# Incorporating Consumer Judgments Into Aggregate Choice Models

ABSTRACT - Consumers' judgments about choice alternatives are incorporated as covariates in aggregate multinomial logit choice models. Hypothetical multiattribute choice alternatives were presented to consumers in two formats: first as sets of choice alternatives and second as conjoint profiles. Aggregate choice models were estimated for the multiattribute alternatives using an ANOVA formulation, and also estimated using the conjoint profile ratings as a covariate in an ANCOVA formulation. Including the covariate provides a measure of the overall preference for the alternative after taking into consideration its attributes. Implications of including covariates in choice models are discussed.

##### Citation:

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W. Steven Perkins (1992) ,"Incorporating Consumer Judgments Into Aggregate Choice Models", in NA - Advances in Consumer Research Volume 19, eds. John F. Sherry, Jr. and Brian Sternthal, Provo, UT : Association for Consumer Research, Pages: 644-648.
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Consumers' judgments about choice alternatives are incorporated as covariates in aggregate multinomial logit choice models. Hypothetical multiattribute choice alternatives were presented to consumers in two formats: first as sets of choice alternatives and second as conjoint profiles. Aggregate choice models were estimated for the multiattribute alternatives using an ANOVA formulation, and also estimated using the conjoint profile ratings as a covariate in an ANCOVA formulation. Including the covariate provides a measure of the overall preference for the alternative after taking into consideration its attributes. Implications of including covariates in choice models are discussed.

INTRODUCTION

In aggregate consumer choice models, respondents' choices are gathered by survey, then analyzed in an effort to understand the factors affecting those choices. Consumer choices are modelled as a function of either the utilities for the choice objects themselves or the utilities for the attributes comprising the objects. Parallel to traditional conjoint analysis, these utilities are often estimated with dummy variable regression or ANOVA, using categorical independent variables. Aggregate level models of consumer choices typically do not consider the simultaneous effects of choice objects and choice attributes. In addition, they do not consider the effects of continuous variables, as in logit models used with scanner data. Thus, the applicability of these models is restricted in terms of the choice phenomenon which can be modelled realistically and in terms of the types of data which can be included in the model. These two limitations can be addressed by including choice related covariates in a new model which draws concepts from market share analysis and from hybrid conjoint analysis.

This paper outlines previous models used in consumer choice and market analysis, then investigates the advantages of combining elements from both. A model which might be termed an aggregate hybrid choice model is proposed and its application illustrated in a transportation context. Implications for including covariates in aggregate consumer choice models are discussed.

DEVELOPMENT OF THE MODELS

All of the models addressed in the present research stem from Luce's (1959) choice axiom, which states that the probability of choosing one alternative from a set of alternatives can be modelled as the utility for that alternative divided by the sum of the utilities for all the alternatives in the choice set. Often formulated in marketing as the multinomial logit (MNL) model, this approach has been used extensively for both studies of consumer choice and studies of market share.

Consumer Choice Models

Batsell and Lodish (1981), Mahajan, Green, and Goldberg (1982), Louviere and Woodworth (1983), and others have applied the MNL model to the analysis of consumer choices derived from experiments and surveys. An alternative's share of choices is modelled as the utility for that alternative divided by the utility for all alternatives in the set.

The design of consumer choice studies will be briefly outlined. Typically, the respondent's task in such research is to choose one alternative from each set of available alternatives (e.g., Louviere and Woodworth 1983), or to allocate fixed resources to the alternatives in each set (e.g., Mahajan, Green, and Goldberg 1982). Parallel to traditional conjoint analysis, multiattribute alternatives can be constructed from a factorial design. Alternatives could also represent wholistic objects, such as actual soft drinks. One approach to constructing the choice sets is to consider each alternative as a factor in a second factorial design, with two levels on each factor: include the alternative in the set or exclude it. Unique sets of alternatives will be generated from this two step process. Besides the alternatives, Louviere and Woodworth (1983) suggest that each choice set contain a "none of these" option which serves as a baseline for comparison.

