle of the week but females plan for higher numbers of activities in the last day of the weekend (Sunday) and the first day of the weekdays (Monday). Income becomes significant for the last day of the weekdays (Friday), with a negative effect. It indicates higher income people plan for lower number of activities on Friday compared to lower 163

income people (the behavioural plausibility of which is unclear). Higher household automobile ownership and possession of driving license levels give people higher modal accessibility and influence them to plan more activities. Intuitively this finding is justified and these variables help to link the activity-agenda formation model with the other components of an integrated model of short-, medium- and long-term household decisions (e.g. an auto ownership model) in a meaningful way. The total working hours of the workers, which is a skeleton activity component, is highly significant in every day-specific model. This variable shows a similar negative effect in every model, except for the whole week model, where the sign is opposite but statistically insignificant. This implies that this variable captures the within-day dynamics in time allocation behaviour. Work is a fundamentally different type of activity. People earn money through work, whereas they usually spend money for participation in other activities. The negative sign of this variable indicates that the work activity acts as a temporal peg, not only in the case of activity scheduling, but also at the activity-agenda formation level. If people spend more time in working, they allocate less time to other activities, rather than reducing time from the composite activity. Whereas in the case of the whole week aggregate model, the interpretation of the positive sign of this variable is that people who plan larger amounts of time for work throughout the week allocate lower amounts of time for composite activities rather than reducing time from the other activities. It also implies that the aggregate weekly model fails to capture the within-day dynamics in time-use and activity planning behaviour. The activity specific dummy variable in the baseline utility component gives significant insight into the behavioural process. In this case the absolute values and signs of the coefficients do not have any practical significance, but the relative values indicate the corresponding importance of individual activities in agenda formation. In other words, these variables can be interpreted as relative direct utility gain or relative direct satisfaction or relative preference. Figure 8.2 shows the plotted values of this variable corresponding to each day.

164

Monday

Tuesday

Wednesday

Thursday

Friday

Saturday

Coefficient of Activity Specific Dummy Variable

Sunday

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

Activity Type

Figure 8. 2 Relative Importance of Individual Activity Types in Day-Specific Agenda Formation

In general the shapes of the curves for the day-specific agenda formation models are similar to that of the weeklong model as discussed in Chapter 7. But the variations of the relative preferences across the week are also clear in the figure. It is interesting to note that Act 11 and Act 12 show same preference in Sunday model and both of these two types are social activities in general. The possible explanation is that people involve in all types of social activities in the weekends and do not differentiate between visiting/hosting type social activities from other social activities compared to the weekdays. Also Act 06, the personal shopping activities receives more preference in Sunday than other days of the week. Such variations indicate the day-to-day variations in activity behaviour. 165

The variables in the additional utility component are key variables and they define the attraction/detraction potential of the activities under consideration. The variable ‘travel ratio’, which can be considered as the time cost of the activity, has a negative effect in all models. Intuitively it is sensible that an activity that involves longer travel time reduces the relative interest in that activity compared to others that involve lower travel time. But it is interesting to note that this variable becomes statistically insignificant for the case of Sunday. The justification is that travel time often becomes an insignificant factor for activity planning in the weekends. The difference between Sunday and Saturday is that Saturday is the beginning of the weekend and it may carry the time pressure developed throughout the week, and as a result, travel time does significantly affect activity planning on Saturdays. The variable ‘number of possible activity location’ also shows a negative effect. It indicates that the higher the number of possible locations the person needs to travel for any activity; the lower the frequency for that activity. Most importantly, this negative sign indicates the activity classification used in this study is sufficiently disaggregated. Also this variable needs cautious interpretation as this is not the observed number of locations, but rather a stated value. The variable indicating the total number of executed activities of each activity type under consideration is highly significant in every day-specific model. This is a key variable that defines the day-to-day dynamics in time-use and activity/travel behaviour. It also introduces the dynamic linkage between activity scheduling and activity-agenda formation. The sign of this variable is positive. It appears that the positive sign captures the repeated participation in specific activities or serial non-participation in certain activities. As indicated in Figure 8.1, the maximum observed frequency of some activities are very high compared to some other activities, and in practical life our all activities are not uniformly distributed throughout the week. Rather we participate in specific activities again and again and do not frequently participate in others.

8.5 Summary and Conclusions This chapter describes a day-specific activity-agenda formation model for a multiday planning period. It compares the results of considering individual days as the cycles 166

of agenda formation rather than the whole week as the rhythm. The models developed in this chapter are specified to capture the within-day dynamics of time-use and activity/travel behaviour by incorporating ‘total working hours’ in the model and day-today dynamics are accommodated considering ‘previous day’s total executed activities’ as variables. These two types of variables also make the activity-agenda formation models sensitive to the activity scheduling process. The incorporation of the variable, ‘travel ratio’ introduces transportation system performance inside the activity-agenda formation model. A number of other socio-economic and activity-specific variables give insight into the behavioural process of time-use and activity/travel behaviour. The models show significant goodness of fit to the observed data. Significant variations in behaviour are obvious throughout the week. The starting (Monday) and ending (Sunday) of the week are distinctly different from the other days in terms of goodness of fit to the observed data, number of statistically significant variables, the effects of travel time in activity/travel planning etc. The models also replicate our repeated participation and serially non-participation in some activities. Compared to the week-long agenda formation model it is clear that considering a whole week as the unit of planning period suppress much of within-day as well as day-to-day dynamics of activity-agenda formation. Thus, in order to capture dynamics of activity behaviour, a multi-day modelling span is appealing, but the day should be the planning unit rather than the week as a whole.

167

CHAPTER 09: INVESTIGATING INTER-ACTIVITY CORRELATION IN TIME ALLOCATION BEHAVIOUR OF ACTIVITY-AGENDA FORMATION 9.1 Introduction Our activity/travel patterns are shaped by our expectations of the outcomes of different activities (Gärling et al., 1999). The perceptions of the outcomes of activities are basically the time-use perceptions within a continuous time domain. Thus activity classification is a question of time allocation to different objectives (Bhat and Koppelman, 1999; Pas, 1998). For these reasons, modelling an individual’s time-use or activity pattern requires addressing the interrelationships among different activity/trip types properly (Meloni et al., 2004). Despite the paradigm shift towards the activitybased travel demand analysis in last two decades, the process of evolving activity patterns and the reasons for changing the patterns over time are still not very clear in the transportation literature (Doherty, 2006). Activity classifications are often made based on common, broad terms like ‘mandatory’, ‘discretionary’, ‘obligatory’ etc. The challenge is to investigate how far we can go in defining basic activity types. Different authors investigate time allocation behaviour to different activity types (Meloni et al., 2004; Chen and Mokhtarian, 2006; Bhat and Misra, 1999; Bhat, 2005; Kockelman, 2001). It is clear that time allocations to different activity types are shaped by time budget constraints, which define the activity planning time-span. To date no one has considered a comprehensive activity planning paradigm in investigating time allocation behaviour. The perceptions of time use in different activity types are not always disjoint. Perception may be interrelated in many ways and also may be different at different stages of the decision making process, e.g. planning stage, execution stage etc. In fact, the definition of time per se may vary at different stages of the decision making process (Litwin, 2005). Hence, the generic classification of activity types needs proper investigation. In order to determine the fundamental relationship among different generic activity types requires proper econometric specification. Simple statistical data analysis does not necessarily unveil generic relationships. Also the econometric techniques should be 168

comprehensive enough to address multidimensional interactions in time-use decisions. The data should correspond to the appropriate stages of the decision making process. For example, trip diary data may not give sufficient information about the activity level decision-making process. Even a single or two-day activity diary that contains only the scheduled activity information may not provide information of activity planning stage trade-offs in time-use among different activity types. To unveil the interrelationships among different time-use decisions, this chapter investigates the perceptions and decisions at the activity planning stage level, rather than the scheduling stage level. This chapter investigates the time allocation behaviour to non-skeletal activity types using a multivariate econometric technique. It extends the econometric framework developed and tested in the previous two chapters and uses a different estimation technique to deal with the extraordinarily large number of parameters to be estimated. Considering the whole week as the planning period, the chapter investigates the total weekly time allocation behaviour among non-skeletal activities. It considers the allocation of time given the time budget rather than modelling the frequencies with given average duration (as was the case in the previous two chapters). The objective is to investigate the time allocation behaviour other than frequency. The total time budget is derived considering a 7-day time period. The reason for considering the whole week to derive time budgets is the limited number of observations available to estimate the model with its large number of parameters. In order to investigate heterogeneity in all forms, all parameters are considered as multivariate normal distributed. This general modelling assumption makes it almost impossible to estimate using the conventional estimation procedure used in Chapter 7. As an alternative approach, a Bayesian estimation procedure is used. The rest of the chapter is organized as follows: the next sections discuss the modelling framework; estimation technique; data used for empirical investigations and interpretation of the empirical results. The chapter concludes with a summary of important results.

