A CAUSAL MAPPING APPROACH TO CONSTRUCTING BAYESIAN ...

SCHOOL OF BUSINESS WORKING PAPER NO. 289 A CAUSAL MAPPING APPROACH TO CONSTRUCTING BAYESIAN NETWORKS†

Sucheta Nadkarni∗ • Prakash P. Shenoy∗∗

November 2000***

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Manuscript received:

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Sucheta Nadkarni is an Assistant Professor in the Department of Management at the University of Nebraska at Lincoln, College of Business Administration, P.O. Box 880491, Lincoln, NE 68588-0491. Email: [email protected] ∗∗

Prakash P. Shenoy is the Ronald G. Harper Distinguished Professor at the University of Kansas School of Business, 1300 Sunnyside Av, Lawrence KS 66045-7585. Email: [email protected] ***

The research reported in this paper has been supported by two grants from the Kansas University Business School PhD Summer Research Fund, and by a grant from the Kansas University General Research Fund to the second author. An earlier version of this paper was presented at INFORMS-Philadelphia in November 1999. We are grateful to Sonali Murthy and Greg Freix, for their comments and discussions.

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TABLE OF CONTENTS Abstract ...................................................................................................................................... 1 1 Introduction .......................................................................................................................... 1 2 Causal Maps ......................................................................................................................... 2 2.1 Construction of Causal Maps........................................................................................ 3 3 Bayesian Networks ............................................................................................................... 8 3.1 Semantics..................................................................................................................... 9 3.2 Making Probabilistic Inferences ................................................................................. 11 4 Using Causal Maps to Construct Bayesian Networks .......................................................... 11 4.1 Modifying Causal Maps ............................................................................................. 12 4.2 Deriving Parameters................................................................................................... 17 4.3 Validating the Bayesian Network ............................................................................... 18 5 A Case Study: IT Application Outsourcing Decision........................................................... 19 6 Summary and Conclusions.................................................................................................. 27 References ................................................................................................................................ 28

A CAUSAL MAPPING APPROACH TO CONSTRUCTING BAYESIAN NETWORKS Sucheta Nadkarni • Prakash P. Shenoy Abstract This paper describes a systematic procedure to construct Bayesian networks from domain knowledge of experts using the causal mapping approach. We outline how causal beliefs of experts can be represented as causal maps, and how the graphical structure of causal maps can be modified to construct Bayes nets. Probability encoding techniques can be used to assess the numerical parameters of the resulting Bayes nets. We illustrate the construction of a Bayes net starting from a causal map of a systems analyst in the context of an information technology application outsourcing decision. Index Terms: Causal maps, cognitive maps, Bayesian networks, Bayesian causal maps

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Introduction

Two different approaches have been used to construct Bayesian networks—data-based approach and knowledge-based approach. The data-based approaches outline procedures by which Bayesian networks can be constructed using data [1]. The knowledge-based approach emphasizes the importance of domain knowledge of experts in constructing Bayesian networks. The knowledge-based approach is especially useful in situations where domain knowledge is crucial and availability of data is scarce. Recently, there has been a growing interest in the use of causal maps to represent domain knowledge of decision-makers [2, 3, 4]. Causal maps are cognitive maps that represent the causal knowledge of subjects in a specific domain. Causal maps (also called cognitive maps, cause maps, etc.) have been used extensively in the areas of policy analysis [5] and management sciences [6, 7] to represent salient factors, knowledge, and conditions that influence decision making. Since causal maps represent domain knowledge more descriptively than other models such as regression or structural equations, they are useful tools to construct Bayesian networks. Moreover, causal maps lend themselves to different types of statistical analysis including matrix algebra and network analytic methods [5, 8, 9], system dynamics [10, 11], decision trees [12] and neural networks [13]. In this study, we use the theory of causal maps to construct Bayesian networks. An outline of the remainder of the paper is as follows. In Section 2, we discuss the definition and construction of causal maps. In Section 3, we discuss Bayesian networks, their semantics,

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and the process of making inferences. In Section 4, we propose a procedure for constructing a Bayesian network starting from a causal map. In Section 5, we discuss a case study of an online ticketing application outsourcing decision in a technology organization. Finally, in Section 6, we conclude with a summary and a statement of future research. 2

Causal Maps

Causal maps are directed graphs that represent the cause-effect relations embedded in managers’ thinking [14]. [3] defines a causal map as a “directed graph characterized by a hierarchical structure which is most often in the form of a means/end graph.” Causal maps express the judgment that certain events or actions will lead to particular outcomes. Causal maps make the following three assumptions about cognition in the context of decision making: • • •

Causal associations are a major way in which decision problems can be described and understood; Causality is the primary form of post-hoc explanation of decision outcomes; and Choice among alternative decision actions involves causal relations.

The three components of a causal map are nodes representing causal concepts, links representing causal connections among causal concepts, and strengths (can be positive or negative) representing causal value of causal connections. Figure 1 depicts a causal map of a systems analyst in the context of an information technology application outsourcing decision. Concepts. A concept is a single ideational category [15]. There is no universal meaning of a concept in a causal map. Rather, its meaning is determined by other concepts to which it is linked in a map. A concept can be a single word such as ‘feasibility’, a composite word such as ‘hardware cost’, or a more complex phrase such as ‘flexibility in customization.’ The final coded map in Figure 1 shows concepts denoted by composite words (software cost) and complex phrases (in-house IT cost, time to market and IT application outsourcing). Causal connections. A causal connection is the tie that links two concepts together. A causal connection is defined in terms of an antecedent-consequence relationship and is represented with a unidirectional arrow. A concept at the tail of an arrow is taken to be the cause of the concept at the head of the arrow. In Figure 1, for example, Software Cost is a cause of In-house IT cost and In-house IT Cost is an effect of Software Cost. A causal connection can be positive or negative. A positive connection indicates that an increase in the causal concept leads to an increase in the effect concept whereas a negative connection indicates that an increase in the causal concepts leads to a decrease in the effect concept. Figure 1 shows both positive and negative causal connections. An increase in Software Cost leads to an increase in the In-house IT Cost which implies a positive relation. Similarly, an increase in In-house IT Cost causes companies to

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Outsource IT Applications. On the other hand, if a company focuses on a shorter time to market, it will outsource its IT application. This indicates a negative relation between Time to Market and Outsourcing IT Application. Figure 1. A Causal Map of a Systems Analyst for an IT Application Outsourcing Decision

S: Software Cost + C: In-house IT Cost

T: Time to Market −

+ O: Outsourcing IT Application

Causal value. A causal value represents the strength of a causal connection. Different techniques have been employed to derive the strength of the causal connection including social networks and matrix algebra [5, 15, 9], decision theory [12], system dynamics [10, 11] and Bayesian probabilities [16]. The choice of techniques used to define the strength of causal connections is determined by the purpose of analysis. 2.1

Construction of Causal Maps

There are four major steps in constructing causal maps. These steps are shown in Figure 2 and the different considerations involved in each step are discussed in the following paragraphs. Figure 2. Major Steps in the Construction of Causal Maps STEP 1: Causal Mapping Approach

STEP 2: Data Elicitation

STEP 3: Derivation of Causal Maps

STEP 4: Analysis of Causal Maps

Causal mapping approach. The first step in the construction of causal maps involves selection of an approach to construct causal maps. Two major approaches can be employed to

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construct causal maps: confirmatory and exploratory [15]. The differences between the two approaches are shown in Table 1. The purpose of a confirmatory approach is to test prior hypothesis relating to a specific domain by answering the question: “Does the text contain what I expect it to contain?” On the other hand, the purpose of an exploratory approach is to inductively explore a new or unfamiliar domain by posing the question: “What does the text contain?” The choice of approach taken to construct causal maps affects the data elicitation process as well as the coding process. In a confirmatory approach, the concepts in the causal maps are defined a priori and these concepts are imposed on the data elicited, whereas in the exploratory approach, the words are drawn from the texts themselves. Hence, in the confirmatory approach, investigators know the number of concepts in the causal map. On the other hand, in the exploratory approach the concepts emerge from the data. Table 1. A Comparison of the Confirmatory and Exploratory Approaches for Constructing Causal Maps Confirmatory Approach

Exploratory Approach

1. Basic Question Addressed:

“Does the text contain what I expect it to contain?”