The data are often aggregated across respondents, resulting in the frequency with which each alternative was chosen from each set. Louviere and Woodworth (1983) sum discrete choices across respondents; Mahajan, Green, and Goldberg (1982) average subjects' allocations across alternatives. Batsell and Lodish (1981), on the other hand, present an individual level choice model.

One model employed in analyzing aggregate consumer choice data is the analysis of variance (ANOVA) formulation operationalized by Louviere and Woodworth (1983) as:

ln (m

_{is}) = u + u_{i}+ u_{s}+ E_{is}[1]

where

m

_{is}= number of times alternative i was chosen from set su = intercept

u

_{i}= main effects for alternatives (i=1,2,...,I)u

_{s}= main effects for choice sets (s=1,2,...,S)E

_{is}= error term

The dependent variable is the log of the number of times alternative i was chosen from set s, across respondents. The m_{s} control for the influence of choice set and are usually not of interest. When the "none of these" option is included in the choice set, then the effect of each alternative i = m_{i} - m. Parameters representing the utilities for the alternatives could be estimated by dummy variable regression. Mahajan, Green, and Goldberg (1982) discuss a related ANOVA formulation of the problem.

Louviere and Woodworth (1983) and Louviere (1988a) illustrate several variations on this basic model. For example, if the m_{i} represent multiattribute alternatives constructed by the analyst, then alternatives could be examined at the level of the attributes comprising the objects. In this case Model 1 could be re-written as:

where all terms are as defined before except the Z_{ik} are dummy variables denoting the level of alternative i on attribute k, and the B_{k} are the estimated parameters for each attribute k.

Proposed Models

Cooper and Nakanishi (1988), among others, illustrate the use of the MNL model in analyzing market shares. Often labelled the attraction model, the market share for a brand is modelled as its attraction relative to the attraction of all the brands in a market. The attraction for a brand is, in turn, seen as a function of its marketing efforts. This model has been used to examine the effects of promotions, for example, on market shares (Guadagni and Little 1983). The data usually come from scanner data or panels. Cooper and Nakanishi (1988, p 118) point out that the MNL formulation of the attraction model is equivalent to the analysis of covariance model (ANCOVA), which can be expressed as:

Parallel to the consumer choice equation shown in Model 1, the effects of brands (alternatives) and time periods (choice sets) are captured by m_{i} and m_{s}, respectively. In addition, the market share model includes the marketing effort (e.g., promotions) for brand i at time s, X_{is}, as a covariate.

The proposed models to be investigated in this study apply this ANCOVA formulation, typically seen in market share analysis, to aggregate consumer choices. Using Model 3, the effect of a covariate could be investigated in conjunction with the utilities for the choice alternatives. A covariate could also be included in Model 2, resulting in:

Note that the covariate, X, is indexed by i and s indicating that it varies by alternative and choice set. One possible variable to use as the covariate is a measure of the consumers' overall rating judgments about the alternatives chosen from a set. These judgments could come from a traditional, profile at a time, conjoint task. To calculate the covariate, consumers' judgments about the alternative chosen from a set can be aggregated by:

where C = 1 if respondent r chose alternative i from set s, and zero otherwise. And where X_{ir} is respondent r's overall judgment about alternative i. Mathematically this is simply the mean rating given for the choice object by all people who chose it from that set. Note that as in hybrid conjoint, the X_{is} and the Z_{ik} could be correlated, resulting in biased estimates. We can test this by comparing Models 2 and 4.

This covariate would be analogous to the use of self-explicated judgments in hybrid conjoint (e.g., Green 1984, his equation 2). In hybrid, responses to conjoint profiles can be modelled as a combination of respondent level utilities for the alternatives and group level utilities for product attributes. In Model 4, the choices are a function of the set level preference for the alternative, X_{is}, plus the "market" level utilities for attributes, Z_{ik}. Thus, both the decompositional aspects of Model 2, breaking the choice object down to its component attributes, and the total compositional aspects of Model 1, considering the choice object as a whole, are incorporated. On the other hand, including the judgmental covariate into Model 3 may have a small effect on the explanatory power of the equation because the ratings, X_{is} should be somewhat redundant with the estimated alternative utilities, m_{i}.

