Some Comments on Multi-Attribute Preference Models

Donald R. Lehmann, Columbia University
ABSTRACT - This paper discusses the problems in comparing multi-attribute models of preference. It begins by commenting on three particular papers in the area. The paper then discusses some of the problems with comparing multi-attribute models and proposes a general type of model which seems worth further investigation.
[ to cite ]:
Donald R. Lehmann (1982) ,"Some Comments on Multi-Attribute Preference Models", in NA - Advances in Consumer Research Volume 09, eds. Andrew Mitchell, Ann Abor, MI : Association for Consumer Research, Pages: 562-565.

Advances in Consumer Research Volume 9, 1982      Pages 562-565


Donald R. Lehmann, Columbia University


This paper discusses the problems in comparing multi-attribute models of preference. It begins by commenting on three particular papers in the area. The paper then discusses some of the problems with comparing multi-attribute models and proposes a general type of model which seems worth further investigation.

The field of multi-attribute model examination has grown rapidly and seems close to maturity. Consequently many papers compare various models. This paper proceeds by commenting on three such papers in specific and then on the area of individual-level preference models in general.


The paper by Wahlers (1981) uses an experimental manipulation to examine the impact of the number of choice alternatives and the number of characteristics on the rule used by consumers to evaluate products. The paper is basically sound and the results seem plausible. Thus many may decry the lack of theoretical explanation for the choice models. On this issue I side with the author who has a simple and appropriate interest in seeing which fits best without any great theoretical pretense. I similarly applaud his restrained and brief summary. What follows is a series of suggestions and comments:

1. Some of the underlying models seem flawed. In particular, the variability-weighted models in fact double-weight variability since the characteristics with the greatest variation produce greater variation in the Ej's and hence are already weighted more heavily.

2. One would expect it would be very difficult to separate the model used at the individual level. In this regard several other papers are worth perusing including Beckwith and Lehmann (1973), Bettman (1979), Lehmann (1971), and Wright (1975) as well as some recent work by Einhorn and the elimination-by-aspect and elimination-by-tree approaches (Tversky, 1972; Tversky and Sattath, 1979).

3. The use of undergraduate students to evaluate life insurance policies may introduce a serious bias. Since the purchase of life insurance is not likely to be under serious consideration by most undergraduates, one could reasonably hypothesize that their objective would be to find a method to finish the task. Since a lexicographic procedure is faster, they would be expected to use one. Hence the results are biased toward the use of a lexicographic rule.

4. If subjects used a lexicographic rule, then they would not normally rank all the alternatives, but rather would discard them until the best emerged. Since subjects are required to rank all the alternatives, they are forced to use a more complete procedure than may be typical.

5. The hypotheses, while perfectly reasonable statistically, are not exciting. A more positive hypothesis (e.g., lexicographic models will do better for more complex situations) seems better to represent the author's (or at least my) expectations. It also is consistent with Bettman's (1981) position on the importance of situational impact on use of overall evaluation in choice processes. Put more dramatically, by adhering to the form of science (in this case by using a null hypothesis that nothing is going on) we may retard rather than enhance the growth of knowledge.

6. The method of analysis is fairly simple. As one reviewer pointed out (and the author recognized), use of ANOVA might be more informative than the MANOVA reported in the paper. Specifically a dummy variable regression with R2 as the dependent variable and 5 model dummies, number of alternatives, and number of characteristics as the independent variables (plus some interactions) seems potentially interesting. Also use of an adjusted R2 seems preferable. Moreover, the results that are reported tend to be fairly sterile. While Tables 1 and 3 are interesting, they also raise some questions. For example, for the case of 3 characteristics the average correlation is .767, .559, and .661 for 4, 8, and 12 alternatives respectively. This apparent non-monotinicity seems worth at least a comment. Moreover Table 2, which reports F statistics from a MANOVA, while a fairly standard way to report results, seems unnecessary. What would be more useful would be to report the impact of the choice alternatives on the dependent variable.

7. It can be argued that the wrong dependent variable is used. Since choice of life insurance normally involves selecting one policy, then only the first choice is relevant and hence the percent of first choice brands predicted should be used.

8. Since the models are individual in nature, the model which is best for each individual should be computed and then the results aggregated. This prevents a model which is best for a segment of the sample (e.g., 20%) from being swamped by the total results. Given the great margin by which lexicographic beat compensatory models, however, this is very unlikely to change the basic conclusions.