169

9.2 Model Specification and Estimation The specification of the total time allocation to non-skeletal activities under total weekly time budget (T) is Maximize : N

U =∑e

(( β p X p ) + e δ ε j )

ln(e

( βa X ja )

t j + eθ ) +

j =1

1 z (1 1 - exp( ρ)

exp( ρ ))

(9.1)

Subject to :

∑t

j

+ z = T,

j

t j ≥0,

j =1, 2, ............................, N

z ≥0 All notations are the same as in Chapter 7 except, tj, which indicates total time allocated to the specific activity type j. Given this specification the likelihood function is same as before: l (Y | β0 , β a , δ , β p , θ , ρ) =

∏ ([exp(− f j

)

(.)) / exp(δ )] j | J | exp[− exp(− f j (.))] d

j

(9.2)

As the main objective is to investigate the multidimensional interactions in time allocation to different activities, the key assume is that every parameter of the model (the likelihood function of which is expressed by equation 9.2) has a multivariate normal distribution. This assumption requires the multidimensional integration of the likelihood function, thereby introducing considerable computational burden in estimation. It is possible to approximate the multidimensional integral by using the quasi-Monte Carlo simulation technique and the simulated likelihood function method to estimate the model parameters (Bhat, 2005). But in this case, as the number of activities and corresponding parameters are very high, the computation process may become very expensive in terms of time and computer memory. The Bayesian estimation method has recently become popular among researchers and provides a promising alternative to conventional methods

170

(Ma and Kockelman, 2006). The next section discusses the use of the Bayesian estimation technique to estimate such a large set of parameters.

9.2.1 Bayesian Estimation Procedure The Bayesian procedure is fundamentally different from conventional estimation techniques. It does not rely on maximizing any function and desirable estimation properties (e.g. consistency and efficiency) can be attained under less restricted conditions (Train, 2002). It is primarily based on the Markov Chain Monte Carlo (MCMC) simulation method. The strategy is to set up a Markov chain in the parameter space where the researchers update their idea about the parameters based on observed data. The prior idea about the parameters is represented by the probability distributions. Based on the prior distributions and the observed data, the posterior distributions are derived. The Bayes rule of deriving posterior distribution is:

posterior distribution ∞ prior distribution * likelihood function

(9.3)

However, in general the expression of the posterior distribution of the parameter set often does not have any analytical solution to derive moments and other statistical properties of the parameters of concern based on the observed data. The MCMC method overcomes these difficulties using simulation. The MCMC method simulates random draws from the posterior distribution to draw inferences. Two widely used methods -Gibbs sampling and Metropolis Hasting algorithm -- are used to obtain random draws from the posterior distributions (Ma and Kockelman, 2006). Detail descriptions of these methods are available in Metropolis et al. (1953), Hastings (1970), Tanner and Wong (1987), Gelfand and Smith (1990), Smith and Roberts (1993), Tierney (1994), Chib and Greenberg (1995), Gelman et al. (1995) and Train (2002). In this chapter we use the method proposed by von Haefen and Phaneuf (2004), which follows the procedure used by Allenby and Rossi (1999), Train (2002) and Kim et al. (2002). This method specifies diffuse priors and uses a Gibbs sampler with an adaptive Metropolis-Hasting algorithm to simulate from the posterior distribution. The diffuse prior concept indicates the assumption of the parameterized prior distribution of the parameters to insure that the posterior distribution is defined. 171

We can write in general that the parameter set we are concerned about is:

α = ( β p , δ , β a , θ , ρ)

(9.4)

The basic assumption is that the parameters are multivariate normal distributed with mean values and unrestricted variance-covariance matrix: α ≈ N (α , Σ α )

According to equation 9.3:

f (α, Σ α | x) = f (α, Σ α )l ( x | α, Σ α ) / C

(9.5)

Where, C is a proprotionality constant f (α, Σ α | x) is the posterior distribution f (α, Σ α ) is the prior distribution l ( x | α, Σ α ) is the likelihood function The basic approach of estimation is to decompose the parameter space into disjoint sets and simulate each parameter iteratively and conditionally on the others. After a sufficiently long burn-in the Gibbs sampler can generate simulations from the unconditional posterior distributions. Here the precondition is that we have to have prior assumptions (diffuse priors) of the distributions of mean and variance-covariance of the parameters. We assume that the mean has a Normal (N) and the variance-covariance has an Inverted Wishart (IW) distribution. The assumption of Inverted Wishart for the diffuse prior of the variance-covariance parameters is widely used because of its simplicity and resemblance to the normal distribution. For details of the properties of this distribution, see Brown et al. (1994). So the prior distributions are:

172

α ≈ N (α fixed , ηI k ) Σ α ≈ IW (k , I k ) Where α fixed is the fixed parameter maximum likelihood estimates η is a scaler so that 1/η approaches to zero k is the dimension of the parameter set, α I k is the k - dimension identity matrix Considering the total number of persons under observation, P (where p indicate a particular individual person and P indicates the total number of individuals) and denoting all covariates of concern by x, we can derive the posterior distributions of the parameter set, which are:

f (α | α1 , α2 ,.......α P , Σ α , x1 , x2 ,........, xP )∞N (Α, Σ α / P ) f (Σ α | α1 , α2 ,.......α P , x1 , x2 ,........, xP )∞IW (k + P, (kI k + P S ) /(k + P))

(9.6)

f (α p | α, Σ α , xP )∞l ( xP | α p ).n(α p | α, Σ α ) and P

Α = P −1 ∑ α p p =1 P

S = P −1 ∑ (α p − α )T (α p − α ) p =1

Here, l(.) indicates the conditional likelihood function derive in equation 9.2 and n(.) indicates the normal density function

Following the adaptive Metropolis-Hasting algorithm proposed by Chib and Greenberg (1995), the iterative drawing from the above conditional distributions is done using the following steps: (von Haefen and Phaneuf, 2004)

173

For each iteration i: i

1) For individual p, Setting Σ α = kI k and α p0 = α 0 = α fixed we draw α from N(α P

i −1

, Σ αi-1 )

2) Σ αi is drawn from IW(k + P, (kI k + PS )/(k + P)), where S = P -1 ∑ (α ip−1 − α ) T (α ip−1 − α ) i

i

i

i

p =1

3) α for each individual is smulated using one iteration from the following i p

Metropolis - Hasting algorithm : i

A. For each individual observation simulate a candidate vector α p from N(α pi-1 , r i-1Σ αi ), where r i-1 is a constant and the initial value is set, r 0 = 0.1 B. Calculate the ratio : i

F = i p

i

i

l(x p | α p ).n( α p | α , Σ αi ) l(x p | α

(i -1)

).n(α

(i -1)

i

| α , Σ αi )

taking µ pi , a uniform random draw, the Fpi is compared with µ pi : accept the i

candidate draw parameters if Fpi ≥ µ pi and set α pi = α p . Otherwise set α pi = α pi-1 C. Set r i = (1.01)r i-1 if the proportion of accepted candidate parameters is less then 0.3 Otherwise, r i = (0.99)r i-1 . This is done to increase the efficiency. [see 41] 4) Iterate

The convergence is attained after a sufficient burn-in period (less than 25000 iterations). Even after the burn-in, the draws are correlated over iterations. To reduce the correlation by an order of 10, every 10th simulation after burn-in period is used, Train (2002).

9.3 Data for Empirical Estimation The same data source as used in Chapter 7 is used here, but rather than considering frequency, total time allocation to specific activity types is modelled. The investigation is based on the same activity classification as in the previous chapters. Table 9.1 displays aggregate time allocation statistics for the estimation sample.

174

Table 9. 1 Activity Classification

Activity Group Type Act 01 Act 02 Act 03 Act 04 Act 05 Act 06 Act 07 Act 08 Act 09 Act 10 Act 11 Act 12 Act 13 Act 14 Act 15

Total Weekly Observed Time Spent Individual Activity Items

Basic needs like lunch, coffee etc. but not at home Household obligation: cleaning, maintenance, meal preparation, attending kids, attending pets etc. Drop off / Pick up things like: video rental, dry cleaning, postal mails etc. Shopping: major grocery (at least 10 items) Shopping: convenience store, minor grocery (less than 10 items), drug stores etc. Shopping: personal clothing, houseware etc. Services: doctors / medical appointment etc. Services: saloon/barber/beauty, banking, auto servicing etc. Recreation: hobbies, workout, sports, theatre, other outdoor recreational activities Recreation: at home TV program, video, napping, relaxing etc. Social : visiting/hosting, planned social events, bars/special clubs etc. Social: religious and cultural activities Other type of activities that fall as both social as well as recreational type activities ICT use: telephone (more than 10 minutes), internet shopping, browsing etc. Volunteer activities