“What does the text contain?”

2. Data Elicitation Techniques Employed:

Structured techniques: structured interviews, visual card sorting, repertory grid etc.

Unstructured techniques: In-depth interviews with open-ended questions, secondary documents such as speeches, reports etc.

4. Suitability:

Suitable for well-defined and familiar domains

Suitable for ill-defined and unfamiliar domains

5. Type of Knowledge Captured:

Primarily declarative or generalized knowledge of subjects about a specific domain

Both declarative and procedural knowledge of subjects about a specific domain

The approach employed to construct causal maps affects the choice of techniques used to elicit data. For example, intrusive and structured techniques of data elicitation can be employed in confirmatory studies including structured interviews, visual card sorting and repertory grid. On the other hand, qualitative and inductive techniques such as in-depth interviews involving open-ended questions can be employed in exploratory studies. A major consideration in choice to the approach used to construct causal map is the domain being investigated. For example, confirmatory approach may be useful in clearly defined and familiar domains, whereas exploratory approach is useful for ill-defined and new domains. Finally, choice of approach also affects the type of knowledge represented in the causal maps. For example, causal maps based on a confirmatory approach represent a greater degree of generalized knowledge (also called declarative knowledge) of subjects about the domain being evaluated. This knowledge is developed by individuals over a long period and is relatively stable


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in nature. On the other hand, causal maps based on exploratory approach represent both declarative and procedural knowledge of individuals. Procedural knowledge represents implicit and explicit procedures used by a subject to perform a given task. Procedural knowledge can tell us a great deal about the structure of a given task and the repertoire of procedures that an individual can draw upon as he or she engages in it. In other words, an exploratory approach yields a richer understanding of the processes that individuals engage in decision making as well as helps us get important insight into the general knowledge that individuals have on the domain being evaluated. Data elicitation. The data elicitation step involves collecting raw data in the form of a narrative that can be used to construct causal maps. As discussed in the previous sub-section, the choice of approach (confirmatory versus exploratory) determines the techniques used to elicit data for constructing causal maps. Different techniques have been employed to elicit causal mapping data including structured methods such as the self-Q method [17], open methods based on personal construct theory [9], and textual analysis approach [5]. We use the textual analysis method for constructing causal maps because it provides a mid-range data elicitation technique which is not as intrusive and structured as structured methods and it is not as qualitative as open methods. It does not require the researcher to identify causal concepts prior to or during the interview with subjects. The advantage of this method is that it enables the researcher to let the data drive the concepts rather than eliciting an individual’s cognition from a pre-defined set of concepts [15]. The unintrusive nature of this method is especially important in representing an expert’s description and understanding of an unstructured decision problem. At the same time, it is relatively more structured than the open methods which employ primarily qualitative tools of analysis. This allows numerical analysis of the derived structures. Different sources of data can be employed to conduct textual analysis ranging from primary sources such as in-depth interviews with subjects to secondary sources including speeches, detailed reports and other documents. The choice of data source is determined by the purpose of the investigation. In-depth interviews with open-ended questions are most appropriate for eliciting expert knowledge in new and unknown domains and have been widely used in decisionmaking domains [9]. These interviews are very low on intrusiveness and yield rich understanding of both declarative and procedural knowledge of subjects about a specific domain. Structured methods are useful mainly for testing theories in clearly defined domains or for validation of relations represented in the map. Derivation of causal maps. The narrative yielded by the data elicitation process can be used to construct causal maps. There are four different steps in deriving causal maps using narrative or text yielded by the data-elicitation process [5, 15, 18, 2]. These steps are shown in Figure 3 and discussed in detail in the following paragraphs.

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Identifying causal statements in the narrative. The first step in constructing causal maps is to identify causal statements in the narrative. Causal statements are those that explicitly contain a cause-effect relationship. A causal statement links two different concepts through a causal connector. An important consideration in identifying causal statements is to define rules for recognizing causal connectors. This involves developing a comprehensive list of words or phrases that can be considered as causal connectors. Examples of such words include ‘if-then’, ‘because’, ‘so’, ‘as’ etc. The critical problem in this step is one of reliability and is addressed by [5]. One way of addressing reliability is to use multiple (two or more) raters to independently develop a list of words to define causal connectors as well as independently identify the causal statements by recognizing these connectors in the statements. The extent of agreement between the different raters may provide a numerical criterion to establish the reliability of the causal statements identified in the narrative. Figure 3 shows three causal statements contained in the narrative of a systems analyst. These statements were identified as causal statements because they contain words listed as causal connectors (‘lead to’, ‘cause’ and ‘if-then’). Raw causal maps. Once the causal statements are identified, they are broken into causal phrases, causal connectors and effect phrases to derive the raw causal maps. Raw causal maps represent cause and effect phrases contained in the narrative in the language used by the expert. Figure 3 shows how causal statement 1 is broken into the causal phrase: ‘high software cost,’ the causal connector: ‘can lead to,’ and effect phrase: ‘increase in in-house costs’ to construct raw causal maps. Since increase in software cost leads to increase in in-house cost, it is a positive relation. On the other hand, a shorter time to market leads to organizations outsourcing their IT application which implies that the relation is negative. Finally, increase in in-house costs increases the likelihood of organizations outsourcing their IT applications (positive relation). Reliability is an issue in this step and it is desirable to use multiple raters to derive raw causal maps based on the causal statements. Coding scheme. In a confirmatory approach researchers a priori define a list of concepts that they search for in the raw causal maps. However, in an exploratory approach, the coding scheme is derived from the cause and effect phrases in the raw causal maps. The raw causal maps derived in step 2 are cast in the language of the expert. In spite of their usefulness, the raw maps obscure analysis because of their complexity. Hence, there is a need to design a coding scheme to recast the raw causal maps into the final causal maps. This process of coding is called filtering or aggregation. Aggregation is the process of determining which part of the text to code, and what words to use in the coding scheme. Aggregating phrases in the raw causal maps into generalized concepts can be used to move the coded text beyond explicitly articulated ideas to implied or tacit ideas. Aggregation can also be used to avoid misclassification of concepts due to peculiar wording on the part of individuals.


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Figure 3. An Example of the Procedure for Deriving Causal Maps Identifying Causal Statements in the text

Step 1:

Examples: 1. High software costs can lead to an increase in in-house costs. 2.

A focus on shorter time to market can cause firms to outsource their IT application.

3.

If in-house costs are high then companies are more likely to outsource their IT applications.

