A Multimethod Approach to Validating Multi-Attribute Attitude Models

James R. Bettman, University of California, Los Angeles
Noel Capon, University of California, Los Angeles
Richard J. Lutz, University of California, Los Angeles
[ to cite ]:
James R. Bettman, Noel Capon, and Richard J. Lutz (1975) ,"A Multimethod Approach to Validating Multi-Attribute Attitude Models", in NA - Advances in Consumer Research Volume 02, eds. Mary Jane Schlinger, Ann Abor, MI : Association for Consumer Research, Pages: 357-374.

Advances in Consumer Research Volume 2, 1975      Pages 357-374

A MULTIMETHOD APPROACH TO VALIDATING MULTI-ATTRIBUTE ATTITUDE MODELS

James R. Bettman, University of California, Los Angeles

Noel Capon, University of California, Los Angeles

Richard J. Lutz, University of California, Los Angeles

[The authors gratefully acknowledge support of the Center for Marketing Studies at the Graduate School of Management, University of California, Los Angeles.]

[James R. Bettman, Noel Capon, and Richard J. Lutz are associate professor and assistant professors, respectively, at the Graduate School of Management, University of California, Los Angeles. The ordering of the authors' names is alphabetical; all three contributed equally to the project.]

The strengths and weaknesses of correlational and analysis of variance (ANOVA) approaches to validating multi-attribute attitude models are discussed. The approaches are then applied to the Fishbein and adequacy-importance models, and an adequacy-evaluation model developed from earlier findings. The adequacy-evaluation model is supported reasonably well. The Fishbein model is poorly supported by correlational approaches, and the adequacy-importance model receives little confirmation from ANOVA findings. Multiple method validation approaches are emphasized.

In recent years consumer researchers have focused considerable attention on multi-attribute models of attitude structure. Drawing from the original theoretical formulations of Rosenberg (1956) and Fishbein (1963) a variety of models have been developed, operationalized and tested (Wilkie and Pessemier, 1973). These models have mostly taken the form:

EQUATION    (1)

where, for an individual respondent AJ = Attitude toward brand j; Xij = Belief as to the extent that brand j possesses attribute i; Yi = Some evaluative aspect of attribute i, such as its goodness or badness, or its importance.

The models have varied both in their underlying theoretical formulations and in their operationalizations; however, the methods used for testing the models have been remarkably similar. Typically, a single product class is selected, and respondents are presented with sets of scales designed to measure Yi for selected attributes and Xij for chosen brands on each attribute. Finally, a global Aj measure for each brand is obtained and a cross-sectional correlation analysis performed between AJ and the index EXijYi. The percentage of explained variance has been the criterion employed to compare models, the model with highest r2 being proclaimed as the superior model. An example of this multiple model approach is found in Mazis and Klippel (1973), who compared the Fishbein, Rosenberg, and adequacy-importance models.

Bass & Wilkie (1973) have pointed out several problems with the cross-sectional correlation procedure, particularly the strong assumption of comparability of individual utilities; accordingly, they have suggested a normalization procedure for adjusting for within subject variance in cross-sectional analysis. Although r2 is increased when this procedure is used, this greater degree of fit occurs irrespective of the model to which the data are fitted. In addition, by the very form of the cross-sectional analysis, all subjects are still assumed to be employing the same model.

These difficulties with cross-sectional analysis are compelling reasons for moving to individual level analysis in examining multi-attribute attitude models. The ultimate goal is to "validate" multi-attribute attitude models by identifying which model is most appropriate as a representation of reality in a given set of circumstances. The measure of appropriateness, however, is a function of the researcher's objectives, and these objectives guide the methodology which is used in the validation procedure (Slovic and Lichtenstein, 1971). If prediction is the aim, then a regression approach (Brunswik, 1952, 1956; Hoffman, 1960) is most appropriate. On the other hand, if an understanding of the individual judgment process is the objective, then an analysis of variance procedure relying on factorial designs is most appropriate (Anderson, 1973, 1974).

The purpose of this paper is to examine two individual level approaches to validation of multi-attribute attitude models and to provide empirical data for validating three alternate multi-attribute models. Results of the two individual level approaches will be compared with the results of the standard cross-sectional analysis. This multimethod approach is crucial step in examining model validity (Wright, 1973).

VALIDATION BY REGRESSION

The individual level regression approach to validation relies on a data collection procedure similar to that outlined above for the cross-sectional analysis. However, the interpersonal utility issue is sidestepped by performing individual level regressions, using the data for each brand as an observation. Validity of a model is again determined by a correlational measure: the higher the coefficient, the more "valid" the model. This approach is in the Brunswik tradition (Brunswik, 1952, 1956) in which a major focus is the realism of the task environment. This realism is achieved by presenting scales which are meaningful to respondents in the sense that only these attributes and brands that are familiar to them are included in the questionnaire. Furthermore, by demanding that respondents perform the encoding function for both the predictor and criterion variables, the task is made similar to the judgment task used in normal purchase decisions.