Average Minutes

Minimum Minutes

Maximum Minutes

92

0

1048

573

0

3099

17

0

446

40

0

438

24

0

361

98 26

0 0

842 489

51

0

2480

343

0

2793

768

0

2093

363

0

3546

81

0

1662

49

0

540

124

0

1358

34

0

2205

Activities in Table 9.1 are differentiated if the activities are fundamentally different in nature and/or they have very different average/maximum observed time allocation. For example: Act 04, Act 05 and Act 06 all are shopping activities in general but these are fundamentally different types and also the average and maximum time allocation to these three types are also significantly different. In case of Act 07 and Act 08, both are service type activities but Act 07 (a doctor’s / medical appointment) is more constrained by the “service end” of the activity and the observed average time as well as the maximum time allocation to these to types of activities are distinctively different. Act 09 and Act 10 are both recreational activities but Act 10 represents strictly at-home activities whereas Act 09 can be both at-home and out-of-home. The observed average 175

time allocation to Act 10 is almost double of that of Act09. Act 11 and Act 12 are both in general social activities but they are fundamentally different and their average and maximum time allocation are also significantly different. Each individual is assumed to have the same activity choice set (15 activity types) for non-skeletal activities. For each individual, the total weekly duration (24 times 7 days) minus his/her total weekly work/school duration is considered to be the time budget. Several socio-economic variables are considered in the model specifications. These are the individual’s age, gender, total yearly income in Canadian Dollars, indicator of having driving license, total work/school hours in the week, size of the household of the person and total number of autos in the house. Two activity-specific variables are considered: the ‘number of possible activity locations’ and ‘travel ratio’. The ‘number of possible locations’ represents the spatial distribution of activity space for the person.

9.4 Interpretation of the Model The specification of the agenda utility function accommodates two components of time allocation utility to specific activity type. The exponential function component is the baseline utility, while the logarithmic function component is called the additional utility. A composite activity utility component is added to the sum of the utilities associated with the 15 non-skeleton activity types. The baseline utility in this model represents the baseline preference of allocating time to specific activities relative to each other and collectively relative to the composite activity. The logarithmic function of additional utility accommodates the fact of diminishing utility with increasing amount of time allocated to any given activity. The objective of this chapter is to investigate how far we can go in classifying individual activity types. The non-skeletal activities are classified into 15 generic types. The correlations in time allocation among these activity types are the major concerns of this chapter. These interrelationships are primarily captured by the activity specific dummy variables in both the baseline and additional utility components. The multivariate distribution assumption of these activity specific dummy variable parameters allows investigation of the correlations in time allocation of assumed activity types. In addition to the random parameter assumption another significant extension of the specification 176

presented in this chapter over others presented in the previous chapter is the incorporation of activity specific dummy variables in both the baseline and additional utility components. Table 9. 2 Estimated Models of Time Allocation Parameters Scale Parameter Baseline Utility Component Activity Specific Dummy ActType01 ActType02 ActType03 ActType04 ActType05 ActType06 ActType07 ActType08 ActType09 ActType10 ActType11 ActType12 ActType13 ActType14 ActType15 Constant Age in 10 years Male (Dummy) Income in 1000 CAD / Year Driving Licens (Dummy) Household Size Household Autos>2 (Dummy) Total Working Hours

Values -0.72684

't' Stat -10.0049

95% Credible Set -0.82977 -0.56821

1.053026 2.406973 0.464149 0.214738 0.43694 1.038981 -0.12704 0.644279 1.836885 2.773035 1.853502 0.404741 1.127418 0.555827 -0.15196 -13.3156 0.330925 0.204417 -0.33919 1.288582 -0.03783 -0.31067 -0.17827

19.26196 49.24907 7.687749 3.318802 7.715534 17.18063 -1.83732 11.92673 32.51742 59.25548 34.66059 4.008768 15.8543 7.450949 -2.41386 -166.673 3.97347 2.033671 -9.91937 16.31404 -0.38819 -4.59143 -3.83299

0.935566 2.310323 0.340631 0.091829 0.328967 0.929801 -0.26216 0.536345 1.733168 2.670696 1.749749 0.215316 0.986923 0.409621 -0.2764 -13.4747 0.158741 0.008109 -0.40711 1.131159 -0.23021 -0.43799 -0.26784

Translating Parameter Theta

1.241394

16.49325 1.096131 1.390814

Additional Specific Utility Component Activity Specific Dummy ActType01 ActType02 ActType03 ActType04 ActType05 ActType06

1.640506 2.048266 0.244955 0.060442 0.513881 1.410898

18.74087 19.2059 2.55768 0.915698 6.873188 22.58237

1.475546 1.846964 0.059609 -0.06917 0.356613 1.289699

1.153104 2.499813 0.580269 0.348446 0.547109 1.165068 0.012325 0.750334 1.951995 2.859086 1.959621 0.60045 1.262043 0.70085 -0.02873 -13.1636 0.480342 0.402991 -0.27518 1.439912 0.142157 -0.17372 -0.09071

1.80718 2.254601 0.424017 0.196465 0.65409 1.542573

177

ActType07 ActType08 ActType09 ActType10 ActType11 ActType12 ActType13 ActType14 ActType15 Travel ratio Number of Possible Locations For the Activity

-0.8456 0.984708 0.992083 0.299197 2.948226 1.047073 1.346591 0.107765 -1.35239 -1.82672

-7.30079 12.30449 13.29837 5.780499 40.7986 7.732874 18.50793 1.407486 -21.5489 -23.3114

-1.03852 0.821684 0.84931 0.200841 2.803706 0.79655 1.20852 -0.04781 -1.4769 -1.98261

-0.60652 1.133819 1.130897 0.400885 3.091799 1.334092 1.494455 0.255412 -1.22964 -1.67437

-0.68662

-12.9836

-0.79178

-0.58307

Composite Good Parameter Rho

1.289301

28.00082 1.201284 1.382255

Table 9.2 presents the final estimated parameters for this model. The total number of parameters in the model is 43. The model considers all 43 parameters as multivariate normal variables. So the estimated model includes the 43 parameter value and a 43x43 variance-covariance matrix. The estimation of this enormous set of parameters becomes possible by the means of the Bayesian estimation technique, whereas by conventional methods (e.g., pseudo-likelihood method) it is almost impossible (von Haefen and Phaneuf, 2004). However, this rich parameter set helps us investigate the multidimensional interactions in time allocation to the specific activities of concern. As this chapter is concerned with the interrelationships among the specific non-skeletal activities, so the discussion concentrates on the activity specific dummy variables and their correlation. The values of the dummy variables in this model indicate the relative importance of the corresponding activity types in activity planning (time allocation). Chapter 7 investigated activity-specific dummy variables in the baseline and additional utility components separately. It is seen that the activity specific dummy variables give a similar pattern of relationships but the scale is different when they are considered as separate models. However in this chapter the dummy variables are considered in both baseline and additional utility component simultaneously, resulting in different interpretations. The concentration is on the total weekly time spent on the specific activities, not the frequency of participation. The logic is that for a particular activity type people may 178

allocate a smaller amount of time but the participation rate may be higher or vice versa. So, the results of this investigation have a different perspective than the previous frequency-based investigations. The interpretations here identify the complementary or supplementary effects among activities with respect to total time allocation. In the Additional Utility Component

Coefficients of Activity Specific Dummy Variables

In the Baseline Utility Component

1

2

3

4

5

6

7 8 Activity Type

9

10

11

12

13

14

15

Figure 9. 1 Relative Importance of Individual Activity Types in Time Allocations

The coefficients of the dummy variables are plotted in Figure 9.1. It is seen that the relative importance of the activities has generally a similar pattern in both baseline and additional utility components. Activity types 07 and 15 receive the lowest importance compared to all other activities in total time allocation consistently in both baseline and additional utility components. Activity type 07 is service activities such as doctor’s/medical appointment. This type of activity is often fixed by the service provider, 179

and people have little control to fix or trade-off this activity type’s time allocation. Activity type 15: voluntary activity may also have similar effects. Interestingly the relative importance of these two activities is lower in the additional utility component than the baseline component. The implication is that the person has little control or little benefit/gain for additional time allocation to these activities. Activity type 10: at home recreation activity has a much higher value in baseline utility than in the additional utility component. The implication is that we like this activity, hence the high baseline preference, but the marginal rate of return for allocating higher amounts of time to this activity is low. A similar effect is clear for outdoor recreation activities (activity type 09). Among the three shopping activities (activity type 04, 05 and 06), the major grocery type shopping has higher baseline preference than additional utility gain, whereas the personal shopping activity has the opposite effect. Personal servicing activity (activity type 08) also has an effect similar to personal shopping activity. This is intuitive: we like to spend more time for personal activities but the baseline preference may not be always higher compared to other activities involving inter-personal family commitments. A similar effect is also clear for social activities (activity type 11 and 12). However compared to religious and cultural type social activities the visiting/hosting or other planned social activities receive more importance.

