Modeling Group Preferences Using a Decompositional. Preference Approach. ERIC J. E. MOLIN. Delft University of Technology, 2600 GA Delft, The Netherlands.
Group Decision and Negotiation, 6:339–350 (1997) © 1997 Kluwer Academic Publishers
Modeling Group Preferences Using a Decompositional Preference Approach ERIC J. E. MOLIN Delft University of Technology, 2600 GA Delft, The Netherlands HARMEN OPPEWAL Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands HARRY J. P. TIMMERMANS Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands
Abstract This article examines an extension of the decompositional, conjoint, or stated-preference approach to model group decisions. In the conventional approach, only one member is chosen to be the group’s representative and provide answers for the group as a whole. In this study, all group members are brought together and asked to jointly complete a conjoint preference experiment. The hypothesis is tested that this joint group approach predicts group behavior better than the conventional approach with representatives. The paper presents the estimated part-worth utilities of the group model and compares preference structures of individual group members and groups. Finally, group preference models are tested to determine whether they outperform representative-based preference models in terms of the ability to correctly predict the group preferences for new alternatives. These analyses are performed in the context of residential preferences of co-ops, which are groups of young people, usually not partners, who live together in owner-occupied houses. Key words: group preferences, conjoint analysis, housing preferences
1. Introduction An approach that has received major attention in the study of preferences and choice behavior of individuals is the decompositional, conjoint, or stated-preference modeling approach (for reviews, see Timmermans 1984; Louviere 1988; Green and Srinivasan 1978, 1990). The decompositional approach involves estimating preference functions from respondents’ responses to hypothetical alternatives. These alternatives are combinations of various attribute levels, combined according to the principles of the design of statistical experiments. This allows one to identify preferences under controlled conditions and observe and predict behavior beyond the current domain of experience. For example, one can predict market shares of new products or the behavioral change that results from a specific rise in taxes. This method therefore is very suitable if one wants to evaluate alternative managerial actions or policies before they are implemented. Therefore, the
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decompositional stated-preference approach can be applied if one wants to model preferences or choices in complex decision problems to predict choice behavior under new conditions. To date, decompositional or stated-preference approaches typically have been applied to model the choice behavior of individuals. However, many choice problems involve group choice processes, in particular the choice of durable products. For example, when households chose their place of residence, usually all household members take their part in the decision-making process. The conventional approach to study these household or group decisions involves asking a representative group member. Often the member who is considered to be most involved in the decision task under investigation is approached to provide responses that are assumed to be valid for the group. However, the preferences of this representative may differ from the preferences of the fellow group members, and what is more, the representative may not be fully aware of these other group members’ preferences (Davis, Hoch, and Ragsdale 1986) and their influences on the group process. Therefore, the validity of a group model based on the responses of only one representative is in doubt. An alternative approach would be to obtain responses from all the group members, aggregate these responses and estimate one group model. However, this aggregation approach has three major difficulties. The first is that the social and power structure of the group may imply that group members do not all have the same influence on the group decision. It is not clear how these different influences should be measured. The second difficulty is that group members’ preferences may be unstable and change during the group decision-making process. The social psychological literature (Moscovici 1985) suggests that this may happen, for example, if group members are confronted with deviant group members. Thus, the validity of measures of group members’ preferences are in doubt if they are measured before the group process has taken place. Consequently, the validity of the aggregated group model based on these measures can also be questioned. A final, more fundamental problem is that aggregation may not always lead to well, defined social or group utility functions (Coombs 1964). In this paper, therefore, we propose an alternative approach to modeling group preferences and choices that avoids the difficulties just discussed. The essence of this approach is that all group members are brought together and asked to jointly complete a conjointpreference experiment. This approach stimulates a group decision process and is assumed to lead to results similar to the real decision-making process. In the stimulated discussion, group members have to discuss the interview questions, solve their possible disagreements, and come up with joint answers. Thus, the joint answers are the result of the group interaction process, in which group members may have a different influence on the group decision and may have changed their preferences. However, these processes need not be measured explicitly, because their result, the joint answers, are sufficient to estimate a group model directly at the group level. We hypothesize that this simple and efficient method leads to a better group-preference model than the method where only one group member is interviewed. Here, this hypothesis is tested and the proposed approach is illustrated in an application that measures residential preferences of co-ops. This is a good example of a decision-
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making process in which group members have to reach a joint decision. We present part-worth utility estimates of attribute levels that are obtained from the experimental group task. To assess the predictive ability, we compare observations of group preferences for new hypothetical alternatives with predictions obtained from the estimated models. In addition, we examine whether group-based preference models can outperform conventional, individual models. This is possible because group members, independent of each other, also completed a conjoint preference experiment. This paper is organized into three sections. In the method section, the basic assumptions of the stated preference approach first are discussed to set the context of our approach. Next, we present the applied model and details about the residential choice application. The analysis and results section presents the estimated part-worth utilities, examines the similarity between the individual and group answers, and tests which model best predicts a series of new residential profiles. In the conclusion section, the results and the implications for future research are discussed.
