Multiattribute Preference Models For Consumer Research: a Synthesis

ABSTRACT - This paper synthesizes the compositional and decompositional approaches to modeling consumer preferences. Towards this, the similarities and differences between the two approaches in terms of attribute identification, model formulation, data collection, parameter estimation, and reliability and validity testing are examined. Implications for modeling of consumer preferences are discussed and some extensions are proposed.


Arun K. Jain, Vijay Mahajan, and Naresh K. Malhotra (1979) ,"Multiattribute Preference Models For Consumer Research: a Synthesis", in NA - Advances in Consumer Research Volume 06, eds. William L. Wilkie, Ann Abor, MI : Association for Consumer Research, Pages: 248-252.

Advances in Consumer Research Volume 6, 1979      Pages 248-252


Arun K. Jain, State University of New York at Buffalo

Vijay Mahajan, Ohio State University

Naresh K. Malhotra (student), State University of New York at Buffalo


This paper synthesizes the compositional and decompositional approaches to modeling consumer preferences. Towards this, the similarities and differences between the two approaches in terms of attribute identification, model formulation, data collection, parameter estimation, and reliability and validity testing are examined. Implications for modeling of consumer preferences are discussed and some extensions are proposed.


The modeling of consumer preferences among multiattribute alternatives has been of great interest and concern to consumer researchers. Preference modeling involves identification of the choice alternatives, attributes associated with the alternatives, estimation of the relative contribution of these attributes, and the specification of a conceptual model underlying the choice process. Over the years, two different research approaches for estimating the consumer preference function have emerged: compositional and decompositional. For the compositional or build-up approach the total utility for a multiattribute alternative is obtained as a weighted sum of the alternative's perceived attribute levels and associated value ratings as separately (and explicitly) judged by the consumer. In contrast, the decompositional approach utilizes a consumer's response to a set of "total" profiles of a choice alternative to derive preference functions.

The focus of this paper is to compare and contrast the compositional and decompositional approaches. This is done by first examining the issue of identification of the relevant attributes. We then present a general model formulation which encompasses the two approaches. Next, we focus on data collection, estimation, reliability testing, and validation involved in the two approaches. The paper concludes with a brief discussion of some new developments in the field of multiattribute preference modeling.


An important, but frequently overlooked issue in the use of multiattribute decision models is the determination and selection of a relevant set of attributes. This is of concern in applications using compositional models in which respondents are asked to evaluate competing alternatives along each of several attributes, and in decompositional models in which respondents rate or rank profiles formed using various combinations of attributes. The attribute selection problem is especially critical in research employing the decompositional approach because the number of profiles to which respondents must react can become quite large if the number of attributes is not kept to a minimum. There are ways to reduce the number of profiles in the decompositional approach, given a fixed number of attributes, through the use of orthogonal arrays (Green, 1974), but the importance of keeping the number of attributes to a minimum remains.

As noted by Wilkie and Pessemier (1973), an entirely satisfactory method for attribute generation and selection has not yet been developed. A particularly attractive approach to attribute identification is the Kelley's Repertory grid (Kelley, 1955; Frost and Braine, 1967). It involves presenting respondents with triplets of competing brands (or choice alternatives). The respondent is asked to think of a way in which any two of the three brands are similar to each other and different from the third one. This process is continued with new triplets of competing brands, until the respondent has exhausted his repertoire of alternative bases for differentiation. The respondent is also required to provide the relative salience of each attribute he has identified in brand preference. The similarity and relative salience of the various constructs across the sample provide a basis for selecting an attribute set for use in the multiattribute choice models.


The general main effects multiattribute preference model consisting of n attributes with each attribute defined at mi levels may be formulated as:


The formulation in (1) is a representation of the fundamental additive consumer preference model. Note, that the compositional model is a specific case of (1) when attribute levels are ignored. In such a case (1) reduces to:


This represents the traditional compositional model as identified by Wilkie and Pessemier (1973).

In the case of the decompositional model for consumer l, aijl is the part-worth contribution associated with the j-th level of the i-th attribute and Xijlk represents the presence (= 1) or absence (= 0) of the j-th attribute level in the k-th choice alternative.

Thus, it is observed that both the compositional and decompositional approaches can be represented by the same fundamental model (1). However, in the decompositional approach explicit recognition is accorded to the levels at which an attribute is presented in a particular choice alternative.


The operationalization of the compositional model will require the researcher to obtain information about the importance weights, ail, and beliefs, Xilk, from the consumers. This data is generally obtained on rating scales assumed to have interval properties. Considerable attention has been paid to the conceptualization, generality, measurement and halo effects associated with beliefs and importance weights. An excellent discussion of these issues is provided by the definitive work of Wilkie and Pessemier (1973) and hence is not pursued here.