180

Individual Activity Types

4 0.001 0.14 0.09 0.95 0.12 -0.03 0.18 0.09 -0.15 0.1 -0.3 -0.04 0.05 -0.07 0.2

5 0.11 0.27 -0.01 0.12 1.05 0.17 0.1 0.1 0.17 0.06 0.07 -0.31 0.06 -0.06 -0.13

6 0.03 0.02 -0.03 -0.03 0.15 0.76 0.11 0.05 0.12 0.06 0.22 -0.07 0.08 0.01 -0.15

7 0.06 0.23 -0.06 0.21 0.13 0.12 1.48 0.15 0.14 0.16 0.29 -0.14 0.25 -0.08 -0.03

8 -0.02 0.03 0.26 0.09 0.10 0.04 0.18 1.01 -0.06 0.04 0.16 0.07 0.16 -0.15 -0.03

9 0.02 0.15 0.03 0.00 0.15 0.09 0.15 -0.05 0.76 0.13 0.13 0.16 0.14 0.03 0.1

10 0.11 0.13 0.03 0.07 0.05 0.04 0.14 0.03 0.08 0.52 0.15 0.14 0.1 0.05 -0.07

11 0.09 0.13 -0.06 0.06 0.07 0.18 0.34 0.15 0.11 0.10 0.91 0.01 0.06 0 0.11

12 -0.19 -0.21 0.18 -0.05 -0.45 -0.09 -0.24 0.10 -0.07 -0.01 -0.03 2.02 -0.18 0.09 0.28

13 0.06 -0.03 0.12 0.05 0.06 0.07 0.31 0.17 0.12 0.08 0.05 -0.26 1.01 0.02 -0.05

14 0.04 -0.25 -0.32 -0.08 -0.08 0.01 -0.12 -0.20 0.03 0.04 0.00 0.17 0.03 1.67 -0.01

15 0.09 -0.20 0.21 -0.02 -0.15 0.05 -0.05 -0.04 0.10 -0.06 0.12 0.48 -0.05 -0.01 1.40

2. The Lower Triangular Contains the Implied Correlations

181

1. The Upper Triangular Contains the Variance-Covariance Matrix (Bold face number indicates the‘t’ statistics greater than or equal to 1.64)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Individual Activity Types 1 2 3 0.77 0.14 -0.10 0.17 -0.07 0.84 -0.11 -0.08 1.09 0 0.16 0.09 0.12 0.28 -0.01 0.04 0.02 -0.03 0.06 0.21 -0.08 -0.02 0.03 0.25 0.03 0.19 0.04 0.15 0.19 0.04 0.11 0.14 -0.06 -0.15 -0.16 0.12 0.07 -0.03 0.12 0.07 -0.21 -0.24 0.09 -0.19 0.17

Table 9. 3 Activity Specific Dummy Variables in Baseline Utility Component

Individual Activity Types

5 0.29 -0.32 -0.14 -0.30 1.49 0.04 -0.12 -0.01 -0.16 0 0.07 0.06 -0.1 0.05 0.11

6 -0.18 0.41 -0.20 0.01 0.05 1.15 0 0.17 0.03 -0.07 0.1 0.12 0.06 -0.04 0.12

7 -0.01 -0.08 -0.11 -0.02 -0.17 0.00 1.43 -0.28 0.14 0 0.09 0.02 0.07 -0.17 0.06

8 -0.21 0.53 0.20 0.07 -0.01 0.21 -0.39 1.31 -0.07 -0.07 0.05 -0.11 -0.03 0.27 -0.05

9 0.20 0.04 0.19 -0.13 -0.20 0.04 0.17 -0.08 1.08 0.08 0.06 0.12 0.08 -0.11 -0.07

10 0.07 -0.03 0.30 0.10 0.00 -0.07 0.01 -0.08 0.08 0.97 0.02 0.09 -0.04 0.06 0.12

11 0.01 0.56 -0.08 -0.28 0.12 0.14 0.16 0.08 0.09 0.03 1.95 0.01 0.12 -0.14 0.14

12 0.17 -0.64 -0.54 0.43 0.11 0.21 0.05 -0.21 0.20 0.14 0.02 2.70 0.13 -0.17 0.23

13 -0.24 0.11 0.43 -0.14 -0.13 0.07 0.08 -0.04 0.09 -0.04 0.18 0.23 1.12 0.02 0.15

14 -0.23 0.17 0.48 -0.20 0.07 -0.05 -0.27 0.40 -0.15 0.07 -0.26 -0.36 0.03 1.70 -0.1

15 -0.20 0.03 0.24 0.23 0.15 -0.05 0.08 -0.06 -0.08 0.14 0.23 0.43 0.19 -0.15 1.31

2. The Lower Triangular Contains the Implied Correlations

182

1. The Upper Triangular Contains the Variance-Covariance Matrix (Bold face number indicates the‘t’ statistics greater than or equal to 1.64)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Individual Activity Types 1 2 3 4 -0.14 1.82 -0.32 -0.50 -0.23 2.55 0.19 0.30 -0.38 0.08 2.27 -0.03 -0.12 0.15 -0.02 1.58 0.17 -0.16 -0.08 -0.19 -0.13 0.24 -0.12 0.01 -0.01 -0.04 -0.06 -0.02 -0.14 0.29 0.11 0.05 0.14 0.02 0.12 -0.1 0.05 -0.02 0.2 0.08 0.01 0.25 -0.04 -0.16 0.08 -0.24 -0.22 0.21 -0.17 0.07 0.27 -0.1 -0.22 0.08 0.25 -0.12 -0.12 0.02 0.13 0.16

Table 9. 4 Activity Specific Dummy Variables in Additional Utility Component

Tables 9.3 and 9.4 present the variance-covariance matrices of the activity dummies together with the implied correlation coefficients, for the baseline and additional utility components respectively. It is interesting that the activity covariances are more negative for additional utility gain than for baseline preference. For example, the covariance of activity type 01 is negatively correlated only with activity type 03 and activity type 08 in baseline preference, whereas it is negative with respect to activity types 02, 03, 04, 06, 07, 08, 13, 14 and 15. Similar results hold for all other activity types. The behavioural implication of this finding is clear: activity types have generic minimum time requirements and at that generic level the complementary or supplementary effects are very low. Activity types are fundamentally different at the baseline preference level. The allocation of additional time to specific activity types, however, introduces competition due to time budget constraints. This picture becomes clearer if we investigate the implied correlations among the activity types. The implied baseline correlations are very low for all cases. The highest implied correlation is 0.28 between activity type 02 and 05 in baseline preference. Activity type 02 is household obligation activities and activity type 05 is shopping (minor grocery, convenience store, drug store etc.). Both of these two types are small household errands, and hence show some correlation (still it is less than 0.5). The positive sign of this correlation indicates that when we plan for one activity we usually plan for the other as well. The largest correlation in the additional utility component is -0.38, which is between activity type 01 and 03. The negative correlation indicates a substitution effect, if we increase time allocation to one activity the time allocation to the other will reduce. In general, the correlations are higher for the additional utility component than for the baseline utility component. The above findings comply with the general findings of Doherty (2006) that at a fundamental level activity types (here type is indicated by activity attributes) are independent and different from each other, Doherty (2006). General activity classifications such as ‘mandatory’, ‘flexible’, ‘discretionary’ etc. may not reveal the behavioural elements of time allocation and activity planning. This finding also justifies 183

the IID assumption used to formulate the activity-agenda formation models in the earlier chapters.

9.5 Key Findings and Conclusions The time allocation behaviour and activity classification of non-skeletal activities in activity planning is investigated in this chapter. The investigation is accomplished by using a multivariate econometric technique. The econometric technique is designed to replicate the activity planning process by using Kuhn-Tucker optimality conditions. Activities of 15 generic types and individuals’ time allocation behaviour to these activities for a 7-day planning period are investigated. The concept of activity utility is used to derive a model of time allocation behaviour. Utility of each activity type is considered to have two parts: baseline utility and additional utility. The baseline utility represents the baseline preference in time allocation to the activities and the additional utility component indicates the marginal satisfaction due to additional time allocation to a specific activity. Activity-specific dummy variables are used in both baseline and additional utility components to investigate the inter-activity relationships in both elements (baseline preference and additional time allocation). All parameters of the econometric model are considered to have multivariate normal distributions. A Bayesian estimation technique is used to estimate the parameters. The estimated model reveals very plausible behavioural insights into time allocation and activity planning. It proves that the non-skeletal activity classification used for agenda formation modelling is generic enough to have minimum correlation in time allocation to the activities (both baseline preference and additional time allocation). The investigation also proves that the salient features of the activities are most important in classifying activities rather than aggregate labels like ‘mandatory’, ‘flexible’, ‘discretionary’ etc. The chapter contributes to the existing literature of activity/travel demand modelling in two ways. The econometric investigation gives similar and comparable findings as that of statistical data analysis by Doherty (2006). This chapter also presents a comprehensive application of the Bayesian estimation technique in activity/travel demand modelling. 184

