Are the Models Compatible For Empirical Comparison? An Illustration With an Intentions Model, an Expectations Model, and Traditional Conjoint Analysis

Rajan Nataraajan, Auburn University
Paul R. Warshaw, California Polytechnic State University
ABSTRACT - Before models are compared empirically, it must be ascertained that they are indeed comparable at a theoretical level. Unfortunately, the literature does not contain a standard procedure for making theoretical comparisons of models. The authors attempt to fill this lacuna by suggesting a scheme for checking the compatibility among models prior to empirical comparison.
[ to cite ]:
Rajan Nataraajan and Paul R. Warshaw (1992) ,"Are the Models Compatible For Empirical Comparison? An Illustration With an Intentions Model, an Expectations Model, and Traditional Conjoint Analysis", in NA - Advances in Consumer Research Volume 19, eds. John F. Sherry, Jr. and Brian Sternthal, Provo, UT : Association for Consumer Research, Pages: 472-481.

Advances in Consumer Research Volume 19, 1992      Pages 472-481


Rajan Nataraajan, Auburn University

Paul R. Warshaw, California Polytechnic State University


Before models are compared empirically, it must be ascertained that they are indeed comparable at a theoretical level. Unfortunately, the literature does not contain a standard procedure for making theoretical comparisons of models. The authors attempt to fill this lacuna by suggesting a scheme for checking the compatibility among models prior to empirical comparison.

Currently there is a plethora of models and techniques in marketing. These have emerged from several perspectives. Some are based on economic utility theory, some are purely attitudinal in nature, and others appear to be based on both economic and psychological perspectives. There are also those that are based on the interface of economics and probability theory, and some are purely stochastic in nature. Unfortunately however, our understanding of marketing phenomena in general and the prediction of consumer behavior in particular does not appear to have reached a reasonable level of perfection (Hoyer 1984; Jacoby 1978). One way to enhance this understanding is to significantly increase the extent of empirical comparisons of existing models and techniques in a variety of situations within the consumer- marketplace domain. The revelations from such comparisons would aid not only in model selection for various situations but also in the building of new models and techniques.

However, before models are compared empirically, it must be ascertained that they are indeed comparable. A theoretical comparison of the chosen models would reveal whether or not the models are actually comparable and if not, it would reveal the specific points of incompatibility among them. In some cases, it may be possible to get around the points of incompatibility and then make a "correct" empirical comparison. Currently, there does not seem to be any standard procedure for carrying out theoretical comparisons of models and techniques. In this paper, we suggest such a scheme, and then illustrate it with three selected models.


The suggested scheme for a theoretical comparison of models is depicted in Figure 1, and consists of six main steps. Step 1 deals with the contextual terms (e.g., reliability, involvement, perceived control etc.) pertaining to the impending empirical testing. In this step, a clear explanation of the test context, and a semantic as well as a methodological clarification of the contextual terms figuring therein are furnished. In step 2, the selected models are compared in terms of purpose. This essentially involves answering the following questions : (a) What is the main reason for the existence of each model? (b) What can be accomplished through the use of each model? (c) Is there compatibility among the chosen models with respect to (a) and (b)? In step 3, the models are compared on focus, and this involves answering two questions, and they are: (a) In a theoretical sense, what does the model basically stress? (b) What is the required level of analysis, individual or group? In step 4, the models are compared on theoretical base and structure. In step 5, their boundaries and constraints are compared.

In each of the above steps, the assumptions of the models are taken into account at appropriate junctures. Relevant issues (if any) are raised and discussed in light of the above assumptions, and tentative conclusions are drawn. Based on all the tentative conclusions, overall conclusions are drawn (step 6), which pave the way for speculations on performance of the models.