In the case of the decompositional approach, Xijlk are defined by the manner in which the choice set is constructed. The values of the parameters aijl are estimated on the basis of the reactions of the respondents to the choice set. The reaction of the respondent to the choice set is generally obtained through one of two approaches: A. full profile and B. trade off.

In the full profile approach respondents are presented with a set of choice alternatives. These alternatives are described in terms of all associated attributes. The attribute levels across the choice set are varied systematically according to Some experimental design (Green, 1974). The respondent is required to rank order the alternatives in the choice set in order of his preference. On the other hand in the trade off approach the respondent is asked to rank the various combinations of each pair of attribute levels from most preferred to least preferred. Figure 1 shows an illustration of these two approaches as applied to consumer evaluations of banks.

Thus, it will be observed that the respondent is asked to provide a greater amount of information in the compositional approach as compared to the decompositional approach. Furthermore, while in the decompositional approach the respondent is required to provide only ordinal (or weaker, e.g., categorical) information, the compositional approach requires the respondent to provide the data on an interval scale. However, it should be noted that in the decompositional approach the respondent is required to process a greater amount of information since he is forced to make trade offs between alternatives defined in terms of two or more attributes.


The decompositional approach requires the use of some optimizing procedure to estimate the model parameters, aijl. This is not essential in the case of the compositional approach. The major focus of current research in model estimation under the two approaches is highlighted in the following.

Compositional Approach

An important concern among the researchers using compositional approach has been to represent attribute determinance in model formulation. Myers and Alpert (1976) suggest that attribute determinance includes but goes beyond "importance." They argue that it is the attribute determinance which should be included in the fundamental model (1).



An approach for operationalizing determinance involved (Alpert, 1971):


In light of the above, model (2) can be reformulated as follows:


The various approaches to identify lil may be broadly classified as: (a) direct questioning, (b) indirect questioning, and (c) observation and experimentation. In the direct questioning approach, the respondents may be asked to indicate perceived differences among the choice set on the preselected attributes. The various indirect approaches to identify lil include covariate analysis (Alpert, 1971; Myers and Alpert, 1976), standard deviation (Berkowitz, et al., 1976; Mahajan, Jain, Thangaraj, Ravichandran and Acito, 1977; Wilkie and Weinreich, 1972), and entropy (Mahajan, Jain, Thangaraj, Ravichandran and Acito, 1977; Wilkie and Pessemier, 1973). The third approach -- observation and experimentation --would involve varying the size of the choice set, the number of attributes, and their levels. The effect of such variations should be reflected in the values of lil. In particular, indirect approaches to identify lil have been in favor with researchers in consumer behavior (Mahajan, Jain, Thangaraj and Goodwin, 1977). For example, Wilkie and Weinreich (1972) have used standard deviation as a measure of lil. More specifically, they defined the determinance of an attribute i:


where the importance weight of the i-th attribute is standardized across the choice set EQUATION.

Berkowitz, et al., (1976) have employed the standardized standard deviation, EQUATION, in defining the determinance of attribute i:


Zeleny (1976) prefers to label lil as contrast intensity among the choices in the i-th attribute rather than perceived differences as suggested by Alpert (1971). Furthermore, Zeleny has labeled Di , the determinance attribute, as the dynamic attribute weight. Finally, Zeleny labels stated importance weight, ail, as static attribute weight. He redefines (3) as follows:


In (6), X*ijkl labeled as anchor point, represents the maximum value on each attribute across the choice set for the l-th respondent (X*ikl = max k (Xikl)), and Fikl describes the relative proximity of a particular alternative to the respondent's anchor point. Mahajan, Jain, Thangaraj and Goodwin (1977) have proposed the use of standardized standard deviation, based on Fikl, as a measure of contrast intensity.

Decompositional Approach

The various methods to estimate parameters in the decompositional approach may be broadly classified as (Jain, et al., 1978):

- Monotone regression methods such as MONANOVA (Carmone, et al., 1978; Green and Rao, 1971; Green, Wind and Jain, 1972; Green and Wind, 1973; Green, et al., 1977; Green and Tull, 1978; Jain, 1975; Kruskal, 1965; and Rao, 1977), and JOHNSON (Davidson, 1973; Johnson, 1974, 1975);

- Mathematical programming methods such as LINMAP (Parker and Srinivasan, 1976; Pekelman and Sen, 1974; Srinivasan and Shocker, 1973);

- Econometric methods such as Ordinary Lease Squares (OLS); and,

- Stochastic modeling methods such as the LOGIT, PROBIT and TOBIT models (Cox, 1977; Doyle, 1977; Krishnan, 1977; MacFadden, 1970; Punj and Staelin, 1976).