2. Method 2.1. Standard decompositional preference approach Before focusing on the measurements of the present research project, we will discuss the main characteristics of the decompositional preference modeling approach. This approach collects respondents’ overall preferences for hypothetical alternatives, which consist of combinations of relevant attributes. The overall preferences are decomposed into separate utility contributions of the attribute levels. This decomposition is an efficient way to estimate preferences, because the hypothetical alternatives (profiles) are constructed according to the principles of the design of statistical experiments. This technique allows control over the correlation structure among the attributes: The attributes vary independent of each other, which allows an unbiased and efficient estimation of preference structures. These preference structures can be estimated from responses to an experimental design that is created in the following way. First, the attributes influencing the decision-making process under investigation are elicited and categorized into a set of levels. Then, these attributes are combined according to some experimental design (often a fractional factorial design) to create the hypothetical choice alternatives of interest. Next, the respondents are requested to evaluate the attribute profiles in terms of their overall preferences. The respondents have to trade off the advantages and disadvantages of the profiles to express their overall preferences, which is the opposite of the compositional approaches where the attributes are evaluated separately. The main object of analysis is to decompose the overall preferences into the separate utility contributions of the attribute levels. The overall preferences observed on a rating scale often are assumed to approximate an equal interval measurement scale. This assumption allows one to use regression analysis to decompose the overall preferences into part-worth utilities.
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342 2.2. Hierarchical integration information
An operational problem related to the application of decompositional preference approach in modeling complex decisions, such as housing choice, is that many attributes influence the choice under investigation. Inclusion of all relevant attributes in one profile would result in an experimental task too demanding for respondents. To avoid this problem, in the present study, we use the hierarchical information integration (HII) approach (Louviere 1984; Louviere and Timmermans 1990; Oppewal, Louviere, and Timmermans 1994). This approach assumes that people who are faced with complex decision problems, first divide the relevant attributes into a smaller number of decision constructs. Next, they evaluate each decision construct separately and then combine these evaluations to arrive at some overall preference or choice. For example, in the housing choice, one evaluates separately the characteristics of the house and the characteristics of the residential environment and then combines these two evaluations to arrive at a final evaluation. The assumption that subjects divide the attributes in decision constructs implies that direct trade-off takes place only between attributes that belong to the same decision construct and, at a higher level, between the different constructs. This assumption allows one to break down the experimental task into subexperiments, which include only the attributes belonging to one of the constructs. The trade-off between the constructs can be derived by adding one further, bridging experiment that includes constructs only (Louviere 1984; Louviere and Timmermans 1990) or by including constructs as additional factors in each subexperiment (Oppewal et al. 1994). The construct levels are expressed as hypothetical ratings on the selected constructs.
2.3. Subjects and application Our application focused on modeling the residential preferences of co-ops. Co-ops are groups mainly of young people with lower incomes—for example, students or the unemployed—who live together in owner-occupied houses: These dwellings typically consist of a room for each individual, with shared facilities such as bathroom, kitchen, backyard, and joint sitting area. Often, people who wish to live together cannot find appropriate accommodation. Rental housing of this type is not available and, because of their lower incomes, they are not granted mortgages to buy houses. However, when unified in housing associations, they are granted mortgages because risks can be divided among co-op members. Although these housing associations formally become the house owners, the co-ops can choose their own residence. That is, co-op members, usually three to five persons, jointly decide which house to buy. Co-ops participating in this study were all located in Nijmegen, a medium-sized northwestern European city. Their addresses were obtained from an organization that seeks to help co-ops to form housing associations and buy houses. Twenty-eight co-ops were contacted, 14 of which completed all the experimental tasks. The 14 groups involved a total of 53 co-op members. However, only 41 members completed their tasks individually, as 12
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members were instructed to complete their initial tasks in pairs; that is, in subgroups from the total group. To limit the length and complexity of this paper, we refrain from reporting the results for these subgroups.