However, this approach has a number of drawbacks (Anderson, 1962; Sidowski & Anderson, 1967), the most serious of which is the use of r2 as a measure of fit. Birnbaum (1973) has shown how errorless interval data conforming to a perfect linear pattern can lead to a correlation coefficient for an incorrect multiplying model greater than that for the correct adding model. Conversely, errorless interval data conforming to a perfect multiplicative pattern can lead to a correlation coefficient for an incorrect adding model greater than for the correct multiplying model. Birnbaum further indicates that errors in measurement can greatly exaggerate this effect, with the result that data fit to incorrect models could result in much higher correlations than data fit to correct models.

Another problem is that interval scaling must be assumed for Xij, Yi, and the criterion Aj. This is a particularly crucial assumption to make for data used to test a multiplicative model; in fact, Xij and Yi should really be ratio-scaled for invariant results. Any relaxation from interval to ordinal data for the predictor variables can play havoc with degree of fit for a multiplicative model. Further, the researcher must decide whether to code the predictor scales as unipolar (e.g.1 to 7) or bipolar (e.g., -3 to +3), which is not necessary for the ANOVA approach.

Finally, the use of a correlational approach, even at the individual level, means that all respondents' data are being compared with a single, monolithic, model of attitude formation. That is, the model becomes the focal point, with each individual's data being evaluated on how well they "fit" the model. Because each respondent's data are handled in a prespecified manner, there is no opportunity for the discovery of new relationships through the invaluable scientific processes of induction and serendipity. A respondent either fits the model, or he does not. While those who fit the model are valuable in providing support for the model, the data of respondents who do not fit the model are not being fully utilized. The ANOVA approach described in the next section overcomes this serious drawback.

VALIDATION BY ANOVA

The ANOVA approach, a methodology directed toward the analysis of individual judgment processes, is quite different from the regression approach, where the goal is prediction. The major use of ANOVA has been in studies of clinical judgment (Hoffman, Slovic and Rorer, 1968; Anderson, 1969, 1972; Goldberg, 1968) and information integration (Anderson, 1962, 1973, 1974). The methodology involves the development of a series of cue dimensions and stimulus levels on each cue dimension. These cue dimensions become orthogonal factors in a factorial design where the stimulus levels are the levels on each factor. Subjects are presented with profiles representing combinations of stimulus levels from each cue dimension and requested to make a judgment. In total they are presented with all possible combinations of the full factorial design and at least two replications. In one clinical judgment study, for instance, radiologists were presented with a 3x25 complete factorial arrangement of six dimensions of information about an ulcer and asked to judge whether the ulcer was benign or malignant (Hoffman, Slovic and Rorer, 1968) . They were asked for two replications of the 96 cases, 192 judgments in total.

The major advantage of this procedure is that specific tests can be developed for various types of rules for combining the dimensions: adding, averaging, multiplying, or more complex models (e.g. a(b+c) or ab+cd) (Anderson, 1973). Both ANOVA and graphical interpretation of data are useful. The specific tests and techniques used are detailed in later sections. Further, the assumption of interval data is required only for the criterion variable, a major advantage over the regression framework. In fact, by use of functional measurement, scale values can be developed for the predictor variables rather than assumed, as in the regression methodology (Anderson. 1970).

The major disadvantages of the methodology are the lack of realism involved in the factorial task and the fatigue associated with making a large number of judgments. [To some extent the large number of judgments can be reduced by assuming that higher order interactions are negligible, in which case main effects and lower order interactions can be studied with fewer stimuli, either by eliminating within cell replications or by using fractional factorial designs (Anderson, 1972).] The factorial data structure departs substantially from the Brunswikian notion of having cues representative of the subject's normal environment. Also, the systematic factorial structure may bias subjects toward more systematic combination rules. Finally, the subject no longer has to perform an encoding task for the predictor variables. as under the regression methodology. and the stimuli which are developed to test multi-attribute models are devoid of content and low in mundane reality. A final disadvantage of the ANOVA approach lies in the interpretation of interactions, which may arise from problems with the response scales, such as floor and ceiling effects, as well as representing a true relationshiP (Anderson. 1968; Bogartz and Wackwitz, 1971).

VALIDATION OF MULTI-ATTRIBUTE ATTITUDE MODELS AT THE INDIVIDUAL LEVEL

Regression

As pointed out above, the data collection procedure for individual level regression analysis is similar to that for cross-sectional analysis. The researcher chooses a product class, identifies brands within that class, and generates a series of relevant attributes. Respondents are asked to rate each attribute on some evaluative dimension and each brand as to the extent to which it possesses each attribute. Finally, the respondent provides a global affect measure for each brand. The analytic procedure requires regressing the criterion variable of global affect against the sum of the products of the predictor variables, with one observation for each of the several brands for each individual. The success of the model for each individual is determined by the size of the correlation coefficient.

ANOVA

The ANOVA approach, described in detail elsewhere (Bettman, Capon, and Lutz, 1974), is quite different from the correlation approach. As discussed earlier, the methodology is appropriate for examining the individual judgment process when subjects are provided with sets of data, each set being appropriate for the model to be tested. The methodology is described below in terms of an example of comparing competing multi-attribute models of attitude, the Fishbein model, and the adequacy-importance model (Cohen, Fishbein and Ahtola, 1972).