CHAPTER 10: CONCLUSIONS AND DISCUSSIONS 10.1 Summary The activity-based approach to model travel demand emerged over traditional trip-based modelling approaches with the argument that the conceptual clarity, theoretical consistency, and purported unmatched potential for policy application of the activitybased approach can lead to substantially greater understanding and better prediction of travel behaviour (Recker, 2001). However, these key characteristics of the activity-based approach have posed considerable challenges to the development of operational models of travel demand. According to Recker (2001) the inherent complexity of the activitybased approach, which is based on spatio-temporal linkages among a whole collection of activities, rather than the characteristics of an isolated trip, have proven to pose serious demands for the development of the framework or models beyond rudimentary statistical correlations. Recker’s remarks become more germane when the travel demand model is intended to integrate within an Integrated Land Use Transportation and Environment (ILUTE) modeling system. The challenges are multifaceted and hence the research challenges can be viewed as trade offs between actual complexities of the behavioural processes versus our understanding of the process, as well as between our depths of understanding of the process versus our capacity to model this process. Again, the understanding of behavioural process requires critical observations or detailed observed behaviour (data). This is why focusing on specific issues of activity-based modelling requires an inductive process. The inductive process indicates the step by step investigation of different hypothesis as well as the questions that emerge during these investigations. This thesis follows such an inductive process to address the issues related to the activity-travel generation/demand by developing behavioural hypotheses and testing the hypotheses through advanced statistical econometric techniques. The key outcomes are better understanding of the activity-travel generation process, advanced modelling techniques for the behavioural process and a detailed behavioural framework for future operational model. 185

Through a review of the literature, it is found that existing activity-based travel demand models are in many cases lacking a consistent theoretical foundation, especially with respect to activity-travel demand/generation. Most of the literature to date has mainly focused on the complexities of activity scheduling process. The activity generation component is often considered as an external input to the activity scheduler. The activity generation component in all operational activity-based travel demand model simulates the activity demand from observed distributions, or generates the activity demand in a way that is similar to the trip generation approach of traditional four-stage trip-based models. Suggestions for filling the gaps in existing literature have led to a focus on the underlying activity-travel generation “process”. Relatively weak treatment of the activity generation component is due to the lack of appropriate and consistent theory. The situation is further aggravated by the scarcity of proper data. However, relatively few researchers have been able to suggest details of how to model the tradeoffs involved during the activity generation process prior to scheduling. The much discussed need to define the measuring unit of the benefits of participating in different activities, activity utility, is either overlooked or addressed through adhoc means in the existing literature. This also contributes to the lack of development of a tractable and unifying modelling framework for activity-travel generation. Influenced by the deficiencies of the existing literature this thesis next concentrated on the theoretical investigation of the causal processes of travel demand and their dynamics that are integrated within various socio-economic and spatio-temporal systems involved in trade-offs between earnings and consumption of resources and commodities. Two critical issues are focused in depth: the dynamics of activity-travel generation / demand and the measurement of activity utility to model the activity decision trade-offs. Based on concepts derived from time-geography and economics a conceptual framework for activity-travel generation was devised. The prime objective is developing

a modelling framework that can better integrate the activity-based travel demand model within the ILUTE framework and at the same time ensure that the interrelated decision dynamics are sufficiently addressed. This generalized conceptual framework provides the spring-board to develop empirical models of activity planning/generation, adopt 186

economic and meaningful measuring units of activity utility to derive the models, and find correct answers of the questions that arise during the process of model development, or, in other words testing different hypotheses. The conceptual framework divides the daily or short-term activity-travel demand into two major components according to household activity decision dynamics. The portion of short-term activity-travel decisions that are parts of medium- to long-term household decision processes (e.g. job etc.) are referred in general as skeletal activities. And other than these all are referred to as nonskeletal activities. The idea of this division is to recognize the differential decision dynamics. The demands for skeletal activities (e.g. work, school etc.) are more or less stable within a short period of time, whereas the demands for non-skeletal activities vary within a day or day-to-day. Dividing the activity types into these two major categories also helps the development of a time allocation modelling approach. The hypothesis is that for the short-term travel demand modelling, skeletal activity episodes are modelled as events, not using explicit utility calculations. Both skeletal and non-skeletal activities together form the activity-agenda, which becomes the input to the activity scheduler. Proper investigation of behavioural processes and developing behavioural models requires appropriate and detailed data. Wave 1 CHASE data set of TAPS is the only data source available to date that has extensively detailed information over a week-long time period and it is used in this study. It is collected in a way where the respondents note down information about activity planning and decision making process in situ under realistic planning conditions. Two major limitations of the data set are: information is not complete at the household level of all households in the survey and the survey does not capture the trade-offs involved in adding specific activities into the activity-agenda. The first limitation of incomplete household level information restricts us from developing household-level empirical models. All empirical models tested in this thesis are thus individual based, but efforts are taken to accommodate household level influence on individual’s activity planning behaviour. The second limitation is also important and a deciding factor in devising fundamental assumptions of the empirical models. The assumption that the activity-agenda of non-skeletal activities are the most optimum set of activities that optimizes the total utility of the activity sets are derived by this limitation 187

that we only observe the set of activities to be scheduled, not the trade-offs involved in deriving the set of activities. This also logically leads to the assumption that the first-time added activity information by the respondents are outcomes of the activity-agenda formation process and thereby form the sample set for testing the empirical models of this thesis. However, despite these limitations, this data set provides a rich information set to develop empirical models as well as investigate the key behavioural processes. Having the conceptual framework of modelling activity-agenda formation and the detailed activity-diary survey data, the first attempt is to develop generation models for skeletal activities. Importantly, from the behavioural point of view it is important to keep

such skeletal or fixed part of the generated agenda as minimal as possible because such classification of skeletal versus non-skeletal activities in many ways is dependent on the analysis time frame. Based on the data limitations on household joint activities, only work/school and night sleep are considered skeletal activities. As the skeletal activities represent the medium- to long-term planning, in other words routine or habit, the utilitybased modelling approach of activity generation for short-term (daily or weekly) modelling span does not capture the behavioural trade-offs of such activities. For the skeletal activities the ‘process-based’ approach that follows the sequences of concerned time chunks of the total modeling span as sequences of events is a more appropriate modelling approach. So to model the generation of skeletal activities (work/school and night sleep), the day is divided into four time events: ‘before work gap event’, ‘work event’, ‘after work gap event’ and ‘night sleep event’. Here the ‘work’ and ‘night’ sleep are the skeletal activities and the two gap events are defining the total time availability for the non-skeletal activities. The idea is that a series of models, one for each event, defines the skeleton of the activity-agenda. For a single-day modelling span it provides the nucleus for scheduling capturing the within-day dynamics and trade-offs between skeletal versus non-skeletal activities, and, for weeklong modelling span, in addition to within-day dynamics it captures the day-to-day dynamics of activity behaviour. For modelling the time allocation to the above mentioned skeletal activity episodes two types of econometric approaches are considered. The best one is selected based on better fitting the observed data. The econometric approaches tested are: hazard188

based duration model and multilevel linear model. However, the results show that for the ‘before work gap event’ and ‘work event’ duration the proportional hazard model of Gompertz baseline hazard distribution with Gamma heterogeneity gives better fit of the observed data. For the ‘gap after work event’ duration the accelerated time hazard model of Log-logistic baseline hazard distribution assumption with Gamma heterogeneity gives better fit and for the ‘night sleep event’ duration multilevel linear model gives better fit. Only the ‘night sleep event’ model shows statistically significant household level random effects. For the other components of the skeleton, the household level random effects are not statistically significant. Household level effects on these components are explained by the household level variables like household size, household structure, household automobile etc. Some of the key findings of this modelling exercise are that the competition between motorized (auto and transit) and nonmotorized (walk and bike) modes for commuting is clearer rather than competition between autos and transit. Total work duration of the previous day influences workers to start later but work longer. One important finding is that the personal attribute ‘age’ does not enter in any model significantly. This contrasts with models in the literature in which age is the most commonly used index variable in operational models to derive start time-duration of the skeleton activities from the observed distributions. Given the modelled skeleton, the gaps in the skeleton schedule define the total time availability for non-skeletal activities. An important issue that needs clarification before modelling the generation of non-skeletal activities is the sequencing of the nonskeletal activities at the stage of agenda formation. That is, the start time and duration relationship of non-skeletal activities in activity-agenda is a critical issue. However,

the proper investigation of this issue demands an appropriate econometric framework to identify potential causal relationships between start time and duration of the non-skeletal activities. This investigation is done assuming four possible relationships: ‘the start time selection is conditional upon the duration determination’, ‘duration determination is conditional upon the start time selection’, ‘start time selection and the duration determination are simultaneous decision process’ and ‘the start time selection and duration determination are not correlated decisions but rather are independent of each 189