THE STUDY

From an applied point of view, the objective of the study was to determine consumer preferences for different modes of public transportation at given prices and given levels of scheduling convenience. Transportation has often been studied in choice analysis (Ben-Akiva and Lerman 1985, Louviere 1988b). The sponsor of the project, an inter-city bus line, was interested in comparing consumer preferences for bus and train trips, and also for bus and plane trips. This marketing problem provided an opportunity to compare aggregate consumer choice models estimated in the more common ANOVA multinomial logit formulation with those estimated by the proposed ANCOVA model. In particular, does the inclusion of a consumer judgment covariate improve the explanatory power of the models?

Materials and Procedure

To generate the multiattribute alternatives considered in this study, 3 attributes, each having 2 levels, were selected after consulting with corporate management and reviewing previous research. The first attribute, Z_{1}, mode of transportation, could be a bus or one other mode. One group of respondents chose between bus and plane alternatives; the other group, between bus and train alternatives. The second attribute, Z_{2}, price, could be low or high, with the high prices approximating the actual cost of taking a 350 mile trip, and the low price about 1/3 less. Finally, the third attribute, Z_{3}, arrival and departure scheduling convenience, could be either "very convenient" or just "convenient." Eight alternatives were then generated based upon all the combinations of the 3 attributes at 2 levels each.

Developing the choice sets entailed a double conditional design, as explained in Louviere (1988a). First, 4 of the multiattribute combinations were selected. Specifically the following multiattribute alternatives were of interest:

Alternative 1: bus, low price, convenient

Alternative 2: bus, high price, very convenient

Alternative 3: other mode, low price, very convenient

Alternative 4: other mode, high price, convenient

Second, these 4 alternatives were then treated as factors in a 2^{4} factorial design, in which each alternative was either included or excluded from the choice set. The design generates 15 choice sets with 1 to 4 alternatives, plus the "none of these" option, in each set. Respondents considered each set then circled the one alternative they preferred the most.

In addition, consumers' gave their overall judgment about the 8 multiattribute alternatives created from the 2^{3} design. Each alternative was presented in a traditional conjoint profile format. Respondents judged how likely they were to take the trip described in each profile and circled a number ranging from 0 to 100.

In terms of administration, every respondent received a 4 page questionnaire which started with an explanation of the nature of the project (but no identification of the sponsor) and a brief statement asking respondents to think about a trip of 350 miles when answering, then the 15 choice sets, the 8 conjoint profiles, and several demographic questions.

Samples

Using a convenience sample, interviewers completed usable questionnaires with a total of 100 travelers from three locations: an inter-city bus terminal, a train station, and an airport. Group 1 respondents consisted of 26 inter-city bus riders and 26 plane riders; variable Z_{1} could be a bus or a plane. Group 2 respondents consisted of 24 inter-city bus riders and 24 train riders; variable Z_{1} could be a bus or a train.

Analysis

The input data for the analysis consisted of the number of times each of the 4 alternatives, plus the "none" option, was chosen from each set, and the ratings for those same 4 alternatives. The rating for the "none" option was assumed to be zero; the ratings for the other 4 alternatives not involved in the choice task were not analyzed.

To analyze the data, multiple regression equations were estimated for Models 1 through 4 for Group 1, the bus and plane riders, and estimated again for Group 2, the bus and train riders. Dummy variable coding of the categorical independent variables follows Louviere (1988a); in particular for Models 2 and 4, the low values for each attribute (and "bus") were coded as -1 and the high values as +1. In all cases, the equations were estimated by a weighted least squares method because choice frequencies are often heteroscedastic (Louviere and Woodworth 1983). The observed frequency of choices, m_{ai}, were used as weights in the general linear models procedure of SAS (SAS Institute 1979).