The paper by Sirgy and Danes (1981) compares the power of various mathematical forms of models related to the discrepancy between self and product images to predict response to products. As such it is very much parallel to the paper by Wahlers (1981) in both topic and approach.

My major question has to do with why one would want to apply self-image to brand choice given the poor performance of personality-type variables in general in predicting brand choice (Kassarjian, 1971; Wells, 1975) and the fact that product attributes both predict better and are more actionable managerially. What would be interesting would be to see if self-image either a) adds significantly to the predictive power of attribute-based models or b) is related to benefit-segments derived from attribute models. Also I would expect that self-image, in conjunction with basic economic and life-style variables might explain product-class choice (e.g., designer jeans), but not brand choice.

Some specific comments on the paper follow:

1. Why should the interactive model be converted into the particular continuous form shown in (1)? PM can be written as PIV + (PIV-SIV). This suggests a product becomes more desirable as the product image (PIV) improves and as self image (SIV) decreases. Why not just use PIV-SIVs the simple difference form, or 3PIV-SIV? Also consider the one-attribute example in Table 1. Several problems become obvious. First, the coding scheme used makes a big difference in the results, which is predictable given the interval nature of the data. Second, some of the conclusions seem illogical. For example, for the 1 to 5 coding alternative h should be better than alternative g and yet the model rates them in the opposite order. In short, the interaction model in formula (7) is questionable.



2. All the models seem likely to be highly collinear. I would like to see a report on the correlations which emerge in this particular study in terms of both the raw variables (P, AS, IS) and the predictions.

3. The questionnaire may induce a form of halo effect (Beckwith and Lehmann, 1975). By first giving liking response and then the ratings (the paper implies this order), subjects may rate a product (e.g., MGB) as having those attributes they also value, hence making product-image and self-image more congruent.

4. It is unclear exactly how the analytical results were generated. It appears that each product was analyzed across respondents. It would seem to be more consistent with the spirit of the models to analyze within subject across products, although the design only gives 4 observations per subject. Also standardizing the data within person might be considered.

5. Given the results in Table 1, it is not clear which differences are significant. More importantly, the simpler models (absolute difference or difference squared) seem to do at least as well as the more complex interactive model and the best of these are the appropriate standard of comparison. Moreover, the use of the F-test in footnote 6 seems inappropriate since the expanded model does not imbed the simpler one so the impact of adding another variable is confounded with the mathematical form chosen. In any event it appears that neither the self-image model in general nor the interaction model in particular is very strong predictively.


The paper by Evans (1981), like the other two on this session, focuses on comparing the predictive performance of models--this time, those based on the perceived risk involved in products. In extending Peter and Tarpey (1975), the paper uses six dimensions of risk. Again the question of why not to use product-specific attributes seems relevant. It seems hard to believe that individuals use six dimensions of perceived risk to evaluate brands within a product category.

The major extension in this paper involves an application of equity theory, While this is innovative and hence worth considering, it is very difficult to see how equity theory leads to equations (4) and (5) or even why one would want to apply it to brand choice. Even more importantly, (4) and (5) could be combined into a single equation such as:


This model counts fair gains as positive, discounts fair losses, discounts unfair gains, and counts unfair losses as negative. As such it seems more closely related to equity notions than the two models presented.

Some other comments:

1. The questions seem likely to be difficult to answer. Hence one would predict noisy data and low R's (which in fact occur).

2. The reliability coefficients appear to have been calculated across the 6 dimensions of risk. Since they are supposed to be independent, the fact that they are highly related suggests either a) a severe measurement problem or b) that the assumption of independence is not justified.

3. Table 2 seems to indicate gains are fair and losses un fair. Given this typical reaction, a model of gains minus losses such as the net utility model seems most appropriate.

4. The results of Table 5 seem similar to Peter and Tarpey (1975), with the exception of Pinto.

5. The key results seem to be in Table 7. These indicate a) that none of the models work well, indicating perceived risk is not a good predictor of behavior vis-a-vis product-specific attribute models and b) that the equity models used are basically failures.