other’. According to the original activity classifications of CHASE, the non-skeletal activities are classified into 7 major categories: Household Obligation activities, Drop off/Pick up activities, Shopping activities, Service activities, At-home Recreation activities, Out-of-home Recreation activities and Social activities. For each of these activity types the four causal relationships are tested using discrete-continuous and continuous-discrete econometric approaches. The discrete-continuous approach uses a multinomial logit model for start time selection as the time of the day, followed by a loglinear duration model with endogeneity correction for the multinomial sample selection. The continuous-discrete approach also uses a multinomial logit start time selection model with an endogeneity correction for the log-linear duration model using a control function approach. Both of these approaches are robust econometric frameworks and track the relationships between the start time and the duration from different angels. The empirical results of the models reveal little evidence of a strong relationship between the start time and the duration of non-skeletal activities during the activityagenda formation. No activity type shows the existence of any relationship throughout the whole day except Household Obligation activities. Although Household Obligation activities show a significant relationship throughout the whole day the relationships are not consistent. It is found that the relationship is different in the afternoon (4:01 pm to 7:00 pm) than for the rest of the day. This evidence suggests that the sequencing of nonskeletal activities along the time scale is not an important issue in activity generation models. So modelling non-skeletal activity generation can fairly be defined as modelling the time allocation (total time allocated or the frequencies for the given average durations) to the non-skeletal activities without concern for the sequencing (start time) of these activities, leaving activity sequencing to be determined within the subsequent activity scheduling component. For modelling time allocations / frequencies of non-skeletal activities the concept of activity utility is used. Defining the activity utility is a critical research question. Defining the utility of activity episodes depends on the perception of time use. In activity based modelling time plays a dual role: time as resource and time as commodity. Planning of activities is basically allocating limited time resource to the 190

competing activities and executing the activities is basically consuming the corresponding allocated time. This conception matches with the activity-based modelling very closely. Modelling activity-agenda (which is the activity planning) should consider the time as resource to be allocated and modelling activity scheduling (which is the executing of planned activities) should consider the time as the commodity. Winston’s (1987) definition of utility provides an excellent consistency with these time definitions. He defines the utility of activity as consisting of two parts: the Goal utility and the Process utility. The Process component of utility is derived during the execution process of the activity and the Goal component is defined by the end state accomplished by the activity. Goal utility here represents the direct utility of activity episodes derived from accomplishment of the activity. Modelling activity-agenda formation should be based on Goal utility calculation. Having the Goal utility definition of non-skeletal activities, modelling activityagenda under time budget limitations is a large-scale demand system problem. Large scale demand systems consist of a large number of specific candidate activity types and must allow for both the possibility of non-participation in any activity (i.e. a corner solution) and the non-negativity of activity participation rate or time allocation (whichever is being modelled). Application of Kuhn-Tucker optimality conditions in deriving the time allocation optimization model is a promising approach to ensure these requirements. Based on these understandings an econometric framework is devised to model the time allocation / frequencies of non-skeletal activities under total time budget limitations. The specification conforms to the Random Utility Maximization (RUM) approach with endogenous random error components. The proposed framework is flexible enough to model either total frequencies of non-skeletal activities given the average duration or total time allocation to the individual activity types. The general specification of the proposed agenda formation model for non-skeletal activities falls in the general category of multiple discrete-continuous models. Moreover it is designed to handle the trade-offs in time allocation in different non-skeletal activities and to all other undecided activities together defined as composite activity. The composite activity is synonymous to the Hicksian composite good concept that provides time slack within the 191

time budget constraints. Once the structural parameters of the model are estimated, the model becomes a constrained optimization model to derive activity-agenda of nonskeletal activities. Within the model specification, the total utility of the specific activity is divided into two parts: the baseline utility and the additional utility. The baseline utility component refers to the baseline preference of the specific activity compared to the composite activity and the additional utility component refers to the additional preference of one specific activity to the other. In addition to a number of household socio-economic and activity-specific variables, the activity-specific dummy variables are used to identify the alternate specific effects of the non-skeletal activity types. Heteroskedasticity in the activity behaviour is accommodated using random coefficients for some covariates. A number of alternative specifications of the model are tested considering a weeklong time budget. The non-skeletal activities are disaggregated into 15 generic types. Athome basic need activities and Night sleep are together considered as composite activities. The 15 non-skeletal activity types are: Basic need (Out-of home), Household Obligation, Drop off/Pick up goods, Major Grocery shopping, Non-Grocery or Minor Grocer shopping, Personal shopping, Service (Doctor/Medical appointment), Service (Personal

maintenance),

Out-of-home

Recreation,

At-home

Recreation,

Social

(Visiting/hosting), Social (Religious and Cultural), Social (all other types), ICT (Information and Communication Technology) use, Volunteer activities and All other activities that do not fall in any of the other categories. The total time spent for the skeletal activities (work/school) is considered as a covariate of the non-skeletal activity-agenda formation model. The specification that accommodates activity-specific dummy variable in the baseline utility component gives the better fit (higher Rho-square value) of the observed data. In addition to testing the model specifications to investigate the applicability of the utility-based large scale demand system modelling in activity-agenda formation, a number of behavioural insights into the activity-agenda formation process are gained. The negative effect of travel time in activity participation justifies the travel as a constraint. It is also seen that spatial dispersion of the potential activity locations negatively influences the activity 192

participation planning. It is also clear that higher income people have larger activity sets to perform and that income has the same effect across the population. Whereas, age, gender and household size affect the activity-agenda formation from positive to negative across the population. The empirical experiment of the model specification for week-long activityagenda formation modelling predicts the optimum weekly frequencies of non-skeletal activities, given their average durations. The concept of using average duration is to address the issue of peoples’ perception about average time required to participate in a specific activity. This also allows future scope for accommodating learning and adaptation of the perception of time use in specific activity types in response to different policy measures by introducing dynamic feedback between the activity scheduler and activity generator. The specification of the agenda formation model using Kuhn-Tucker optimality condition basically models the virtual price of any non-skeletal activity as an endogenous function of frequency of the activity and the time allocated to the composite activity. The given average duration of the specific non-skeletal activity provides the conceptual linkage between the observed activity demand and the structure of preference in agenda formation. An individual decides to consider any additional activity participation decision when the virtual price and the average duration are equal. On the other hand, if the virtual price of the activity is lower than the average duration, the average duration acts as the reservation price for that activity, duration below which that allows the activity to be considered in the activity-agenda. The week-long agenda formation model reveals that Drop off/Pick up goods activities are the least preferred activity. Intuitively this activity type does not give much direct utility per se but is a necessary support for other activities. The volunteer activities also seem to receive lower preference; a possible reason may be that the people receive mental satisfaction from this activity type other than high direct utility per se. The most preferred activity type is seen as At-home Recreation and it makes sense that we enjoy this type of activity very much. Household Obligation type activity also receives high preference; intuitively as a social being we place considerable importance on completing household responsibilities. Among the three types of Shopping activities it is clear that 193

the Personal shopping returns higher direct utility compared to the other two types. Among the three types of Social activities, it is seen that Visiting-Hosting type social activities are more preferable. Activities involving ICT (Information and Communication Technology) shows to have lower direct utility than direct interactive social activities but e-shopping receives higher utility than Major Grocery type shopping activities. The above discussion is based on a week-long activity-agenda model. However considering a typical day as the modelling span is a commonplace in activity-based travel demand modelling practice. The typical day refers to a hypothetical day and the intention is to overcome the day-specific features of a week. But our activity-travel behaviour shows considerable variation across the week. This discussion is related to the question of what should be the appropriate modelling span, a typical day or a typical week. The model discussed above is for a week, but considering the whole week as the planning period. So it is necessary to test whether there are considerable variations in day-to-day activity planning that might be suppressed if the whole week is considered as the planning period. So, as the next step of investigation, activity-agenda formation models are estimated for each day of the week and the results are compared with the previous week-long planning period model. In order to capture the within-day

dynamics of activity travel behaviour the skeletal activity components (total time spent on work/school activity) are entered into each model as covariates. The day-to-day dynamics are accommodated by considering the ‘previous day’s total scheduled activities’ as a variable of the next day’s activity-agenda formation model. These two variables are very important in the sense that they address the dynamic feedback from activity scheduler to the activity generator. Both of these two variables are highly significant in models of all days of the week. This proves that considerable variations of activity behaviour occur across the week. The weekday and weekend trade-off in activity behaviour is clearly visible in the model results. It is seen that people participate in a higher number of different non-skeletal activities at the beginning and the end of the week, whereas in the middle of the week serial non-participation in some activities are clear.