Causal Phrase

Causal Connector

High software costs

Lead to

+

Focus on shorter time to market

Can cause

−

High in-house costs

If-then

+

Step 2:

Effect Phrase Increase in in-house cost Firms to outsource IT application Firms are more likely to outsource

Coding Scheme

Step 3:

Raw Phrase 1. High software costs 2. Increase in In-house Costs 3. Focus on shorter time to market 4. Firms outsource IT application 5. High in-house costs 6. Firms are more likely to outsource

Coded Concept Software Cost In-house Cost Time to Market Outsource IT Application In-house Cost Outsource IT Application

Final coded causal map

Step 4:

Software Costs + In-house Cost

Time to Market +

−

Outsource IT Application

However, it is possible to over-generalize where meaningful differences in the phrases in the raw causal maps are lost. Although currently there is no mathematical criteria for determining the appropriate level of aggregation, inter-coder reliability can be used to address the issue. More specifically, two or more coders could analyze a subset of raw causal maps and independently suggest a level of aggregation. The extent of concordance between the multiple coders could

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substitute for a mathematical criterion. The subjective judgment being made is about “when is critical information in the raw causal maps not being lost due to aggregation?” A number of techniques can be used by investigators to extract concepts from the text ranging from relatively non-automated techniques to highly automated techniques. One nonautomated approach typically used when taking an exploratory approach involves a close analysis of the text. In this procedure, the investigator might read a text and list all the phrases (cause and effect) in the raw causal maps and then generalize them into a set of concepts. This can be done by creating a file containing comprehensive examples of exact words or phrases in the raw causal maps that correspond to each generalized concept. A more automated approach might involve the use of a text-analysis program to identify all words used in the text. The reliability of this aggregation can be established by using multiple coders in this process and by measuring the degree of concordance between the coders. A similar method called the pre-test sorting technique has been recommended by [19] to assess inter-rater reliability. This technique involves providing multiple raters with the generalized concepts and the raw phrases and then asking them to sort the raw phrases by the concepts. Assessment of inter-rater convergence in the sorting process can be used to examine the reliability of the coding scheme. Figure 3 shows how phrases used by a systems analyst in the raw causal maps are coded into generalized concepts. For example, ‘high software cost’ is coded as ‘Software Cost,’ and focus on shorter time to market’ is ‘Time to Market.’ Both ‘increase in in-house IT cost’ and ‘high inhouse IT cost’ are coded into a single concept of ‘In-house IT cost.’ Finally, ‘firms outsource IT applications’ and ‘firms are more likely to outsource IT applications’ are coded as ‘Outsource IT Application.’ This coding was independently done by two information systems experts other than the subject and there was 100 percent convergence on the casting of raw phrases into concepts. Coded causal map. Finally, the coding scheme developed in step 3 is used to recast the raw causal maps into coded maps. A coded causal map is a network of concepts formed from causal statements in a narrative depicting directionality (cause-effect) and sign (positive and negative) of the relations between the concepts. Two statements are linked if they share one concept. For example, causal statement 1 and causal statement 3 in Figure 1 share the concept “In-house IT Cost” thus resulting in the network of “Software Cost In-house IT Cost Outsourcing of IT Application.” 3

Bayesian Networks

In this section, we briefly describe the semantics of Bayesian networks. A procedure for constructing a Bayesian network starting from a causal map is described in Section 4.


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Bayesian networks have their roots in attempts to represent expert knowledge in domains where expert knowledge is uncertain, ambiguous, and/or incomplete. Bayesian networks are based on probability theory. A primer on Bayesian networks is found in [20]. A Bayesian network model is represented at two levels, qualitative and quantitative. At the qualitative level, we have a directed acyclic graph in which nodes represent variables, and directed arcs describe the conditional independence relations embedded in the model. Figure 4 shows a Bayesian network consisting of four discrete variables: Software Cost (S), In-house IT Cost (C), Time to Market (T), and In-house Development versus ASP (O). At the quantitative level, the dependence relations are expressed in terms of conditional probability distributions for each variable in the network. Each variable X has a set of possible values called its state space that consists of mutually exclusive and exhaustive values of the variable. In Figure 4, e.g., Software Cost has two states: ‘high’ and ‘low;’ In-house IT Cost has two states: ‘high’ and ‘low;’ Time to Market has two states: ‘long’ and ‘short;’ and In-house Development Versus ASP has two states: ‘In-house Development’ and ‘ASP.’ If there is an arc pointing from X to Y, we say X is a parent of Y. For each variable, we need to specify a table of conditional probability distributions, one for each configuration of states of its parents. Figure 4 shows these tables of conditional distributions—P(S), P(C | S), P(T), and P(O | C, T). 3.1

Semantics

A fundamental assumption of a Bayesian network is that when we multiply the conditionals for each variable, we get the joint probability distribution for all variables in the network. In Figure 2, e.g., we are assuming that P(S, C, T, O) = P(S) ⊗ P(C | S) ⊗ P(T) ⊗ P(O | C, T), where ⊗ denotes pointwise multiplication of tables. The rule of total probability tells us that P(S, C, T, O) = P(S) ⊗ P(C | S) ⊗ P(T | S, C) ⊗ P(O | S, C, T). Comparing the two, we notice that we are making the following assumptions: P(T | S, C) = P(T), i.e., T is independent of S and C; and P(O | S, C, T) = P(O | C, T), i.e., O is conditionally independent of S given C and T. Notice that we can read these conditional independence assumptions directly from the Bayesian network graph as follows. Suppose we pick a sequence of the variables such that for all directed arcs in the network, the variable at the tail of each arc precedes the variable at the head of the arc in the sequence. Since the directed graph is acyclic, there always exists such a sequence. In Figure 4, e.g., one such sequence is S C T O. Then, the conditional independence assumptions can be stated as follows. For each variable in the sequence, we are assuming it is conditionally independent of its predecessors in the sequence given its parents. The essential point here is that missing arcs (from a node to its successors in the sequence) signify conditional

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independence assumptions. Thus, the lack of an arc from S to T signifies that S is independent of T; the lack of an arc from C to T signifies that T is independent of C; and the lack of an arc from S to O signifies that O is conditionally independent of S given C and T. Figure 4. A Bayesian Network with Conditional Probability Tables P(S)

High Low 0.75 0.25

S: Software Cost P(C | S) High High 0.95 Low 0.10

Low 0.05 0.90

C: In-house IT Cost

P(T)

Long 0.50

Short 0.50

T: Time to Market

O: Outsourcing IT Application

P(O | C, T) High, Long High, Short Low, Long Low, Short

High 0.10 0.40 0.30 0.95

Low 0.90 0.60 0.70 0.05

In general, there may be several sequences consistent with the arcs in a Bayesian network. In such cases, the list of conditional independence assumptions associated with each sequence can be shown to be equivalent using the laws of conditional independence [21]. [22] and [23] describe other equivalent graphical methods for identifying conditional independence assumptions embedded in a Bayesian network graph. Unlike a causal map, the arcs in a Bayesian network do not necessarily imply causality. The (lack of) arcs represent conditional independence assumptions. How are conditional independence and causality related? Conditional independence can be understood in terms of relevance. If Z is conditionally independent of X given Y, then this statement can be interpreted as follows. If the true state of Y is known, then in assigning probabilities to states of Z, the states of X are irrelevant. In practice, the notion of direct causality is often used to make judgments of conditional independence. Consider a situation where X directly causes Y and Y in turn directly


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causes Z, i.e., the causal effect of X on Z is completely mediated by Y. Then it is clear that although X is relevant to Z, if we know the true state of Y, further knowledge of X is irrelevant (for assigning probabilities) to Z, i.e., Z is conditionally independent of X given Y. This situation is represented by the Bayesian network X → Y → Z in which there is no arc from X to Z. As another example, consider the situation where X directly causes Y and X also directly causes Z. Although knowledge of Y is relevant to Z (if Y is true then it is more likely that X is true which in turn means that it is more likely that Z is true), once we know the true state of X, then further knowledge of Y is irrelevant to Z, i.e., Y is conditionally independent of Z given X. This situation is represented by the Bayesian network Z ← X → Y in which there is no arc from Y to Z or vice-versa. Finally as a third example, consider the situation where X and Y are two independent direct causes of Z, i.e., X and Y are unconditionally independent. But if we learn something about the true state of Z, then X and Y are no longer irrelevant to each other (if Z is believed to be true and X is false, then it is more likely that Y is true), i.e., Y is not conditionally independent of X given Z. This situation is represented by the Bayesian net X → Z ← Y in which there is no arc from X to Y or vice-versa. 3.2