RESULTS

The results of estimating Models 1 and 3, which consider the alternatives as wholistic objects, appear in Table 1. The estimated utilities for the alternatives are presented, both without and with adjustment for the judgment covariate. Note again that the regression estimated parameters for the l_{i} should be interpreted as the difference between the alternative and the intercept. (The intercept term and set effects are not presented.) The mean judgmental ratings of the alternatives, X_{is}, should be highly collinear with the estimated utilities for the alternatives. In fact, including the covariate decreased the level of significance of the utilities. Evidence for this collinearity is also seen in the fact that the R^{2} values do not increase from Model 1 to Model 3 when the covariate is included. For the bus and train group the covariate has only a marginal (p<.10) level of significance, and was not significant for the bus and plane group.

The more interesting case considers including the covariate in the estimation of the utilities for the attributes which comprise the alternatives. Table 2 presents the results of Models 2 and 4 where attribute utilities are estimated both without and with the judgment covariate. In both groups of respondents, the covariate is significant. As a result, the R^{2} values increase over 20 points with the inclusion of the covariate, up to the same levels found with Model 1. The fact that the explanatory power of Model 2, based on attributes, is below that of Model 1, based on alternatives, could be interpreted to mean that respondents were choosing on the basis of the whole object rather than simply on its component attributes. This interpretation is also encouraged by the large increase in R^{2} with the inclusion of the covariate in Model 4 because the covariate is again a wholistic representation of the choice alternative.

The signs and relative magnitudes of the attribute utilities in Table 2 do not change from Model 2 to Model 4, because the covariate affects the intercept more than the attribute slopes.

There does not seem to be a problem with multicollinearity between the covariate and the attributes. In every equation, price, Z_{2}, had the largest absolute impact on choice. Bus and train respondents were more sensitive to mode of transportation, Z_{1}, than to convenience, Z_{3}; but the opposite occurred in the bus and plane case. Interpreting the coefficient for the covariate requires considering the choice elasticity with respect to the judgment rating, g*X_{is} (1 - m_{is}). In other words, the impact of the covariate is in part a function of the share of choices (Cooper and Nakanishi 1988).

ESTIMATED PARAMETERS FOR CHOICE ALTERNATIVES WITHOUT AND WITH ADJUSTMENT FOR CONSUMER JUDGMENTS

ESTIMATED PARAMETERS FOR ATTRIBUTE UTILITIES WITHOUT AND WITH ADJUSTMENT FOR CONSUMER JUDGMENTS

DISCUSSION

This paper has investigated the inclusion of a covariate in aggregate consumer choice models, in contrast to previous applications in marketing which have typically involved only categorical independent variables. Model 4 in particular presents some interesting possibilities because it allows for simultaneous estimation of the utilities of the attributes and the estimation of an overall alternative effect. There are both substantive and methodological advantages attained from including a covariate. First, the model avoids the assumption that each choice alternative must be considered only as one whole object (i.e., Model 1) and, on the other hand, avoids the assumption that a choice alternative must be considered as simply the sum of its parts (i.e., Model 2). Both alternatives and attributes are represented in the model. If the covariate is insignificant, indicating that the choices depend on the attributes alone, then the formulation reduces to Model 2, the more typical approach. In this study, however, the covariate was highly significant, pointing to the conclusion that consumers' choices involve both overall judgments of the object and weighting of its attributes. In a sense, the covariate captures the "brand equity" effect for the choice alternative above and beyond its attributes. Essentially, we can partition the aggregate choices into the effects due to attributes and the effect due to the object itself. Second, drawing upon previous concepts in market share analysis and in hybrid conjoint analysis, the ANCOVA formulation extends the applicability of aggregate consumer choice models based on survey data to situations involving continuous variables. Thus, the model provides a more flexible approach statistically and what may be a more realistic approach conceptually.