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Compared to the weeklong agenda formation model, it clear that for a dayspecific or multi-day model the time allocation trade-off between specific activities and the composite activities are clearly significant, but when the whole week is considered as the modelling span this behavioural element becomes buried. It is also seen the males plan for a higher number of activities in the middle of the week, while females plan for a higher number of activities in the last day of the weekend and the first day of the weekdays. Intuitively, it is seen that people spending longer hours for work spend less time in non-skeletal activities and more time on the composite activity (At-home basic need and Night sleep activities). In summary, it is clear that a typical day does not have strong behavioural argument over a typical week as the modelling span, but for a typical week, the day-specific agenda or multi-day agenda modelling is more appealing than considering the whole week as a the modelling time span. All of the above discussions on week-long agenda formation versus multi-day agenda formation for non-skeletal activities are based on an arbitrary classification of the non-skeletal activity types. The non-skeletal activities are classified into 15 generic activity types. It is important to verify the classification of non-skeletal activities because the proposed activity-agenda formation model explicitly assumes that the individual activity types are sufficiently disaggregated to have insignificant correlation between each other. Other than for the justification of the mathematical assumptions, it is important to investigate the activity classification of non-skeletal activities from the behavioural point of view because this classification is a question of time allocation to independent objectives that are defined by our expectation of outcome of the activities. According to Recker’s comment mentioned at the start of this chapter, simple statistical analysis does not necessarily reveal the actual behaviour; for this we need robust statistical-econometric approaches. With this objective in mind the earlier discussed utility-based activity-agenda formation model is further extended assuming all structural parameters of the model as multivariate normal distributed. The objective is to investigate the variance-covariance and correlations of the activity-specific dummy variables that are to be considered both in the baseline as well as the additional utility component. This ambitious attempt incurs heavy computational requirements. 195

The previously discussed models of fixed coefficient have a closed-form likelihood function and are estimated using a gradient search algorithm. For random coefficient specifications the pseudo-likelihood method is generally used. But with the assumption of all parameters being multivariate normal distributed, the use of pseudolikelihood method becomes very difficult and time consuming. The obvious alternative estimation technique is MCMC (Markov Chain Monte Carlo) method. The MCMC method is basically a Bayesian estimation technique that sets a Markov chain in the parameter space where the researcher updates the idea about the parameters based on observed data. In order to investigate the intra-activity covariance and correlation in time allocation the complete week activity-agenda is modelled considering the total time allocation to specific activities. As the prime objective is to analysis the time allocation behaviour to competing activity types, the total time allocation model is more appropriate in this application than modelling frequencies given average durations, as was done in the previous models. The activity-specific dummy variables in both the baseline as well as the additional utility components show similar trends as those of previously discussed specifications. Investigating the variance-covariance matrix of the activity-specific dummies and corresponding implied correlations reveals that there are no significant correlations between any two specific non-skeletal activities, both in baseline utility preference as well as additional utility preference. This is a crucial finding that justifies the IID assumption of the likelihood formation for the proposed activity-agenda formation model. It is very important to note that this finding complies with the general finding of Doherty (2006) that at a fundamental level activity types are independent and different from each other.

Given the understandings of the behavioural processes and the tested empirical methods, the next challenge is to operationalize the empirical models. The conceptual framework presented in Chapter 4 envisions the critical elements of a comprehensive activity generations model that has a dynamic relationship with the activity scheduler as 196

well as other components of medium- to long-term household decision making processes within the ILUTE framework. This is a complex and extensive problem, many issues of which have yet to be solved, and for which one thesis would be insufficient. The empirical investigations presented in this thesis tested some hypotheses as well as tested the modelling and computational capacity using activity diary data. Based on the understandings gained in this research, it is argued that the ideal activity generator should have the following salient features: 1. A week-long modelling time frame but considering individual days as the time budget or the generation cycle. As seen in Chapter 8, each individual day of the week is different from each other one. It is necessary to capture this minimum rhythm of activity generation processes. 2. Recognizing the differential dynamics of different activity planning processes, it is important to classify the activity into two basic types: skeletal and non-skeletal activities 3. Modelling skeletal activity generation processes should not be based on utility-based framework for a travel demand model. Rather a processbased modelling approach or input from larger modelling framework (ILUTE) that encompasses the travel demand model is a more behavioural and appropriate modelling approach 4. For non-skeletal activities, a utility-based modelling framework considering the time-budget effect as well as composite activity influences (effect of left over time after considering specific activities within time budget) is important. It is important not only for the activity generation process only but also to establish a dynamic relationship with the activity scheduling process model and other components of an ILUTE framework 5. In terms of output of the activity generation mode, for the skeletal activities the start times and duration should be the outcome. On the other hand for non-skeletal activities the start time is not necessarily an output of the generation model. The time allocation in terms of total allocated

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time within time budget or given the average duration, the total frequencies are the appropriate output of the activity generation model 6. Other than the start time and duration of activities, the travel modes and activity locations should be considered as the linking variables between activity generator and activity scheduler. The attributes of activity episodes are the final decisions of the travel demand model. So these should be entered into the generation models as perceptions, e.g. perception of travel time and number of possible activity locations. An iterative approach of generation and scheduling considering feedback from each other can establish clear behavioural linkages and better prediction of activity-travel demand. 7. Last but not least to mention here, is that there should be a parallel activity scheduling process modelling framework. Considering both generation and scheduling as parallel processes is deemed necessary to make the travel demand model dynamic and behavioural. Based on the conceptions gained in this dissertation, it can be proposed that the first stage of the activity scheduling process model should be a tentative schedule formation component that takes as input skeletal activity information from the activity generator. The other component of the scheduling process model should be an activity rescheduling process component. Application of process utility or expected utility concept for the scheduling process models are worth for further investigations.

Given the above recommendations, the obvious next stage in the development will require the operationalization of some of the components of the conceptual model that have been tested in this thesis. The development of a comprehensive activity generation component is a particularly critical future task The following sections examine several of these themes in greater detail.

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10.2 Complexity of Behavioural Process versus Our Understanding One of the main themes of this thesis is the effort to minimize the gap between actual behavioural processes and our understanding of these processes. According to Axhausen (1998): “(…..) Human activity stream can be conceptualized as a series of projects which at different time frames either retain their distinct project character or become “overhead” everyday life. Modelling can progress either by tracing the dynamics of the projects, spanning in many case multiple days or periods, or by developing tools which generate schedules consistent with real behaviour for any one day essentially ignoring the dynamics of the projects” Here the term “project” indicates a collection of activities with common goal(s). One useful approach to defining our daily activities in a tractable way is to divide life into a finite number of projects. In this case the project elements are distributed along the longitudinal time scale that means different activity components of a project may need to be scheduled on the different days of the week, months, etc. It is conceivable that different projects might have different planning time frames, for example work/school projects are different from a social project. The project concept basically derives from Maslow’s (1970) need hierarchy theory, where he defines life as being composed of a hierarchy of needs, with our activities being generated to satisfy these needs. The conceptual process of understanding the activity needs that evolve over time is very elegant and lucid according to Maslow’s need hierarchy theory or Axhausen’s projectbased theory, but the reality is that we want to model the process. In order to develop models we need evidence or information derived from detailed observation of actual behaviour i.e., empirical data. Collecting data of activity behaviour is always a big challenge. This reality is reflected in Axhausen’s (1998) comment: “Can we ever obtain the data we would like to have?” Even a state-of-the-art data collection tool such as CHASE can not capture the actual process of project-based activity-agenda formation. What we observe is basically 199

revealed outcomes of unrevealed behavioural processes (Doherty, 1998). We can best observe the collection of different types of activities prior to the schedule, which is referred as the activity-agenda in this thesis. Herein lays the contrast between actual behavioural processes and our understanding. Given the psychological theory of human need our understanding in many ways is influenced by our observations. Keeping all of these issues in mind, the concept of referring to activity-travel generation as a “process” in this thesis recognizes the inherent dynamics in activity-travel behaviour that supports integration of travel demand within the ILUTE framework. Since we do not observe the mental simulation process of the individual decision-makers, the reasonable assumption is, for a particular person, the collection of candidate activity episodes for scheduling within a specific time period is the optimum set of activities she/he desires to schedule. Further classification of skeletal and non-skeletal activities gives more scope to sort out some activities that are regular in nature and more of the parts of medium- to long-term household decision process and separate out from the time scope of defining optimum activity-agenda set.