2.4. Design The construction of the design used in the present study involved the following steps. First, the set of relevant attributes influencing housing choice was elicited. Twelve co-op members who were not included in the experiments were interviewed and presented a set of 20 attributes, each written on a separate index card. They first were asked if they would like to add any other attributes that they would pay attention to when choosing a new residence. These additional attributes were written on separate cards. Once they had completed this task, the individuals were requested to rank the cards in terms of importance. The attributes that received the highest average rankings were selected for inclusion in the present experiment. Common with other work on residential preference, these attributes were assigned to one of two underlying constructs: the house and the residential environment. To test the face validity of the definition of attributes and constructs, respondents were requested to classify the attributes as housing characteristics or residential environment characteristics. All 12 co-op members classified the attributes in accordance with our assumed hierarchical structure. We next assigned levels to the identified attributes. To select proper attribute levels, the 12 respondents were asked to indicate for each attribute the value they felt is normal and the maximum or minimum value at which they still would accept an alternative. Based on the results of these analyses, the following attributes were selected for the decision construct “house”: size of individual room, monthly living costs, joint garden, and joint sitting area. Likewise, for the definition of the construct “residential environment” we selected the following attributes: distance to city center by bicycle, building period of the neighborhood, type of the neighborhood, and amount of traffic in street. Table 1 lists these attributes and their levels. Furthermore, we decided to express the construct-evaluation levels as numerical values on a 10-point rating scale, consequently, the values 2, 4, 6, and 8 were chosen as construct evaluation levels. Having selected the attributes and their levels, the profiles were formed by combining the attribute levels into profiles. Because in the “housing quality” subexperiment two attributes and one construct of four levels and two attributes of two levels were used, a total of 43 3 22 or 256 combinations could be constructed. Similarly, 42 3 3 3 22 or 192 profiles can be constructed for the “environmental quality” subexperiment. It is obvious that these are too many profiles to present to an individual or a group. However, it is sufficient to use a much smaller number of combinations to estimate accurately the contribution of each attribute level to the total utility. In the present study, orthogonal fractions of the full factorial design, both involving 16 treatments, were used. Hence, for
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Table 1. Mean estimated part-worth utility contributions of group model (N 5 14) Mean Housing quality subexperiment Size individual rooms 12 m2 16 m2 20 m2 24 m2 Monthly living costs Nlg 225 Nlg 300 Nlg 375 Nlg 450 Garden Yes No Joint sitting area Yes No Hypothetical rating of the environment 2 4 6 8 Environmental quality subexperiment Distance to city center by bicycle 0 min (city center) 10 min 20 min 30 min Building period neighborhood Before 1950 Between 1950 and 1980 After 1980 Type of neighborhood Mainly (semi)detached houses Mainly houses in a row/apartments Traffic in street Destination traffic Heavy traffic Hypothetical rating of the house 2 4 6 8 Intercept
Standard Error
t Value
212.68 2.45 3.55 (8.68)
1.39 1.37 1.18
29.13 20.33 3.00
9.55 3.98 .52 (214.05)
1.74 1.07 1.09
5.48 3.71 0.48
5.83 (25.83)
1.07
5.46
5.51 (25.51)
1.01
5.44
210.11 21.86 2.34 (9.63)
1.62 0.90 1.03
26.24 22.07 2.26
9.05 6.27 22.13 (213.20)
2.62 1.13 1.24
3.46 5.57 21.72
2.74 2.38 (22.36)
0.75 0.61
3.63 20.62
20.94 (0.94)
0.32
22.95
4.57 (24.57)
0.60
7.59
222.64 28.48 10.79 (20.34) 44.52
1.20 1.80 1.44
218.85 24.70 7.51
3.17
14.03
Note: For case of comparison, the part-worth utility contributions of the remaining levels are presented in parentheses.
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both subexperiments, only responses to 16 profiles were required to estimate the preference function for the corresponding higher-order construct. Each of these profiles was printed on a separate index card.