Making Probabilistic Inferences

Inference (also called probabilistic inference) in a Bayesian network is based on the notion of evidence propagation. Evidence propagation refers to an efficient computation of marginal probabilities of variables of interest, conditional on arbitrary configurations of other variables, which constitute the observed evidence [20]. Once a Bayesian network is constructed, it can be used to make inferences about the variables in the model. The conditionals given in a Bayesian network representation specify the prior joint distribution of the variables. If we observe (or learn about) the values of some variables, then such observations can be represented by tables where we assign 1 for the observed values and 0 for the unobserved values. Then the product of all tables (conditionals and observations) gives the (unnormalized) posterior joint distribution of the variables. Thus, the joint distribution of variables changes each time we learn new information about the variables. 4

Using Causal Maps to Construct Bayesian Networks

In this section, we sketch a procedure for constructing Bayesian causal maps starting from a causal map. This procedure consists of three major steps. In the first step, the structure of the causal map is modified to make it compatible with the Bayesian network. In the second step, the numerical parameters of the modified structure are derived using probability encoding techniques. Finally, the Bayesian Network constructed from the causal map is validated using validation techniques from causal mapping literature and operations research literature.

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Modifying Causal Maps

The structure of the causal maps requires modification to make it compatible with the Bayesian network. Four major modeling issues need to be addressed in the modification procedure. These issues are discussed in the following paragraphs. Conditional independencies. A network model can be either a dependence map (D-map) or an independence map (I-map) [22]. A D-map guarantees that vertices (concepts) found to be connected are indeed dependent; however, it may display a pair of dependent concepts as a pair of separated vertices (concepts). An I-map, on the other hand, guarantees that vertices (concepts) found to be separated are indeed conditionally independent, given other variables. However, it may display a pair of independent concepts as connected vertices (concepts). A model that is both a D-map and an I-map is called a perfect map. A causal map is a directed graph that depicts causality between variables as perceived by individuals. Since an arrow between two variables implies dependence, it is a D-map. The absence of an arrow between two variables does not imply a lack of dependence. In other words, a causal map does not guarantee that variables found to be separated correspond to independent concepts, i.e., it is not an I-map. Bayesian networks, on the other hand, are I-maps. Given a sequence of variables, an absence of arrow from a variable to its successors in the sequence implies conditional independence between the variables. Conditional independence is an important issue in making inferences since it specifies the relevance of information on one variable in making inference on another. Thus, if we are to regard a causal map as a Bayesian network, it is important to first convert the causal map model from a D-map to an I-map. This can be done in consultation with the expert (whose causal map is at issue) by ensuring that all dependencies are depicted in the causal map. An adjacency matrix can be used to achieve this. An adjacency matrix is the matrix of all possible direct cause-effect relations among the variables where the (i, j) entry indicates the existence of a direct causality relation from variable i to variable j [5]. The adjacency matrix is represented as an n by n matrix in which the columns and rows are labeled with the names of the variables. The rows represent causes and columns represent effects. For each pair of variables, the subject (whose causal map is at issue) is asked to specify if there is a causal relation (scored initially as 1 for yes, and 0 for no) and if yes, to specify which is the cause and which is the effect. Subject can be instructed that if (s)he considers the two variables to have reciprocal influences, (s)he should indicate which one has the more dominant causal influence (to eliminate the occurrence of direct reciprocal causality wherein a variable is both a direct cause and an effect of another variable). Once the subject has identified the existence of a causal relation, (s)he can then be asked to indicate nature of the relation (positive or negative). Thus when the


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subject is finished, each cell in the adjacency matrix will have one of the three values: −1 for a negative causal relation, 0 for no causal relation, or +1 for a positive causal relation. Figure 5 indicates a part of a Bayesian causal map of a systems analyst relating to the IT application outsourcing decision. The solid arrows (from Net Application Cost Savings to IT Application Outsourcing and Risk Preferences to IT Application Outsourcing) were identified in the original causal map. The dashed arrows (from Labor Market to Feasibility, from Feasibility to IT Application Outsourcing, from Application Process to Net Application Cost Savings and from Application Process to Risk Preferences) were identified in the process of making the original causal map an I-map. These unmodeled dependencies affect the inferences made on Feasibility, Net Application Cost Savings, Risk Preferences and IT Application Outsourcing. For example, in the original causal map, inference on Feasibility, Net Application Cost Savings and Risk Preferences is not conditional on any other variables in the map. For example, Labor Market is not relevant in making inference on Feasibility. Similarly Application Process is not relevant in making inference on Net Application Cost Savings and Risk Preferences. Moreover, IT Application Outsourcing is conditional on Net Application Cost Savings and Risk Preferences, but not on Feasibility. However, in the modified map, Feasibility is relevant to making inference on IT Application Outsourcing. This example illustrates how unmodeled dependencies can change the inferences that can be made on the various variables in the causal maps. After incorporating all possible dependencies between variables, the revised causal map is a perfect map—a D-map as well as an I-map1. An arrow between two variables in the map implies a causal relation between them; whereas missing arrows imply conditional independence. Reasoning underlying cause-effect relations. Causal maps identify individuals’ perceptions of cause-effect relationships between variables based on language rather than the reasoning processes [15]. Studies in managerial cognition indicate that individuals reason by accumulating possibly significant pieces of information and organizing them in relation to each other so as to be able to combine them into a conclusion and decision [24]. Individuals use such reasoning processes to put information together as a cause-effect series of events leading to predicted future courses of events. These reasoning processes are important in decision making and in making inferences about future decision outcomes.

1

If we start with an arbitrary probability distribution, it is not always possible to find a Bayesian network representation that is a perfect map [22]. Our starting point is an expert’s causal model and we are assuming that we can always find a Bayesian network representation that is a perfect map.

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Figure 5. Making a causal map a perfect map

Labor Market

Application Process

Feasibility

Net Application Cost Savings

Risk Preferences

Outsourcing IT Application

Literature on logic suggests that individuals perceive cause-effect relationships based on two types of reasoning: deductive and abductive [25, 26]. A reasoning process is called deductive when we reason from causes to effects, i.e., in the direction of causation. For example, in the medical domain, risk factors (e.g., smoking) are regarded as causes, and the diseases (e.g., lung cancer) as effects. When a physician, confronted with a patient who has been a smoker, reasons that the patient is at risk for lung cancer, (s)he is reasoning deductively. A reasoning process is called abductive when we reason from effects to causes, i.e., in the direction opposite to causation. For example, diseases (e.g., lung cancer) are regarded as causes of symptoms (e.g., positive X-ray). When a physician, after observing a patient’s positive x-ray result, concludes that the patient is probably suffering from lung cancer, (s)he is reasoning abductively. The difference between deductive and abductive reasoning underlying causal statements and their effect on representation of causal linkages are illustrated in Figure 6. Causal statement 1 involves the use of logical deduction and the reasoning is in the direction of causation. This is correctly reflected in the arc from Knowledge, Skills and Abilities (KSAs) to Labor Cost. Causal statement 2 involves abductive reasoning. Since KSAs is a latent variable, and Labor Cost is one of the observable measures of KSAs, the decision maker is making inference about the latent variable KSAs required for IT application based on the observable variable Labor Cost. This does not imply that Labor Cost causes KSAs. The reasoning in this causal statement is in the direction opposite of causation. Causal statements involving abductive reasoning are misrepresented in a causal map by an arc from effect to cause. Such misrepresentation can also lead to redundant circular relations between variables in the causal map. For instance, both the arrows in Figure 6 may be represented in a causal map creating a loop. A distinction between