10.3 Understanding versus Empirical Modelling The conceptual model presented in this thesis provides guidance for developing empirical models. Developing such models poses the same challenge as that mentioned in previous section: bridging the gap between actual behavioural process and our understanding of the process. According to our understanding of activity-travel behaviour, the activity-travel generation process is complex. Mathematical modelling is a simplistic representation of the complex behaviour. Modelling behavioural processes often requires abstraction of reality into tangible or quantitative form. This thesis presents application of a number of advanced econometric modelling techniques for activity-based modelling. Hazard-based duration and multilevel linear models are used for skeletal activities. Hazard models have become a popular modelling technique in transportation. However, in this thesis different forms of hazard models are used: proportional hazard model versus accelerated time hazard model. For accommodating heterogeneity two types of heterogeneity distributions are investigated: Inverse Gaussian distribution and 200

Gamma distribution. For both proportional and accelerated time hazard models, a number of alternative baseline distributions are tested: Exponential, Gamma, Gompertz, Lognormal, Log-Logistic and Weibull distributions (however, only the two best fitting hazard models for each modelled event are reported in this thesis). Such a comparative study has not been reported previously in the literature. On the other hand, the multilevel model is a recent practice in transportation literature. Only a handful of examples are available to date. Multilevel models are very powerful in representing different levels of influences on individual’s behaviour. In this thesis we modelled the household level unobserved influences on individual’s time allocation behaviour to skeletal activities. Hence, both of the applications of hazard-based duration model and multilevel linear model represent significant methodological contributions to the existing literature of activity-travel behaviour. On the other hand, modelling non-skeletal activity-agenda under time budget constrains is implemented as a large scale demand system model. Application of KuhnTucker optimality condition ensures corner solutions (the possibility of non-participation of any activities under consideration). Together with inclusion of the composite activity option this model is a unique example of the application of advanced econometric methods in travel demand modelling. Such large-scale demand system model using Kuhn-Tucker optimality conditions is referred in economics as K-T demand system model. Development of the K-T model in this thesis is the most recent contribution in travel behaviour research literature. The only one example available so far in the literature is the MDCEV (Multiple Discrete Continuous Extreme Value Model) model of Bhat (2005, 2006). Our K-T model is significantly different from MDCEV in formulation as well as application. The K-T model developed in this thesis is also tested for a number of advanced econometric features. In addition to a fixed parameter model specification, the random coefficients of some parameters are tested in order to accommodate preference heterogeneity across the population. For the partial (not all parameters) random coefficient K-T model the conventional pseudo-likelihood method (using Halton sequence to generate pseudo random numbers) is used. For developing a fully random 201

coefficient K-T model (all parameters are multivariate random distributed), it is seen that the conventional pseudo-likelihood method becomes very slow or in some cases almost impossible to use for parameter estimation. As an alternative estimation procedure, the Bayesian estimation technique (MCMC: Markov Chain Monte Carlo) is used. Using the Bayesian estimation technique to estimate a large scale demand system model also contributes to the existing travel demand modelling literature as a recent example of the application of advanced parameter estimations procedure.

10.4 Future Research Efforts This thesis has identified the potential for developing a comprehensive activity generation model. The immediate future research task is to operationalize the developed empirical models for the second version of an existing activity-based travel demand model, TASHA (Miller and Roorda, 2003). The first step is to implement the skeleton formation model to replace the existing empirical distribution method of TASHA. Given the skeletal components, the second stage is to operationalize the K-T model to generate frequencies of non-skeletal activities. Implementation of the skeletal formation model is relatively straightforward, but the implementation of a K-T demand system model for non-skeletal activity generation needs further testing with respect to computational time (i.e., testing the performances of fixed parameter versus random parameters models). Extensive validation tests are necessary as well to measure the performance of the models. Beyond these implementation efforts, however, there remain a number of research questions that need immediate attentions.

10.4.1 Further Investigation Necessary One of the main reasons for defining activity generation as a ‘process’ is the dynamic interrelationship between activity generation and activity scheduling. For a single day model there is little scope for considering dynamic feedback between the activity generator and the activity scheduler. But for multiple-day modelling dynamic feedback is very much important. The models developed in this thesis consider some variables that connect the generator and the scheduler dynamically. For skeleton formation model, the previous day’s total time spent for work/school addresses the dayto-day dynamics in skeletal activity demands. For non-skeletal activity frequency 202

modelling the total time spent on skeletal activities (work/school) addresses the possible trade-offs involved in fixed versus flexible activity decisions. Incorporation of the previous day’s total number of executed activities in the following day’s activity agenda formation model addresses the dynamic links between activity generator and the activity scheduler. Yet there is ample scope to address further dynamic linkages between generator and scheduler. Incorporation of travel time in the generation models is the first attempt to make the activity generation model sensitive to the activity scheduler. The travel time variable used in the generation models refers to the travel time perception that develops over time. There is scope to incorporate learning and adaptation of the travel time perception into the generation model explicitly. For multiple-day modelling a separate module can be developed that explicitly models the travel time perception updating at the end of each scheduled day to give input to the following day’s generation component. Such additional effort will make the activity-based travel demand model more sensitive to the various TDM and TSM measures that affect the transportation network performances. Similar to travel time perception, the dynamic updating of the average durations of the activities needs to be incorporated into the activity generation models. Development of non-skeletal activity agenda takes the average durations of the activities as given input. Here the average duration refers to the perception of time requirement for performing the activity. It is necessary to address the issue of updating this perception over time. For multiple-day modelling a separate module can be developed that will update the duration perception of the non-skeletal activities based on the previous day’s scheduling. This is in some sense related to the travel time perception updating; the updated travel time perception can get into this module as an input to address the complex activity-travel relationships. The skeletal activities in this thesis are modelled as episode events rather than utility-based calculation. It is desired to develop models for explicit utility-based calculation for the skeletal activity demands. However for the short-term travel demand modelling it remains outside the scope, but to better integrate the travel demand module with other components of the ILUTE framework this issue should be addressed in the 203

ILUTE framework explicitly. There is scope to develop a model that connects mediumto long-term household decisions, e.g. job/school choice, housing choice (location and type), and automobile-ownership, through use of explicit utility-based calculations within the skeletal activity (work/school) generation model. One critical limitation of the models developed in this thesis is the lack of household-level interactions explicitly within the household members’ activity-agenda formation models, leaving the models open to accusations of incompleteness. Although household-level effects are incorporated in terms of introducing household-level random effects as well as household-level socio-economic variables, the models do not address intra-household joint activities. This limitation is due to lack of data: the Wave 1 of TAPS CHASE survey data available during this study is not complete at the household level. If we had the complete data set available, it was possible to develop intrahousehold task allocation model for Household Obligation activities and intra-household joint activities. Given the intra-household joint activity demands, the individual’s activity-agenda can be modelled excluding the time required for those activities. But total time spent for intra-household joint activities should be considered in the individual’s agenda formation models as variables to recognize their influence, similar to the way in which the skeletal activities (work/school) are modelled separately but enter into the nonskeletal activity-agenda formation model. Another important issue needing further investigation is activity location choice. This thesis has considered the question of whether start time needs to be considered at the activity generation level, but it is also necessary to investigate whether activity location(s) choices should also be taken into consideration at the activity-agenda formation level or not. This issue is related to the travel time perception updating as described earlier.

10.4.2 Data Requirement Almost all of the further investigation requirements as described in the earlier section depends upon the availability of activity diary data containing multi-day and multi-person (complete at the household level) information. On obviously related question that has been remained open in the thesis is defining the rhythm of life. The 204

models developed in this thesis are intended to support both single-day as well as multiple-day activity generation models. It is justified that a multi-day modelling framework is better than a single-day model. But what the modelling span that fairly encompasses the rhythm of activity-travel behaviour should be still remains unanswered. It is obvious that even for a week-long model the beginning and end days remain censored as we don’t model before and after those days. Assuming a week as the rhythm of activity-travel behaviour, successive iteration of a week-long model can overcome the issues of end-censoring but it is necessary to justify whether the week we are modelling represent a typical week that covers the variations of the dynamics of activity-travel behaviour sufficiently. The data source available during this study, Wave 1 of TAPS, CHASE survey is a week-long activity diary survey. So for the first and last day the observations are left and right censored consecutively. The findings from this thesis provide encouragement to look for datasets that have similar information as in the TAPS Wave 1 CHASE survey but which are also complete at the household level and have information for time periods greater than one week In addition to possible future data collection efforts within the Toronto area, it is also logical to use data sources collected in other areas that contain the information that we are interested in. Two possible such data sources for future investigation are: the Quebec City Panel Survey (QCPS) (Lee-Gosselin et al, 2006) and mobiDrive (Axhausen et al, 2002). The advantage of QCPS is that it is similar to CHASE in design and it is complete at the household level (all household members participated in the survey). The important criterion of mobiDrive is that it is a six-week travel diary survey. In general a significant amount of research in terms of investigation as well as model development remains before the activity generation component of activity-based travel demand model play its full role in fulfilling the basic requirement of activity-based modelling: modelling the derived demand per se. In some ways the thesis opens the door of opportunity for further research in this area and points towards the possibility of developing empirical operational models.

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10.5 Final Remarks Activity generation modelling is an engaging research topic because it must deal with the interactions of different household decisions, which differ from each other in terms of planning and execution dynamics. In general, the activity generation component of travel demand should model the derived activity demands that result from the interactions among long-, medium- and short-term household decisions. From the ILUTE point of view this is the component that acts as the interface between the travel demand module and all other modules of an integrated modelling framework. The step by step, inductive research approach adopted within this thesis attempts to look at this long-neglected topic in a holistic way, by reviewing the existing literature, developing a conceptual framework, asking critical questions regarding behavioural hypotheses, and using advanced econometric techniques to find answers to several critical questions and to begin the development of operational models. The enduring contribution of this thesis depends on its attempts to define previously undefined or loosely defined concepts by sketching a modelling framework, defining critical definitions, applying advanced econometric modelling techniques, and exposing critical issues for further investigation and model development, with the overall intention to make travel-demand models sufficiently sensitive to different policy measures as well as to better integration them within an ILUTE framework.

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