There are several avenues for improvement upon the model and for future research. This project was limited in terms of the number of respondents and in the number of alternatives considered. More interesting designs could have been employed in the construction of the alternatives and choice sets. The focus of the research was instead on the effect of the covariate. Future research could consider using other variables such as income or age as covariates, as well as self-explicated data. Also other methods of calculating the covariate could be devised, though it must vary by both alternative and set, or its effect will be absorbed by the dummy variables. Though it was not a problem with these data, the covariate could be related to the choice attributes. The structure of the model is limited to the extent that these are correlated, biasing the estimates. It is often assumed that the utilities for alternatives should not differ by choice set, following from the independence from irrelevant alternatives (IIA) property of Luce's individual choice axiom. According to Ben-Akiva and Lerman (1985), however, this property need not hold at the group level. They suggest that logit models should incorporate socioeconomic variables, for example, to capture market place heterogeneities. Further study is needed in marketing on the effect that including covariates has on the IIA property.

There have been relatively few published research studies in marketing using aggregate choice modelling based on consumer surveys or experiments, particularly when compared to the number using conjoint analysis, its close relative. Even a recent review of the commercial use of conjoint (Wittink and Cattin 1989) and a recent overview of new directions for research in conjoint (Green and Srinivasan 1990) have little to say about the aggregate choice approach. The models investigated in this project may expand the applicability of the aggregate approach to more marketing problems.

The author would like to thank Gary Graley, Director of Market Research at Greyhound Lines, Inc., for his assistance in conducting this research. Frank Mulhern and Kate Searls provided helpful comments on a previous draft of the paper.

REFERENCES

Batsell, Richard R. and Lodish, Leonard M. (1981), "A Model and Measurement Methodology for Predicting Individual Consumer Choice," Journal of Marketing Research, (February) 18, 1-12.

Ben-Akiva, Moshe and Steven R. Lerman (1985), Discrete Choice Analysis: Theory and Application to Travel Demand. Cambridge, MA: The MIT Press.

Cooper, Lee G. and Masao Nakanishi (1988), Market-Share Analysis, Boston: Kluwer Academic Publishers.

Green, Paul E. (1984), "Hybrid Models for Conjoint Analysis: An Expository Review," Journal of Marketing Research, (May) 21, 155-169.

Green, Paul E. and V. Srinivasan (1990), "Conjoint Analysis in Marketing Research: New Developments and Directions," Journal of Marketing, (October) 54 (4), 3-19.

Guadagni, Peter M. and John D. C. Little (1983), "A Logit Model of Brand Choice Calibrated on Scanner Data," Marketing Science, 2, 3, (Summer), 203-238.

Louviere, Jordan J. and Woodworth, George, "Design and Analysis of Simulated Consumer Choice or Allocation Experiments: An Approach Based on Aggregate Data," Journal of Marketing Research, (November) 20, 350-367.

Louviere, Jordan J. (1988a), Analyzing Decision Making: Metric Conjoint Analysis. Sage University Paper, Beverly Hills: Sage Publications.

Louviere, Jordan J. (1988b), "Conjoint Analysis Modelling of Stated Preferences,"Journal of Transport Economics and Policy (January), 93-119.

Luce, R. Duncan (1959), Individual Choice Behavior: A Theoretical Analysis, Westport, Connecticut: Greenwood Press.

Mahajan, Vijay, Paul E. Green, and Stephen M. Goldberg (1982), "A Conjoint Model for Measuring Self- and Cross-Price/Demand Relationships," Journal of Marketing Research, (August) 19, 334-342.

SAS Institute Inc. (1985), SAS User's Guide: Statisitcs, Version 5 Edition. Cary, NC: SAS Institute Inc.

Wittink, Dick R. and Philippe Cattin (1989), "Commercial Use of Conjoint Analysis: An Update," Journal of Marketing, (July) 53 (3), 91-96.

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##### Authors

W. Steven Perkins, Pennsylvania State University

##### Volume

NA - Advances in Consumer Research Volume 19 | 1992

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