2.5. Measurement task and procedure In both the individual task and group task, subjects were first requested to rank the experimental profiles in terms of overall preference as a place to live with their group. Next, they were asked to rate each profile on a rating scale ranging from (1) extremely unattractive to (100) extremely attractive. In addition, in the individual task group members were asked to express their expected group ratings. Furthermore, before conducting the experimental task, respondents familiarized themselves with the attributes and the construct summary measures by rating eight additional attribute profiles on a ten-category rating scale. The measurement procedure involved two steps. First, group members conducted a written task that contained the individual conjoint-preference experiment and some other questions. Respondents first received a letter in which the research project was announced. They were then contacted by phone and asked if they were willing to participate in this study. Those who agreed to participate received the written tasks delivered at home. After the interviewers explained some of the tasks, they requested the group members to fill out the questionnaires independent of each other. Approximately one week later, the interviewer collected the individual tasks and made an appointment for the group task. In the group task, which was supervised by the interviewer, all the group members jointly filled out a second questionnaire, which contained the experimental group task, including the same sets of profiles as in the individual task. If some co-op members were unwilling or unable to participate, the remaining participants were asked to imagine that these persons were not involved in the relocation of the co-op. So, in these cases, the group was redefined to include only the group members who were willing and able to participate in the group task.
3. Analysis and results 3.1. Part-worth utilities of the group model The aim of the analysis is to decompose the overall profile evaluations or utilities into the separate contributions of the attribute levels. Therefore, it is necessary to assume some combination rule that represents the way respondents combine their attribute evaluations to arrive at an overall preference rating. In the present study, we assume that the respondents may compensate low evaluations of some attributes for high evaluations of one of the remaining attributes. This combination rule can be approximated by a simple maineffects-only model.
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Multiple regression analysis was used to estimate a series of models, one for each group and each individual. In each model the dependent variable is formed by the profiles’ overall ratings, the independent variables by the coded attribute levels. Effect coding was used to represent the attribute levels. This enables one to interpret the estimated regression coefficients as part-worth utilities of the attribute levels. The part-worth utilities can be interpreted as the utility contributions to the overall preference, expressed as deviations from the regression intercept, which is equal to the mean overall profile evaluation. The results obtained for the groups indicate that simple main-effects-only models predict the observed groups’ preference ratings for the experimental profiles quite well: The mean Pearson product moment correlation between the group’s predicted and observed scores is 0.94. Table 1 summarizes the part-worth utilities for the attribute levels and their estimated standard error and t values. These results suggest that residential utility increases with (a) increasing room size, (b) decreasing living costs, (c) decreasing distance to the city center, and (d) increasing age of the neighborhood. The utility functions all are monotonically increasing or decreasing. Table 1 also demonstrates that co-ops prefer houses with a joint sitting area, a garden, and neighborhoods with mainly row houses or apartments and only destination traffic. These results are consistent with our a priori expectations. Table 1 also shows that the average utility increases monotonically with increasing construct-evaluation ratings of the environment and the house. The difference between the part-worth utility assigned rating 2 and rating 8 of the “hypothetical rating of the house” is more than twice as large as the estimated part-worth utility difference of the similar range of the “hypothetical rating of the residential environment.” This suggests that co-ops consider the construct “house” to be more important than the construct “environment”.
3.2 Comparison between the individual and group preference structures The mean parameters of individual part-worth utilities were very similar to the mean group parameters reported previously. Hence, to limit the length of this paper, we do not report them. This is not to say that the individual and group parameters in the same group are identical. The preference structure of a group can differ substantially from the preference structures of its group members. One way to examine the difference between preference structures of groups and individuals is to calculate correlations between the observed preference ratings for the experimental profiles obtained for the group members and those for the group. Group members and groups provided 16 ratings for both the housing and the residential environmental profiles. The mean correlation between the group members’ ratings and the corresponding group ratings is 0.63. Therefore, despite the similarity in preference structure between the group and its group members, this similarity is certainly not perfect.
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3.3 Predictive validity We hypothesized that the predictive ability of the models based on the group task is better than models based on the individual tasks. To test this hypothesis, we determined how well each model predicts the group’s preferences. We measured group preferences for new choice alternatives by including hold-out profiles in the group task. Hold-out profiles are profiles constructed in the same fashion as the other experimental profiles, but they are not used to estimate the model. Five hold-out profiles (see table 2) were constructed. Four of these were similar in type to the experimental profiles. The remaining hold-out showed all attributes in one profile and included no summarizing construct evaluations. To test the predictive ability of the models, we compared the group hold-out observations with predictions based on group and individual models. Hold-out preference predictions are calculated by summing the estimated part-worth utilities and the intercept. The predicted preferences are compared with the observed preferences by calculating the absolute difference between the observations and the predictions. This absolute difference is expressed on the original 100-point rating scale and can be interpreted as the prediction error. Table 3 presents the average prediction error of the group and individual models. The table demonstrates that, for most hold-out profiles, the prediction error is smaller for the group models than for the individual models. Moreover, a t test shows that, over the five hold-outs, the mean difference between the models is significant at the a 5 0.05 level. Therefore, the results of our analyses suggest that the group preference models better predict the preference for the hold-out profiles than the conventional, individual-level models.