An Illustration

Let us assume that a researcher wants to empirically compare the external predictive validity of a behavioral intentions model, a behavioral expectations model, and traditional conjoint analysis in a reasoned choice situation within the consumer-market place domain; note that any other set of models would be just as effective in illustrating our scheme. Since the theory of reasoned action (Ajzen and Fishbein 1980) has been the most widely adopted attitude framework within social psychology (Warshaw and Droge 1985), we choose it as our behavioral intentions model. For our behavioral expectations model, we use a modified version of Warshaw (1980)'s behavioral intentions model. We have picked conjoint analysis (Luce and Tukey 1964; Green and Rao 1971) mainly because, in recent times, it is probably the most widely used marketing research tool in the industry for measuring consumers' multiattribute utility functions (Green 1984). The surveys conducted by Cattin and Wittink (1982; 1989) provide evidence for the increasing use of conjoint analysis in the industry.

Note that in the interest of making the illustration clear and effective, a hybrid conjoint model was not chosen. The self-explicated part of hybrid conjoint models bears a close resemblance to attitudinal models in the sense that both rely on direct consumer input. Consequently, if a hybrid conjoint model is chosen, the distinction between "compositional" and "decompositional" would become blurred, thereby reducing the "contrast" effect between the attitudinal models and conjoint analysis.



Since it was felt that having such a clear "contrast" would enhance clarity and comprehension of our scheme, traditional conjoint analysis was chosen for this illustration.

To ascertain theoretical compatibility among the above models, we apply our scheme as follows:

Step 1

Here, there are two contextual terms, external predictive validity and reasoned choice. The term external predictive validity refers to the extent of agreement between what is predicted by a model and what actually occurs in reality. The qualification "external" warrants that the test setting be real and not contrived or hypothetical. The term reasoned choice is an off-shoot of the term "reasoned action" (Ajzen and Fishbein 1980) and simply refers to "reasoned actions" in a choice situation; the qualification "reasoned" refers to rationality.

Step 2

Here, the three models are compared in terms of their purpose. To facilitate presentation, the acronyms TRA, BEM, and CAS are used to refer to the theory of reasoned action, the behavioral expectation model, and traditional conjoint analysis respectively.

TRA: Ajzen and Fishbein (1980) have renamed the Extended Fishbein model and promoted it as a viable theory to predict and explain virtually any type of human behavior. Since they view consumer behavior as just any other behavior of interest, and that no novel or unique processes need to be invoked to explain or predict it, TRA may be used to explain and predict consumer behavior. Further, Ajzen and Fishbein (1980) recognize that consumer behavior is human action involving a choice among various alternatives. In view of this, by restricting its generality to consumption choice, TRA may be used for predicting consumer choice. The hypothesis underlying the application of TRA to consumer choice situations would be that a consumer has a certain level of "intention toward choosing an alternative" (the predictor of choice behavior) for each of the alternatives in the choice set, and would end up selecting that alternative for which the consumer has the highest level of the above predictor.

BEM: This model has been designed specifically for the purchase situations which is, by and large, characterized by the choice process. Therefore, the use of BEM as a predictive model of consumer choice is justified. The hypothesis underlying the application of BEM to consumer choice situations would be that a consumer has a certain level of "expectation toward choosing an alternative" (the predictor of choice behavior) for each of the alternatives in the choice set, and would end up selecting that alternative for which the consumer has the highest level of the above predictor.

CAS : In an essentially pragmatic discipline like marketing, CAS is used to estimate consumers' preferences among multiattribute stimuli. However, the ultimate purpose of doing this is to aid the marketer in the task of prediction of behavior in the market place with greater exactitude (Leigh, Mackay, and Summers 1984). This seems to be an accurate assessment of the role of CAS because for whatever intermediate purpose it is used in marketing, there is always the implicit assumption that it will help in the revelation of the behavioral tendencies of the consumer based on which better marketing strategies could be developed. Thus, the ultimate purpose is to help in the prediction of choice behavior in the market place. The hypothesis underlying the application of CAS to consumer choice situations would be that a consumer has a certain level of "total utility toward choosing an alternative" (the predictor of choice behavior) for each of the alternatives in the choice set, and would end up selecting that alternative for which the consumer has the highest level of the above predictor.

Issues: The proponents of TRA and BEM imply that the algebraic formulations in their approaches correspond to the consumers' cognitive processes, and thus, the models are primarily concerned with explanation of behavioral phenomena. Prediction is relegated to secondary status. In contrast, CAS does not assume that consumers actually process cognitively according to the maximization principle (subject to constraints) but only that consumers choose as if they did. Thus, in a sense, CAS is more concerned with the end result rather than any cognitive process that may occur in the mind of the consumer prior to the end result. Perhaps because of this, Green and Srinivasan (1978) have opined that users of CAS have been concerned more with prediction than explanation.