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deductive and abductive reasoning behind the causal linkages is essential to establish accurate directions of linkages in causal maps. The emphasis in deriving causal maps should be on the causal theory underlying the causal statements rather than the language used. Figure 6. Distinguishing Between Deductive and Abductive Reasoning Statement 1: If knowledge, skills and abilities required for in-house application are high, then the labor cost for in-house application will be very high. Causal map based on statement 1: Knowledge, Skills & Abilities

Labor Cost

Statement 2: If the labor cost is high, then it implies that a high level of knowledge, skills and abilities are required for in-house application. Causal map based on statement 2: Knowledge, Skills & Abilities

Labor Cost

Distinguishing between direct and indirect relationships. The procedure for deriving causal maps does not provide for a distinction between ‘direct’ and ‘indirect’ relationships between concepts [3, 4]. This distinction is important to identify conditional independencies in the causal maps. Figure 7 depicts how a lack of distinction between direct and indirect relationship affects conditional independence assumptions in a causal map. In Figure 7, both Application Process and Financial Cost Savings affect Application Outsourcing. In the modified Bayesian causal map, there is no linkage between Application Process and Application Outsourcing implying that Application Process impacts Application Outsourcing decision strictly through Financial Cost Savings. If we have complete information on Financial Cost Savings, any additional information on Application Process would be irrelevant in making inferences about Application Outsourcing Decision. Moreover, this change also affects the inferences made on Application Cost Savings. In the original causal map, Application Cost Savings is not conditional on any other variable and Application Process is not relevant to making inferences on Application Cost Savings. However, in the modified map, Application Cost Savings is conditional on Application Process.

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Figure 7. Distinguishing between Direct and Indirect Relations Original Causal Map Application Process

Bayesian Causal Map Application Process

Application Cost Savings

Application Outsourcing

Application Cost Savings

Application Outsourcing

A clear distinction between direct and indirect cause-effect relations is important for three reasons. First, it helps us understand the nature of relations between variables. It tells us whether the effect of a variable on another is completely modeled by the effect of the first on a third mediating variable (which in turn is a cause of the second). Second, if Application Process (in Figure 7) affects Application Outsourcing Decision only through Financial Cost Savings (in Figure 7), then an arrow from Application Process to Application Outsourcing decision is redundant and increases the complexity of the representation. Finally, distinction between direct and indirect cause-effect relations allows incorporation of conditional independencies in causal maps. As we have seen earlier, conditional independencies are critical in making inferences on the variables in large causal maps. Eliminating circular relations. Causal maps are directed graphs and are characterized by a hierarchical (or acyclic) structure. However, circular relations or causal loops destroy the hierarchical form of a graph. Circular relations in the causal maps violate the acyclic graphical structure required in a Bayesian network. It is therefore essential to eliminate circular relations to make causal maps compatible with Bayesian networks. Causal loops can exist for two reasons [2, 3, 4]. First, they may be coding mistakes that need to be corrected. Second, they may represent dynamic relations between variables across multiple time frames. Coding mistakes can be rectified by clarifying causal linkages between variables in terms of deductive versus abductive reasoning or direct versus indirect linkage; issues already discussed in previous paragraphs. However, if causal loops exist despite these clarifications, then they can be eliminated by aggregating the variables into a single variable. In causal maps, causal assertions of individuals are aggregated (or clustered) into broader concepts. All variables or nodes in circular relations are of the same hierarchical status and so if aggregated to a single node, the general form of the causal map can still be hierarchical.


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In addition to coding mistakes, feedback loops may indicate dynamic relations between variables over time. In such cases, part of the linkages in the loop pertains to a current time frame and some linkages pertain to a future time frame. In such cases, deaggregating the variables into two time frames can often solve the problem of circularity. Figure 8. Deaggregating Variables over Time Net Application Value-added

IT Application Outsourcing


t1

Net Application Value-added

t2


For example, Figure 8 shows a reciprocal causal relation between IT Application Outsourcing and Net Application Value-added and reasoning underlying this circular relation. Arrow t1 implies that a high net application value-added from outsourcing causes companies to outsource their IT application. Arrow t2 implies current application outsourcing decision can affect future net-application value added. The circular relation has resulted from aggregation of the variable IT Application Outsourcing across two time frames: t1 and t2. After de-aggregating IT Application Outsourcing into two time frames, we get an acyclic relation between the three variables. To make the causal map acyclic, we arbitrarily retain one of the two relations and exclude the other from the causal map. An acyclic structure of the causal map is essential to the inference process and to make causal maps compatible with Bayesian networks. Bayesian networks are unable to represent reciprocal causal relations. 4.2

Deriving Parameters

Once the structure of causal maps is compatible with BNs, numerical parameters of this modified structure need to be assessed so that the propagation algorithms in the Bayesian network can be used to make inferences. Derivation of parameters of the Bayesian network. The causal map has been used primarily to qualitatively describe the variables used by experts to describe a particular decision domain. The focus of causal maps is to analyze the structure of the map using network analysis techniques [27]. Consequently, the uncertainty associated with the different variables in causal map is not captured by a causal map. All variables are assumed to have the same level of uncertainty. A Bayesian network allows a decision-maker to make inferences on the different variables in the network based on the information about other variables in the network. In order

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to be able to make inferences, we need to assess uncertainty associated with every variable in the map and the interactive effects of multiple causal variables on effect variables. One common way of capturing uncertainty of the variables in a Bayesian network is to measure a person’s ‘degree of belief’ for that variable conditional on the states of its parents. This uncertainty associated with the variables in a decision model is sensitive to the context in which the certainties have been established. The process of measuring degrees of belief is commonly referred to as probability assessment or probability encoding procedure. Defining parameters. Many different probability encoding techniques are available (for a detailed review see [28]) wherein a subject responds to a set of questions either directly by providing numbers or indirectly by choosing between simple alternatives or bets. The choice of response mode (direct or indirect) as well as the choice of a method within each mode depends on the preferences of the subject. [28] describes three direct response-encoding methods—cumulative probability, fractiles and verbal encoding—to elicit probabilities. In the cumulative probability method, the subject is asked to assign the cumulative probability associated with a variable conditioned on the states of its parent variables. The probability response can be expressed either as an absolute number (0.30), as a discrete scale (“three on a scale from zero to ten”), or as a fraction using a discrete scale (“three in ten”). Verbal encoding uses verbal descriptions to characterize events in the first phase of the encoding procedure. The descriptors used are those to which the subject is accustomed to such as “high,” “medium” or “low.” The quantitative interpretation of the descriptors is then encoded in a second phase. The form chosen to express the probability (absolute number, percentage, fraction or verbal) should be the one most familiar to the subject. When a variable has many parents, the number of probability assessments can be reduced by assessing the nature of the relationship between the variable and its parents such as noisy-OR, noisy-AND, etc. [29, 30]. Once the parameters of the causal map are identified, propagation algorithms can be used to make inferences about the variables in the causal maps. 4.3

Validating the Bayesian Network

We propose validation procedures for both qualitative and quantitative stages of constructing Bayesian causal maps. In the qualitative stage, we extend the reliability and validity techniques suggested by causal mapping studies [5, 15, 3, 2] to the modification procedures proposed in our study. A typical method used to establish reliability of the cognitive mapping procedure is to achieve a consensus among multiple raters for all the stages of the cognitive mapping procedure. Accordingly, the modifications to the original causal map (described in Section 4.1) can be made through a consensus between multiple raters. For example, modifications agreed to by two or more raters can be retained, whereas those for which agreement cannot be reached can be thrown