Table 2. Five hold-out profiles
House Size of individual rooms Monthly living costs Joint sitting area Garden Utility environment
Environment Building period of neighborhood Distance to city center by bicycle Type of neighborhood Traffic in street Utility house
Hold-out 1
Hold-out 3
Hold-out 5
24 m2 f 375 Available Available 6
12 m2 f 375 Not available Available 4
20 m2 f 300 Available Not available —
Hold-out 2
Hold-out 4
Before 1950 0 min (Semi)detached Destination 8
After 1980 20 min Row/apartment Heavy 2
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Table 3. Mean prediction error of group and individual models for five hold-out profiles
Group Individual
1
2
3
4
5
Mean
N
10.1 (6.6) 9.7 (8.4)
8.5 (7.8) 10.4 (9.1)
9.2 (7.5) 15.2 (11.2)
8.5 (5.2) 14.6 (9.2)
9.9 (10.9) 12.1 (10.3)
9.2 (4.2) 12.3 (5.0)
14 41
Note: The prediction error is calculated as the absolute difference between the observed and the predicted preference. Standard deviations are in parentheses.
4. Conclusion and discussion Stated-preference models usually are based on the answers of individuals to experimental profiles, even if the preference formation of interest is the result of a group process. In the latter case, one group member is selected to provide answers for the group as a whole. This assumes that these group representatives are aware of their fellow group members’ preferences and the different influences these may have on the group decision. However, as group members typically only have limited knowledge of these matters, this assumption can be questioned. The aim of this paper was to examine an approach where all the group members are involved in a stated preference experiment. The essence of this approach is that group members are brought together and asked to provide joint answers to the experimental profiles. We hypothesized that group models based on such measures better predict group preferences for new alternatives than models based on individual tasks. To this extent, the individual group members also completed a stated-preference task independent of each other. We therefore were able to make predictions for hold-out preferences based on the group models as well as on individual models. We compared these predictions with the observed group scores. Our results suggest that the group models outperform the individual models in terms of predicting a set of hold-out profiles, which means that our hypothesis was confirmed. The results of the analyses further indicate that our group modeling approach has potential in that the estimated models perform well and have estimated part-worth utilities in anticipated directions. These results have some important managerial and research design implications. If similar results can be replicated in future research, models are in doubt that attempt to represent or predict group-level decision-making processes from measurements of individuals. Apparently, it is critical to have the total group involved to improve the reliability and validity of the measurements and the model. It is widely acknowledged that choices represent a different psychological process than evaluating an alternative. This has led to the development of conjoint-choice approaches, for example. In these approaches, profiles are placed into choice sets and respondents are asked to choose one of the profiles rather than evaluating the profiles one by one (e.g., Louviere and Woodworth 1983).
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We chose a rating task, however, because this task allows one to estimate a separate model for every individual and group. This allowed us to examine, for each group, which model predicted best. The choice approach does not allow one to estimate a model for each subject, because the required task would be too demanding. Although the choice approach could have yielded other substantial results, the question whether it would lead to better individual or group model predictions is an empirical one that still needs to be answered. Finally, one could use the present model to identify the weights of the group members in influencing the final outcome for example, by comparing the similarity of group members’ individual preference structures with the corresponding group preference structure. However, this is only an a posteriori assessment. The HII method that was used in this study to handle the large number of attributes in our application also can be extended to estimate a separate parameter for each group member (cf. Timmermans et al. 1992). Under certain assumptions these parameters can be interpreted as the group members’ influences on the group’s decision. This extension is the focus of our ongoing research and will be the subject of future publications.
Acknowledgements Part of this article has been presented at the Sixth International Research Conference on Housing, Beijing, September 1994. At the time of writing this paper, the authors were, respectively, a Ph.d candidate, an assistant professor, and a professor at the Urban Planning Group at the Eindhoven University of Technology. Harry Timmermans was also the Carthy Foundation Professor of Marketing at the University of Alberta, Edmonton, Canada. This research was supported by a grant from the Economic, Social-Cultural and Environmental Research Foundation, which is a part of the Netherlands Organization for Scientific Research (NWO/ESR).
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