Tentative Conclusions: In light of the foregoing, it may be concluded that if the purpose is prediction of consumer choice behavior in the purchase phase, then the three models are definitely comparable.

Step 3

In this step, the models are compared in terms of their main focus. TRA and BEM stress the subjective perceptions (salient subjective consequences) and evaluations rather than objective measures. It is to be noted that the saliency concept inherent in these models implies individualization in that the salient beliefs about the consequences of behavior may be different from individual to individual. In the ideal application of any of these two models, the analysis (including the elicitation of salient beliefs) should be done totally at the individual level, and conclusions drawn at the individual level only. In other words, the ideal application in the consumer choice context would be to explain and predict individual choice behavior.

CAS focuses on the characteristics of the choice objects. In other words, it is really an object based approach. Objects are analyzed in terms of certain basic features (attributes), whose juxtaposition in a particular product is viewed as the basis of choice. Thus, the preference is initially defined on individual attributes (e.g., prefer low price; prefer black color), and choice is effected on the objects (e.g., prefer a low priced, black colored car among the many cars). However, there is the implicit behavioral assumption that preferences are a manifestation of the subjective perceptions and evaluations of the individual. Further, the saliency aspect figures in CAS also, but in the form of salient attributes of the object. As regards the level of analysis, it is the same as in TRA or BEM. The ideal application of CAS would be to elicit salient attributes for every individual, conduct analysis at the individual level, and draw conclusions on preferences (or choice behavior) only at the individual level.

Issues : In the operationalization of any of these three models, the ideal application referred to above, does get diluted in rigor. From a marketing decision point of view, behavioral prediction at the individual level is of very little use because that would be like the extreme of treating every individual as a separate segment. This, of course, would be realistic and proper in many industrial marketing situations. For most consumer good situations however, unless these individual predictions can be meaningfully aggregated and some concrete conclusions drawn at the target market level, realistic and economical marketing strategies cannot be formulated. But aggregation dilutes theoretical rigor. For instance, in the operationalization of TRA or BEM, aggregation actually takes place in two stages. First, the saliency aspect gets diluted because individual salient beliefs are aggregated and a few modal salient beliefs are obtained. These are then used in a questionnaire designed for the entire sample. The purity of measurement and analysis at the individual level gets tarnished at this stage itself because some of the modal salient beliefs may not be salient to every respondent. The second dilution takes place when the results of the individuals are aggregated to draw conclusions at the sample level.

In CAS, the salient attributes (and levels) of the product for each individual are aggregated, and only a few modal salient attributes (and levels) are used to construct profiles or attribute-level combinations. In other words, the perceived attributes (and levels) are assumed to be constant across individuals in the sample. This assumption of homogeneity of perceptions has been questioned by Ritchie (1974). Despite the implicit assumption in CAS that differences in perception are captured totally by the individual preferences, this homogeneity of perceptions assumption can only be deemed as the first dilution of the saliency or the individual level analysis aspect. The second dilution in CAS takes place when the results are aggregated to draw conclusions at the target market level. However, it must be pointed out that in applications of CAS, the individual differences are retained to a relatively greater degree because the second aggregation takes place usually through a choice simulator, which is a relatively more rigorous method.

Tentative Conclusion: In light of the foregoing, it may be concluded that despite the difference in focus, there is compatibility among the three models because they are all essentially individual level models, and the ideal application of any of these models would be at the individual level. But in the operationalization of these models, this ideal state gets tarnished in every model owing to aggregation. However, it is realized that without aggregation, there would be very little use for these models in a pragmatic discipline like marketing. So it seems that it does not serve any useful purpose to debate the comparative theoretical rigor of these models because they all lose rigor when they are operationalized, at least in marketing scenarios.