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out. Such inter-rater reliability also reduces the possibility that researchers’ own interpretations have contaminated the modification process. Validation of Bayesian causal maps involve establishing that the modifications made to the original causal map measure what they are intended to measure. This validation has to be established at the qualitative level as well as the quantitative level. Typical practice suggests that researchers check the interpretation of variables in a causal map with the subjects involved. This can be extended to the modification procedure in the qualitative phase wherein modifications can be made to the original causal maps after consultation with the subjects involved. At the quantitative level, sensitivity analysis approach from operations research can be used to validate the map [31, 32]. Sensitivity analysis consists of examining the posterior marginals of decision variables under different scenarios and then corroborating these marginals with the domain expert. The sensitivity analysis procedure is illustrated in the next section in the context of a case study. 5

A Case Study: IT Application Outsourcing Decision

This section describes a case study of a construction of a Bayesian causal map. First, we illustrate how starting from a causal map, we constructed the qualitative structure of a Bayesian causal map. We show how additional information can be collected from a subject to address the modeling issues discussed in Section 4.1 as well as to derive the numerical parameters of the Bayesian causal map. Second, we show how a Bayesian network software can be used to draw probabilistic inferences in a Bayesian causal map. Decision context. We used a real-time IT application outsourcing decision analyzed by a systems analyst of a big-five consulting firm. We chose this decision context for two major reasons. First, IT application outsourcing is an emerging domain and the boundaries of this domain are not clearly defined. Therefore, this domain is appropriate for the exploratory approach of constructing causal maps. Second, the decision alternatives, outcomes and application environmental factors involved uncertainty and required the systems analyst to use his/her intuition. It allowed the analyst to develop his/her own framework in diagnosis, analyses, and recommendations of decision options. The IT application outsourcing decision was as follows. A major airline company had recently decided to develop an online ticketing system. Although the company is a wellestablished company with a well-developed regular ticketing processes, online ticketing is a totally new concept to the company. The decision faced by the airline company is whether to develop the online ticketing system in-house or to use an application service provider’s (ASP) application. The role of the system analyst was to analyze the decision and suggest a recommendation.

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Subject. The subject was a systems analyst in a big-five consulting firm. She had an MBA in information systems and 2 years of experience in systems analysis and design. The subject was a part of the team that analyzed the online ticketing outsourcing decision. Data collection. The subject was asked to provide in writing a detailed description of the airline outsourcing decision. Based on the written description, an intensive interview (two to three hours) was conducted with the subject to elicit her analysis of the decision context and decision recommendations. The open-ended interview technique using probes suggested by [33] was used to elicit knowledge from the subject. This technique is relatively unstructured and ideal for extracting qualitative and subjective knowledge of individuals. The subject was asked to identify factors that she considered important to the decision and to intuitively describe the decision recommendation. The narrative yielded by this interview was used to construct the original causal map shown in Figure 9 below using the textual analysis method outlined in section 2.2. Follow-up interviews were conducted with the subject to modify the structure of the causal map to construct the qualitative structure of the Bayesian causal map. The next few paragraphs discuss this procedure in detail. Causal map of online ticketing decision. The original causal map shown in Figure 9 describes the subject’s causal perceptions of the decision problem in the online ticketing decision. There are 23 variables in the map that can be broadly classified as in-house application cost variables, ASP outsourcing cost variables, risk determinant variables, application environment variables, and decision variables. A brief definition and the possible states of each variable are shown in Table 2. The variable In-house Feasibility was not captured in the original causal map. It was identified in the follow-up interviews conducted with the subject. Constructing a Bayesian network starting from a causal map. The causal map in Figure 9 was used to construct a Bayesian network. The procedure proceeded in two steps. In the first step, we conducted two follow-up interviews with the subject. The first interview was conducted to modify the causal map and address the four modeling issues discussed in Section 4.1. The purpose of the second interview was to validate the modifications made to the original causal map based on the first interview. In the first follow-up interview, the subject was provided with the original causal map and was requested to provide clarifications of the cause-effect relations in the map based on the following four instructions.


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Figure 9. The Original Causal Map of a Systems Analyst for the Online Ticketing Application Outsourcing Decision Knowledge Skills & Abilities Labor Cost Fluctuations in Sales

Labor Market Hardware Cost Software Cost

In-house Application Cost

Diversity of Price Deals Offered ASP Pricing Structure

Maintenance Cost

Product Customization

ASP Outsourcing Cost

Sensitivity of Passenger Data

Online Ticketing Application Cost Business Domain

Process Maturity

Risk Preferences

Reactive Change in Prices

Maintaining Application Currency

Time to Market

In-house or ASP

Application security capability Net Application Value-added

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Table 2. Definition and States of Variables in the Causal Map Variable

Definition

States

In-house Application Cost Variables 1. Knowledge, Skills & Abilities (KSAs)

The set of skills required to successfully design, develop, and implement the online ticketing application in-house such as language skills, programming skills, database skills, process skills, and project management skills.

Broad, Narrow

2. Labor Market

The total number of IS persons available for hiring who have the knowledge, skills, and abilities relevant to the current application domain.

Large, Small

3. Labor Cost

The total cost of hiring individuals possessing the requisite KSAs for designing, developing, and implementing in-house application for inline ticketing.

High, Low

4. Software Cost

The total cost of purchasing and developing the software necessary to design, develop, and implement in-house application including off-the-shelf software modules, developing CASE Tools, and ancillary software.

High, Low

5. Hardware Cost

The total cost of buying the necessary hardware equipment for developing in-house application such as computers, workstations, and networking equipment.

High, Low

6. Maintenance Cost

The total cost of modifying, updating and system testing the necessary application hardware & software. 7. In-house Application The sum total of software cost, hardware cost, maintenance Cost cost, and labor cost. ASP Outsourcing Cost Variables 8. ASP Price Structure The form of fee such as a licensing fee charged by the application service providers (ASPs) for the use of their application. 9. ASP Outsourcing Cost The total cost incurred to outsource the application to an ASP and includes the fee charged by the ASP and any hardware or networking cost incurred. 10. Online Ticketing A comparison of the cost of developing in-house application Application Cost to the cost of outsourcing the application to an ASP to determine which alternative is better cost-wise. Risk Determinant Variables 11. Business Domain Can be either primary to the value chain of the business or it may support the primary activities. Primary activities such as in-bound logistics, manufacturing and sales are central to the business. Supporting activities such as R&D, human resources indirectly affect value creation. 12. Process Maturity Whether the online ticketing process already exists in the company or whether it is totally new to the company. 13. Risk Preferences The risk orientation of the decision-makers and/or corporate culture within the company in terms of willingness to take risk. 14. Feasibility The degree to which development of in-house online ticketing application is technically, legally, and organizationally feasible.

High, Low Relatively High, Relatively Low High, Low Relatively High, Relatively Low In-house>ASP, ASP>In-house

Primary, Supporting

Existing, New High risk, Low risk High, Low


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Table 3. Definition and States of Variables in the Causal Map (continued from Table 2). Variable

Definition

States

Application Environment Variables The periodic variations in the sales, e.g., daily, weekly and monthly. 15. Fluctuation in Sales

High, Low

16. Diversity of Price Deals Offered

The total number of and the complexity of the tariff rates offered by the airline company and the extent to which these are different from each other.

High, Low

17. Reactive Changes in Prices 18. Product Customization

The degree to which airline prices change in response to external environmental (e.g. change in fuel prices) and competitive forces. Refers to the degree to which the online ticketing application needs to be adapted to and supportive of diversity of price deals offered by the airline company and the external environmental factors affecting changes in airline prices. The degree to which the customer data is sensitive to issues of privacy, confidentiality, transmission, storage, and security. The extent to which the application is capable of addressing the data security issues, e.g., restriction of the number of parties who have access to the data processed by and stored in the application.