The common objective of all these procedures is to derive interval scaled partworths, aijl, from ordinal responses. The monotone regression methods utilize gradient-type search techniques to minimize iteratively a measure of badness of fit (referred to as "theta" or "stress") such that the predicted rankings of the choice alternatives reproduce, as closely as possible, the rankings provided by the respondent. Mathematical programming methods use techniques such as linear programming which attempt to minimize the number of violations in terms of the recovery of respondents' preferences. As compared to monotone regression methods, mathematical programming methods permit constraints on partworths and guarantee the global optimum (although there may be more than one solution). The ordinary least squares methods minimize sum of squared deviations between the observed and predicted preference values. On the other hand, stochastic models such as LOGIT model maximize a likelihood function to estimate partworths. Both OLS and LOGIT provide standard errors of partworths in addition to the global optimum. A detailed empirical comparison of these estimation procedures is provided by Jain, et al., (1978).


The various approaches to assess the reliability and validity of the parameters and predictions obtained via compositional and decompositional models are discussed in the following:

Reliability Tests

Both the compositional and decompositional approaches lend themselves to reliability testing. This could be carried out both at the level of model output as well as at the level of input data. In the compositional approach, to obtain the reliability of input data, the researcher can ask the respondents to provide attribute importance, ail, and belief scores, Xilk, at different points of time. The product moment correlations between the two sets of  Xilk and between the two sets of  ail may then be computed as a measure of reliability. Consumer judgments obtained for the second time may be embedded in a larger task. (See Green and Wind, 1973, for example.) Another measure of reliability could be product moment correlation between attitude scores derived from the first data set and those derived from the second data set.

Similarly, to test reliability in the case of the decompositional approach, the researcher may obtain preference rankings of the choice alternatives at two different points in time. Spearman rank order correlations between the two sets of rankings would provide a measure of reliability. Alternatively, following Parker and Srinivasan (1976) the researcher may, for the second ranking task, use a new set of choice alternatives described in terms of the same attribute levels as the first set but avoiding any duplication of alternatives in the first set. Product moment correlations of the parameters estimated from the two choice sets would provide a measure of reliability.

Validity Tests

The interval validity of the compositional model can be obtained in terms of the correlation between the predicted attitude scores, Alk, and the input data. The input data may be in the form of independent ratings of preference ordering of the alternatives in the choice set.

To measure the internal validity of the decompositional approach, primarily three methods are available. First, the researcher may estimate the parameters, aijl, by withholding some of the preference judgments provided by the respondents. The internal validity of the model may then be assessed in terms of its ability to predict the rankings of the alternatives in the hold-out set. A second approach may be to obtain preference rankings of a new set of choice alternatives described in terms of the same attribute levels as the first set. The validity may be assessed in terms of the ability of the model to predict the rankings of the second set based on the parameters estimated from the first set. The procedure can be reversed by predicting preference ranking in the first set based on the parameters estimated from the second set, thus completing a double cross-validation (Green and Srinivasan, 1978). Finally, the internal validity of the decompositional approach may be examined in terms of the ability of the estimated parameters to predict rankings of the input data which formed the basis of such estimates. Additional insights may be obtained by examining goodness of fit measures such as stress values for MONANOVA and LINMAP, theta for JOHNSON and (1 - R2) for OLS.


Multiattribute preference models have been extensively used in marketing. It is expected that this trend will continue over the years. The intent of this paper was to review the two approaches to multiattribute preference modeling and highlight their similarities and differences. Although in most situations both the approaches may be feasible, yet, in particular situations, the researcher may prefer one over the other. For example in new product development research and concept testing, the use of decompositional approach would seem to be more appropriate. Unlike the compositional approach, when using decompositional approach the researcher is not limited to the use of actual brands available in the marketplace for assessing consumer preferences. He may use hypothetical brands described in terms of relevant attribute levels to obtain consumer evaluations and develop their preference functions. This flexibility allows the consumer researcher to explore consumer reactions to new ideas and concepts before actual commercialization.

A particularly attractive feature of the decompositional approach is its ability to provide insight into consumer preferences for alternatives generated from the same attribute set but not included in the original choice set. Thus with a limited set of evaluations the researcher is able to generate a decision calculus which provides information about consumer preferences for a larger set of alternatives.

Much work is currently underway to extend the decompositional approach. In particular the use of stochastic models like LOGIT, PROBIT and TOBIT in multiattribute choice situations is a promising development. These approaches permit the researcher to model consumer preferences by obtaining only limited information from the respondents. For example, instead of obtaining complete preference orderings, the consumer may be asked to provide information only about his first choice. Yet another advantage of these approaches is the flexibility to employ different metrics. For example, using an interest metric, the authors are currently engaged in research designed to capture consumer utilities for various attributes of checking accounts in terms of interest rates. Research is also currently under way to model consumer preferences for different community features in terms of the tax metric.


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Arun K. Jain, State University of New York at Buffalo
Vijay Mahajan, Ohio State University (student), State University of New York at Buffalo
Naresh K. Malhotra


NA - Advances in Consumer Research Volume 06 | 1979

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