Step 4

Here, these models are compared in terms of their theoretical base and structure. TRA is based entirely on concepts of social psychology. BEM is based on a mixture of social psychology (attitudinal formulation), economics (utility maximization/ satisficing principle), and mathematical psychology (probability theory). However, both models belong to the compensatory type, and rely on direct consumer input. Further, each one uses a compositional approach in that responses obtained on simpler components are combined in some fashion to yield a numerical representation of the main component (behavioral intention or behavioral expectation depending on the model). However, there are important structural differences between these two models.

Figure 2 furnishes a pictorial description of TRA. As per this, behavioral intention is the immediate antecedent of behavior. Intention is determined by an attitudinal (personal) component and a normative (social) component. The model can be symbolically stated as,

B ~ BI = w1 (AB) + w2 (SN) where,

B is Overt behavior, BI is Behavioral intention (subjective probability of intending to perform behavior B), AB is Attitude toward performing behavior B (e.g., attitude toward buying a brand; note that this is not attitude toward the brand itself.), SN is Subjective norm (normative influence; the collective perceived influence of "important others"), and w1 and w2 are empirically determined weights denoting the relative influence of the two components. AB is determined as _biei where, bi is the subjective probability that performing the behavior will result in outcome i, ei is the individual's evaluation of outcome i, and n is the number of salient outcomes. SN is determined as _NBjMCj where, NBj is the belief that referent j thinks the individual should/should not perform the behavior, MCj is the individual's motivation to comply with referent j, and N is the number of salient referents.

BEM emerges when the behavioral intention model proposed by Warshaw (1980) is treated as a behavioral expectation model after necessary modifications in the constructs. Essentially, the logic in the model is based on "working backwards" from the antecedents of behavior and deriving a framework of cognitive constructs and their interrelationships with each other and behavior. Assuming that the subjective probability (expectation) of performing a specific behavior (e.g., purchasing the New York Times) is often conditional upon the formation of more global antecedent expectations (e.g., purchasing a newspaper), an operational equation for product purchase contexts is derived, which may be stated as,

BEy = BEY x BEy/Y where,

BE, behavioral expectation, is the individual's estimation of the likelihood that he/she will perform some specified future behavior, Y refers to the product type, and y refers to the specific brand of Y. BEy= Expectation to buy specific brand y, BEY = Expectation to buy product type Y, and BEy/Y = Expectation to buy brand y assuming purchase of product type Y.





Figure 3a illustrates the above formulation. Figure 3b furnishes the antecedents of BEY and BEy/Y. Product type expectation, BEY, is stated to be a function of purchasability (X1) of product type Y and felt need or desire (X2) to purchase product type Y. The antecedents of (X1) and (X2) are as shown in Figure 3b.

Brand choice expectation assuming purchase of product type, BEy/Y, is stated to be a function of relative purchasability of brand y (X3) as compared with alternative brands of Y, relative ability of brand y (X4) to satisfy own product use needs (for instance, in the case of a newspaper, international news, sports coverage etc.), and felt pressure (X5) from others to buy brand y instead of some alternative brand of Y. The antecedents of (X3), (X4), and (X5) are as shown in Figure 3b.

While the origin of conjoint measurement can be traced to the work of some economists of the last century, the field of conjoint analysis formally came into existence only with the work done by Luce and Tukey (1964). Since that article, the field has developed rapidly in a theoretical as well as an applied sense, and consists of a variety of models and generalized techniques (see Green 1984; Green and Srinivasan 1978). CAS is based on the fundamental principles of maximization and decomposition in decision making by rational human beings, and makes use of the occurrence of polynomial structures in the various fields of study. It uses a decompositional approach in the sense that overall judgments of the main component (attribute-level combinations) are broken into numerical measures for simpler components (attribute levels).


Compensation also comes into play here in the sense that the respondent may rate a particular combination that is weak (for the respondent) on one important attribute level highly if other attribute levels in the combination are strong. For a simple mathematical exposition of CAS, we refer the reader to Rao (1977).

CAS essentially involves asking the respondent to give overall or global judgments/evaluations about a set of alternatives and then decomposing these overall judgments/evaluations into separate utilities or part worths that, given some type of composition rule, are most consistent with the respondent's overall judgments or evaluations. In other words, the technique yields utilities from which the original global judgments or evaluations can be closely reconstituted. Note that a part worth is simply the value or importance of an attribute level as perceived by the respondent. Note also that the utility measures (parameter estimates) are statistically derived.