Frequent, Non-frequent High, Low

21. Maintaining Application Currency 22. Time to Market

The cost and level of effort required to maintain the currency of the application through revisions and upgrades.

High, Low

The quickness and agility with which the service can be marketed to the customer. The shorter the time to market, the more efficient the system.

Short, Long

23. Net Application Value-added (NVA) Decision Variables

Comparison of the net value-added (NVA) through either in-house development or ASP's application.

NVA In-house, NVA ASP

24. Online Ticketing Outsourcing Decision

The decision whether to develop in-house application or use the ASP’s application.

In-house, ASP

19. Sensitivity of Passenger Data 20. Application Security Capability

High, Low High. Low

1. Direct causality between variables. The subject was instructed that an arrow between two variables in the map should represent a direct cause-effect relationship only. This resulted in two major changes in the linkages in the original map. First, in the original causal map, Business Domain was directly related to In-house or ASP variable. However, the subject clarified this relation in the follow-up interview and suggested an indirect relationship between Business Domain and In-house/ASP variable. In the modified map, Business Domain indirectly affects Inhouse/ASP through two different variables: Risk Preferences and Application Cost. Second, there was a direct relation between Application Maturity and In-house/ASP variable in the original causal maps. However, in the follow-up interview, it was found that Application Maturity also affects In-house/ASP variable through Risk Preferences and Application Cost. 2. Conditional independence. The subject was instructed that the absence of an arrow between two variables in the map should represent a lack of dependence between the two variables. This resulted in an additional variable and five additional links in the original map. Overall Feasibility was a new variable added to the map. This variable did not exist in the

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original map. First is the link between Labor Market and Overall Feasibility that did not exist in the original causal map. Second is the link between Knowledge, Skills and Abilities and Feasibility. Third is the link between Process Maturity and Product Customization. These variables were shown as conditionally independent in the original map. Similarly, the modified map shows links between Product Customization and Maintaining Application Currency and Feasibility and In-house/ASP that did not exist in the original causal map. 3. Deductive reasoning. The subject was instructed that an arrow should be directed from cause to effect only (deductive reasoning). The original map shows a link from Labor Cost to Knowledge, Skills & Abilities. However, the direction of the arrow is based on abductive reasoning from the observable measure (Labor) to the latent cause (Knowledge, Skills & Abilities). The direction of this arrow changed in the modified causal map from Knowledge, Skills and Abilities to Labor Cost. 4. Similar time frames. The subject was instructed that all variables should pertain to a specific time frame t1. We defined t1 as the period until the final decision of online ticketing application decision was reached (to eliminate circular relations due to relations pertaining to different periods). This resulted in the elimination of two reciprocal relationships in the original causal map. First is the two-way relation between In-house Application Cost and Online Ticketing and second is the circular relation between In-house/ASP variable and Net Application Value-added. At the end of the first interview, the subject was asked to provide a brief rationale or explanation for every link added or deleted in the original causal map. This explanation provided a validity check for modifications made to the map. Based on the suggestions made and the explanation provided by the subject, two raters (one researcher and another IS expert) modified the original causal map through consensus. Modifications agreed to by both the raters were made to the original causal map, and those not agreed to were excluded. A second follow-up interview was conducted to validate the modification process. Accordingly, the subject was provided with a modified causal map (based on the information collected in the first follow-up interview) to check if the modified map correctly reflected the modifications made to the original map. The final modifications were made to the map through close consultations with the subject. The resultant structure of the Bayesian Network is shown in Figure 10. In the second stage, parameters of the model were assessed. The parameters of a Bayesian causal map consist of marginal probabilities and conditional probabilities. To assess the marginal probabilities, the expert was asked to provide the following information. 1. To rate the marginal and conditional probabilities on a discrete scale (0 to 10); and


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2. To identify the type of interactive effects of multiple causal variables on effect variables. For example, whether each causal variable affects the effect variable independently (noisy-OR model), or whether each causal variable affect the effect variables through interactions of two or more variables (noisy-AND), or some combination of the two [29, 30]. Making inferences. We used Netica [www.norsys.com] to make probabilistic inferences using sum propagation. The sum propagation computes the marginal probabilities of all the model variables and updates the marginals with all additional evidence received about other variables. In our case study, we can evaluate each Online Ticketing Application option under different scenarios. The scenarios were defined in consultation with two IS experts (including the subject), and they represent situations in which there are unambiguous prescriptions for Application Outsourcing decisions in the IS literature. We illustrate how predictions can be made about our subject’s perceptions of In-house/ASP decision under different information conditions. We specify two different scenarios and show how our inferences about Application decision option change depending on the external application cost, application feasibility and environment factors. In the first scenario, we consider a favorable labor market and an unstable and complex application environment. In terms of application environment, we consider an unstable market environment as well as a high sensitivity of passenger data. Accordingly we specify the states of the following four firm variables in the map: Knowledge, Skills & Abilities = low, Labor Market = high, Fluctuations in Sales = low, and Sensitivity of Passenger Data = low. Since the case specifically mentioned that online ticketing was a new process for the airline company, we specified Application Maturity = New. Based on this information, we propagate the information to compute the posterior marginals of variables of interest. A comparison of prior and posterior marginals of Application Cost, In-house Feasibility, Net Application Value-added, and In-house/ASP Decision is shown in Table 4. When additional information is received about application cost and environment factors, the posterior probability of Application Cost = In-house < ASP increases from 0.46 to 0.67, that of (in-house) Feasibility = high increases from 0.55 to 0.85 and that of Net Application Value-added = In-house > ASP increases from 0.61 to 0.66. These posterior marginals change our inference about the state of Inhouse/ASP Decision. The posterior probability of In-house Application is 0.54 in comparison to a prior of 0.49. Under the conditions described in scenario 1, our Systems Expert is likely to select In-house Application Development because the cost of in-house development is lower than outsourcing to ASP, the Net Value-added is much higher for In-house development and the feasibility of In-house development is high.

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Figure 10. The Modified Causal Map of the Online Ticketing Application Decision Knowledge Skills & Abilities Labor Cost Fluctuations in Sales

Labor Market Hardware Cost

Diversity of Price Deals Offered

Software Cost

In-house Application Cost

ASP Pricing Structure Maintenance Cost

Reactive Change in Prices

Product Customization Sensitivity of Passenger Data

ASP Cost Online Ticketing Application Cost Maintaining Application Currency

Business Domain Process Maturity

Time to Market

Application security capability Net Application Value-added

In-house or ASP

Risk Preferences

Feasibility

In the second scenario, we considered an adverse labor market and stable and less complex application environment. Accordingly, the states of the two application cost variables and the two application environment variables in the map are specified as follows: Knowledge, Skills & Abilities = high, Labor Market = low, Fluctuations in Sales = low and Sensitivity of Passenger Data = low. As shown in Table 3, the posterior probability of (in-house) Feasibility = low increases from 0.45 to 0.80, that of Application Cost = In-house > ASP increases from 0.54 to 0.56, and that of Net Application Value-added = In-house < ASP increases 0.39 from to 0.58. This implies that in scenario two, our systems expert is more likely to reject In-house Application and select the option of using ASP’s application.