Finding which model consumers use to form preferences is a popular pastime. Research in this area seems to agree that preference can be represented (which does not necessarily imply causality) as some combination of the alternative objects' attribute positions and their utilities. Considerable disagreement exists over the identity of the attributes and the rules consumers use to combine attribute information. From this disagreement stems the tendency to compare models. Unfortunately the competitive testing suffers from several problems.

1. Most of the models are deterministic. The lack of an explicit theory of error in the models makes their testing very difficult. In fact it is probably best to view both the attributes and the positions of objects as stochastic. Hence the attributes are a fuzzy set and membership probability a function of a variety of situational and personal characteristics.

2. The goals of modelers differ. Most tests of competing models are based on predictive ability within the original data set. Yet many other criteria exist, such as under standing process or simplicity. If prediction is the sole goal, then the use of any measure beyond overall preference may not be justified.

3. The data are imperfect. Much of the data used is based on questionnaires, which introduces innumerable possible biases. Other data comes from experiments which raise serious questions of external validity.

4. The models generally have no notion of memory or learning over time. Any rational buyer when faced with repeat purchases in a product class seems likely to seize on shortcuts to make the decision more rapidly. Hence most decisions simply call on routine procedures stored in memory and involve very little or even no information processing (e.g., Lehmann and Moore, 1980).

5. Most of the models predict similar if not identical preference orders for many sets of alternatives. This makes distinguishing among models very difficult and for certain managerial objectives not very crucial (Dawes and Corrigan, 1974; Einhorn and Hogarth, 1981).

6. There is no single correct model. Different individuals use different approaches for different situations (Moore and Lehmann, 1980). Hence even for a single person or single product category the best a researcher could hope to do is predict the probability that each of several models is being used. Thus it seems to be more useful to study the covariates of the model used rather than attempt to find "the" model.

Given these problems it is not surprising that arguments over the correct model persist. To add to that debate, this paper will conclude by briefly presenting another model which subsumes many of the existing models. While the model is not tested, it is a fairly comprehensive framework for considering both information processing and overall preference.

The model, referred to as the statistical satisficing model, assumes the following:

1. Individuals attempt to select a "best buy" based on attributes. The attributes are not completely fixed but vary with information availability, curiosity, etc.

2. The function which individuals use to compute overall preference is compensatory, but is not used without error. (Given most people can't correctly add four numbers in their head, this seems a plausible assumption.) Note that the compensatory function may include the risk (uncertainty) on attributes as well as the expected values much as risk and return appear in finance models.

3. People are busy and attempt to reach a nearly optimal/very good choice quickly (Shugan, 1980).

4. There are "weak" causal schema in memory relating perceptions on the attributes. Hence information on one attribute leads (via a regression-like model with an error term) to perceptions on other attributes (e.g., the relation of price to quality). This process may well be subconscious. It can be visualized as a spider's web, where well traveled paths are stronger and the entire web is both intricate and changing over time.

5. For well-known products, brand name or even package appearance serves as a cue to both other attributes and overall preference (Lehmann, Moore, and Elrod, forthcoming).

Based on this, individuals can be viewed as attempting to select an alternative which, with some level of confidence, they know will not be surpassed in overall utility by an amount greater than the cost of continued search and evaluation. Hence the process may be thought of as the following:

1. Gathering initial bits of information. These are more likely to come on more important dimensions (Tversky, 1972; Tversky and Sattath, 1979) or on dimensions which are salient (e.g., those for which the information is high lighted in a display).

2. Using a) the bits of information already in hand, b) whatever inferences to missing bits of data can be made, and c) an integration rule (e.g., linear additive compensatory) to form an estimate of the overall utility of the alternatives being considered.

3. Considering the statistical probability that either a) by gathering more information about the alternatives being considered or b) by attempting to add more alternatives to the set that the utility of the best alternative will increase substantially. (This suggests a number of interesting studies where an individual's confidence level and required level of improvement to continue evaluating are compared to such factors as general compulsiveness and implied wage rate.) This process is expected to be very inexact.

4. Either making a choice or reverting to (1).

This particular model is not very specific and hence not easy (or maybe even possible) to test. Nonetheless it seems to be a useful organizing framework as well as a normative approach for discussing decision-making. It also, assuming simplicity is not the major criterion? seems to:integrate information processing and integration with preference in a stochastic framework. As such it seems worth further elaboration and investigation.


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