Issues: The general model of conjoint measurement is, strictly speaking, context free and does not provide ground rules to develop some kind of usage typology (what model would be suitable for a particular situation) for conjoint models (Rao 1977). This forces researchers to either rely on past empirical research concerning the performances of various conjoint models or use a trial and error approach or simply assume that a particular model would be suitable for a particular situation and use it. This situation is unlikely to be altered unless - as Rao (1977) has pointed out - a theory for evaluation of multiattribute stimuli akin to multidimensional psychophysics is developed. In contrast to this, with TRA or BEM, a change in context does not alter the basic structure of the model itself. In other words, the same model is applicable in all contexts. However, the basic model accommodates a change in the belief structure of the individual whenever the context is changed.

Tentative Conclusions: Despite differences in the theoretical bases and structure there seems to be compatibility among the models on a broad theoretical level. All these models assume human rationality to prevail in decision making. Also, each model has some form of compensation coming into play in its application. However, there are two key differences between TRA and BEM as one group, and CAS. First, while the attitudinal models adopt a compositional approach, CAS adopts a decompositional approach. Second, whereas the attitudinal models rely on direct input from the respondent for parameter estimation, CAS relies on statistical techniques to derive parameter estimates.

Step 5

Researchers (Bagozzi and Warshaw 1990; Warshaw and Droge 1985; Warshaw et al. forthcoming) have stated that TRA actually applies to a relatively circumscribed domain, and have pointed out its boundary conditions as follows: (i) Behavior is restricted to mean single, observable, reasoned acts performed by an individual. (ii) Outcomes experienced by an individual are explicitly excluded, unless the individual fully has the means to achieve those outcomes, intends to do so, and there is no intervention (and possible prevention) in the form of external situational forces to the achievement of the outcomes. (iii) i and ii are tantamount to saying that behavior is completely determined by one's volitions, and performance is typically under one's self control; in other words, total volitional control must be there for both behaviors and outcomes. It follows therefore that TRA does not make a distinction between a behavior and an outcome; in reality, one typically has much less control over outcomes. Consequently, TRA does not regard succeeding in a race, gaining stamina, lowering cholesterol level, etc. as behaviors because "complete control" will typically not be there in any of them. Thus, TRA does not apply in cases of behaviors occurring because of non-volitional psychological processes (habit, impulse) or situational contingencies (fear, coercion). (iv) Further, phenomena such as goals (desired end-states), plans (mental procedures for achieving these ends), and behavioral expectations (self-predictions of the likelihood of goal attainment and/or behavioral performance -Warshaw and Davis 1985), which act as antecedents to the initiation and/or actual performance of acts, are outside the scope of TRA. It must also be realized that under some circumstances, to state an intention is to express a goal, plan, and expectation. These mental events are often distinct, and combinations of these states can occur. These are brought out in the following examples. One may have a firm intention to stop eating desserts yet possess no plans to do so; one may even believe that such stopping is unlikely. One may have a strong expectation that he or she is going to drink some wine yet at the moment neither intend nor plan to do so. But such combinations of states of intentions, goals, plans, and behavioral expectations do not fall within the boundaries of TRA except when intentions equal expectations. In view of the above, it would be more correct to view TRA as a model designed to explain and predict a wide range of voluntary and reasoned behaviors of interest, and not as a model that can explain and predict virtually any type of behavior as contended by Ajzen and Fishbein (1980).

Strictly speaking, TRA is an unconstrained choice model in the sense that constraints are not endogenous to the model. However, this does not mean that the proponents of TRA have not talked about constraints; constraints are assumed to be in the form of exogenous factors (situational forces that may impede the enactment of behavior). In a sense, TRA implicitly assumes that the individual takes constraints into consideration in decision making. However, there is nothing explicit in this regard in the model.

The boundaries of BEM, by virtue of its design, are restricted to purchase situations. Constraints pertaining to the purchase situation are also introduced (e.g., affordability). It is, therefore, a constrained choice model in the domain of purchase behavior.