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Table 4. Prior and Posterior Marginal Probabilities under Two Different Scenarios Posterior Posterior Marginals: Marginals: Prior Scenario 2 Scenario 1 Variable States Marginals 1. Application Cost: In-house > ASP 0.54 0.33 0.56 In-house < ASP 0.46 0.67 0.44 2. Feasibility: High 0.55 0.85 0.20 Low 0.45 0.15 0.80 3. Net-Application Value-added: In-house > ASP 0.61 0.66 0.42 In-house < ASP 0.39 0.34 0.58 4. In-House/ASP Decision: In-house 0.49 0.54 0.43 ASP 0.51 0.46 0.57 Scenario 1: Knowledge, Skills & Abilities = low, Labor Market = high, ASP Pricing Structure = high, Fluctuations in Sales = high, Sensitivity of Passenger Data = high. Scenario 2: Knowledge, Skills & Abilities = high, Labor Market = low, ASP Pricing Structure = low, Fluctuations in Sales = low, Sensitivity of Passenger Data = low.

6

Summary and Conclusions

The main goal of this paper is to propose a semi-formal method for constructing the graphical structure of a Bayesian network based on domain knowledge. Our method consists of first constructing a causal map and then converting it to a Bayesian network. We call such Bayesian networks, Bayesian causal maps. Bayesian causal maps combine the strengths of causal maps and Bayesian networks and reduce the limitations of both. Using concepts from the literature on causal modeling and logic, Bayesian causal maps clarify the cause-effect relations depicted in the causal maps. They depict dependence between variables based on causal mapping approach (Dmap) as well as a lack of dependence between variables based on the Bayesian network approach (I-map). A Bayesian causal map is therefore a perfect map. Bayesian causal maps consider the reasoning (deductive versus abductive) underlying the cause-effect relations perceived by individuals. This strengthens the validity of the direction of causal relations represented in the map. Bayesian causal maps provide a framework for representing the uncertainty of variables in the map as well as the effect of variables not modeled in the map. Finally, using evidence propagation algorithms, Bayesian causal maps allow us to make inferences about the variables in the map. We have illustrated how Bayesian causal maps can be constructed starting from a causal map, and how it can be used to make inferences about a new product decision in different scenarios. There are some interesting implications of our study. This study enables decision-makers to use causal maps for decision making. Influence diagrams proposed by [32] use Bayesian network models of uncertainty in addition to decision nodes, utility functions, and information constraints. Thus, Bayesian causal maps can be use for normative decision making using the framework of influence diagrams.

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References [1]. Heckerman, D (1996), “Bayesian networks for data mining,” Data Mining and Knowledge Discovery, 1, 79−119. [2]. Huff, A. S. (1990), Mapping Strategic Thought, Wiley, Chichester, UK. [3]. Eden, C., F. Ackermann and S. Cropper (1992), “The analysis of cause maps,” Journal of Management Studies, 29(3), 309−323. [4]. Laukkanen, M. (1996), “Comparative cause mapping of organizational cognition,” in J. R. Meindl, C. Stubbart and J. F. Porac (eds.), Cognition Within and Between Organizations, 1−45, Sage, CA. [5]. Axelrod, R. (1976), Structure of Decision: The Cognitive Maps of Political Elites, Princeton University Press, Princeton, NJ. [6]. Klein, J. H. and D. F. Cooper (1982), “Cognitive maps of decision workers in complex game”, Journal of Operational Research Society, 33, 63−71. [7]. Ross, L. L. and R. I. Hall (1980), “Influence diagrams and organizational power,” Administrative Science Quarterly, 25, 57−71. [8]. Bougon, M. K., K. E. Weick, and D. Binkhorst (1977), “Cognition in organizations: An analysis of the Utrecht Jazz Orchestra,” Administrative Science Quarterly, 22, 606−639. [9]. Eden, C., S. Jones, and D. Sims (1979), Thinking in Organizations, Macmillan, London, UK. [10]. Forrester, J. W. (1961), Industrial Dynamics, MIT Press, Cambridge, MA. [11]. Wolstenholme, E. F. and R. G. Coyle (1983), “The development of system dynamics as a methodology for systems description and qualitative analysis,” Journal of Operational Research Society, 34, 569−681. [12]. Chen, K., J. C. Mathes, K. Jarboe, and J. Wolfe (1979), “Value oriented social decision analysis: Enhancing mutual understanding to resolve public policy issues,” IEEE Transactions on Systems, Man and Cybernetics, 9(9), 567−580. [13]. Wang, S. (1996), “A dynamic perspective of differences between cognitive maps,” Journal of the Operational Research Society, 47, 538−549. [14]. Fiol, M. and A. S. Huff (1992), “Maps for managers: Where are we? Where do we go from here?” Journal of Management Studies, 29, 269−285. [15]. Carley, K. and M. Palmquist (1992), “Extracting, representing and analyzing mental models,” Social Forces, 70(3), 601−636. [16]. Nadkarni, S and P. P. Shenoy (2001), “A Bayesian network approach to making inferences in causal maps,” European Journal of Operational Research, 128(3), 21−40.


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[17]. Bougon, M. (1983), “Uncovering cognitive maps: The ‘self-Q’ technique,” in Morgan, G. (ed.), Beyond Method: A Study of Organizational Research Strategies, Sage, CA. [18]. Fahey, L. and V. K. Narayanan (1989), “Linking changes in revealed causal maps and environmental change: An empirical study,” Journal of Management Studies, 26, 361−378. [19]. Anderson, J. C. and D. W. Gerbing (1982), “Some methods for respecifying measurement models to obtain unidimensional construct measurement,” Journal of Marketing Research, 19, 453−460. [20]. Speigelhalter, D. J., A. P. Dawid, S. L. Lauritzen and R. G. Cowell (1993) “Bayesian analysis in expert systems,” Statistical Science, 8(3), 219−283. [21]. Dawid, A. P. (1979), “Conditional independence in statistical theory (with discussion),” Journal of the Royal Statistical Society, Series B, 41(1), 1−31. [22]. Pearl, J. (1988), Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference, Morgan Kaufmann, San Mateo, CA. [23]. Lauritzen, S. L., A. P. Dawid, B. N. Larsen and H.-G. Leimer (1990), “Independence properties of directed Markov fields,” Networks, 20(5), 491−505. [24]. Jaques, E. and S. C. Clement (1996), Executive Leadership—A Practical Guide to Managing Complexity, Cason, Hall and Company. [25]. Charniak, E. and D. McDermott (1985), Introduction to Artificial Intelligence, AddisonWesley, Reading, MA. [26]. Winston, P. H. (1984), Artificial Intelligence, Addison-Wesley, Reading, MA. [27]. Knoke, K. and J. H. Kuklinski (1982), Network Analysis, Sage, CA. [28]. Spetzler, C. S. and C. S. Staël von Holstein (1975), “Probability encoding in decision analysis,” Management Science, 22(3), 340−358. [29]. Henrion, M. (1989), “Some practical issues in constructing belief networks,” in L. N. Kanal, T. S. Levitt and J. F. Lemmer (eds.), Uncertainty in Artificial Intelligence 3, 161−173, North-Holland, Amsterdam. [30]. Pradhan, M., G. Provan, B. Middleton and M. Henrion (1994), “Knowledge engineering for large belief networks,” in R. Lopez de Mantaras and D. Poole (eds.), Uncertainty in Artificial Intelligence: Proceedings of the Tenth Conference, 484−490, Morgan Kaufmann, San Francisco, CA. [31]. Churchman, C. W., R. L. Ackoff, and E. L. Arnoff (1957), Introduction to Operations Research, Wiley, NY. [32]. Howard, R. and J. Matheson (1981), “Influence diagrams,” in R. Howard and J. Matheson (eds.) (1984), Readings on the Principles and Applications of Decision Analysis, 2, 721−762, Strategic Decisions Group, Menlo Park, CA.

Nadkarni and Shenoy

[33]. Rossi, P. H., J. D. Wright and A. B. Anderson (1983), Handbook of Research Methods, Academic Press Inc., Orlando FL, 1983.

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