A common feature of the two attitudinal models, TRA and BEM, is that they incorporate a normative (influence of important others) aspect through the subjective norm construct (TRA) or the social norm construct (BEM). Another common feature is that no interaction of any kind is considered by them, and other researchers (e.g., Miniard and Cohen 1979; 1981; 1983) have raised questions concerning TRA in this connection.

CAS essentially estimates only preferences even though conclusions about choice behavior are drawn through likelihood of purchase type of measurement, and /or through the use of a choice simulator. The latter method is, strictly speaking, an extension of basic CAS. This is in the same vein as the extension of mathematical programming to predict choice behavior (Bernardo and Blin 1977). Regarding constraints, there is nothing explicit in the model itself. However, users of CAS can create contexts for the respondent, and thereby expect the respondent to take contextual constraints into consideration while rating attribute-level combinations. But this is, no doubt, an assumption that actually stems from the greater assumption of human rationality. Further, the constraints (assumed) are treated as fixed across individuals. Also, there is nothing normative (what ought to be or ethical or both) about the conjoint model. However, CAS, in contrast to the attitudinal models, accommodates interactions among attributes.

Issues: The extent of realism in the choice scenario would particularly affect the effectiveness of BEM. For instance, if a "forced choice" scenario were to be adopted (which is often the case in comparative tests), the effectiveness of BEM would be considerably eroded because the first stage of the model becomes irrelevant (BEY =1, and so X1 and X2 become meaningless).

Tentative Conclusions: In a theoretically rigorous sense, TRA and CAS are unconstrained choice models. On a less rigorous level however, they may be considered as constrained choice models because constraints are there, albeit implicitly. BEM accommodates constraints to choice behavior, and can therefore be considered, both theoretically and pragmatically, as a constrained choice model even though its domain of application is limited to purchase situations.

Step 6

Here, we arrive at overall conclusions. Figure 4 provides a gist of the results of the foregoing structured theoretical analysis. While it is very clear that each of them can be used individually to predict (if not explain) consumer choice behavior in suitable settings, a meaningful comparison of their predictive abilities can take place only when, 1. the choice behaviors are all reasoned behaviors, and 2. the test setting involves a real life choice scenario in the purchase phase with all its vagaries and uncertainties. Any limitation(s) imposed on the test setting that cuts into realism would in turn cut, particularly, into the richness of BEM. In view of the above, while the universal constraints of time and money always interfere with the desires of researchers (forcing them to adopt scenarios that lack realism), it is important to realize that a fair comparison of these three models cannot be done in artificial settings.


In this paper, we have suggested a general scheme for theoretically comparing models before empirical comparison, and determining, given the test setting and other criteria (external predictive validity or efficiency) whether in fact they are comparable under all conditions or only under some conditions or not at all. It should be noted that this is not a comprehensive scheme for discussing the results from an empirical comparison of models. In other words, we are not looking at the problem of determining which is truly a better orange given two oranges. Instead, we are looking at two fruits and determining whether they are both oranges. In the process, one may turn out to be an orange and the other a banana, or one may be a grapefruit and the other an orange, or both may turn out to be oranges of the same strain or different strains. The scheme would also enlighten as to the criteria under which two somewhat different models may be compared meaningfully. For example, a tangerine may be compared to a tangelo or a clementine on sweetness, juice content and vitamin C content.

It should also be noted that we have given only an illustration of the scheme; other illustrations may be given. Naturally, the specific items discussed under the dimensions of our scheme would depend upon the test setting and other criteria specific to the particular impending empirical comparison. However, it does not alter the logic of the scheme. It may also be noted that while alternative structures are possible, the proposed structure lends itself to a logical step by step flow, and thus has "programmable" or "flow chart" appeal.

The desire to sensitize researchers to the need for rigorous theoretical comparisons of models prior to actual empirical comparisons was the sole driving force behind this paper. By suggesting a scheme for doing this, we have endeavored to instill some degree of standardization in the task involved. It is our hope that the suggested scheme would contribute to creating order out of anarchy in model comparisons.




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