The Fishbein Model may be formulated as:

EQUATION    (2)

where Aj = attitude toward brand j; bij = the likelihood that brand j possesses attribute i; ai = evaluative aspect of attribute i, its goodness or badness; and n = number of attributes.

In a similar manner, the adequacy-importance model may be expressed as:

EQUATION    (3)

where Aj = attitude toward brand j; Bij = belief as to the extent to which attribute i is offered by brand j; Ij= importance weight given attribute i; and n = number of attributes.

Each model makes a number of assumptions about how subjects treat data. These assumptions, or model composition rules, as expressed by the basic algebraic formulation of the models, are as follows:

1) The contribution to affect for each attribute is multiplicative for each model; e.g., bijai and BijIi.

2) The powers of the terms in the product for each attribute are assumed to be 1 for both models. [However, a great deal of work has been done on the beliefs-only model, where the power of ai or Ii is assumed to be zero.]

3) The product terms, bijai and BijIi, add over attributes to form an overall affect measure in both models. [Some studies have taken disaggregative approaches and allowed each product term to be weighted by a regression coefficient.]

4) The components themselves, ai, bij, Ii, and Bij, are coded in particular ways as part of the measurement process. Researchers using the Fishbein model have measured ai and biJ on bipolar (e.g., -2 to +2) scales, while adequacy-importance model re- 6 searchers have typically used nonnegative scales (e.g., 1 to 5). [It should be made clear that differences between the two models in terms of the coding schemes used to assign numerical values to scale responses are not inherent to the specific mathematical formulations shown in (1) and (2) above. Obviously, a researcher using data gathered under the Fishbein format could elect to code the scales from 1 to 5, rather than -2 to +2, and vice versa. In practice, however, research using the Fishbein model has treated the scales as bipolar, while adequacy-importance model research has coded the scales on a unipolar basis.]

In this paper the additive assumption of the models is ignored and it is assumed that the powers equal unity. Attention is focused on the multiplicative and coding assumptions. To test these assumptions via the ANOVA approach, the researcher could present profiles representing a hypothetical brand and ask subjects to make global affect judgments. In testing the Fishbein model, profiles of the following type could be employed:

You believe that Brand X is very likely: _: _:X : _: _:very unlikely to possess a quality which you personally feel is: very good : _: _: _: _ : X: very bad. To you, using Brand X would be: very favorable : _: _: _: _: _: _: _: _: _: _: _: _: very unfavorable.

In testing the adequacy-importance model, profiles of the following form would be appropriate:

You believe that Brand X is very high : _: _: X: _: _: very low in possessing a quality which you personally feel is: very important : _: _: _: _: _: X: not important at all. To you, using Brand X would be: very favorable : : : : : : : : : : : : : very unfavorable.

Since five-point scales are used to present the profiles, there would be a total of twenty-five data profiles in the full (5x5) factorial design. Each subject would be given the task corresponding to one of these two models, and the data generated from these factorial designs examined both graphically and by ANOVA. Depending on the particular (implicit) coding scheme used by the subject and the data combination rules assumed, three simple data patterns could emerge, as shown in Figure 1.

The pattern of data in Figure 1(a) -- a set of parallel straight lines -would be found if subjects add the component bits of data, e.g., (ai + bij), irrespective of how they code it. In the ANOVA there would be strong main effects but no interaction. Neither the adequacy-importance model nor the Fishbein model predicts this pattern of results.

The data pattern of Figure 1(b), a set of crossing straight lines, would be found when subjects act as though coding data in a bipolar manner and then multiplying the component bits of data (bipolar multiplying). In the ANOVA there would be no significant main effects but a strong interaction effect. Such a data pattern is predicted by the assumptions of the Fishbein model.

The data pattern of Figure 1(c) -- a diverging fan of straight lines would be found when subjects act as though coding data in a unipolar manner and then multiply the component bits of data (unipolar multiplying). In the ANOVA there are both significant main effects and a significant interaction, concentrated in the bilinear component (Anderson, 1970, 1973). Such a data pattern is predicted by the assumptions of the adequacy-importance model.

FIGURE 1

THEORETICAL DATA STRUCTURES

FIGURE 2

ADDITIONAL (NON-PREDICTED) DATA STRUCTURES

PREVIOUS APPLICATION OF THE ANOVA APPROACH

In a previous study (Bettman, Capon, and Lutz, 1974) profiles of both the Fishbein type and the adequacy-importance type were presented to two groups of undergraduate psychology students. Following a warm-up task each subject rated 50 profiles, two replications each of the 5x5 factorial design. The data was analyzed for each individual subject as a two-factor ANOVA. In addition to the data patterns expected from the three simple models of adding, unipolar multiplying and bipolar multiplying, a number of other patterns were observed, making seven in total. Subjects were classified into these categories on the basis of both significance levels and explained variance, as measured by the w2 statistic (Hays, 1963; Green, 1973). The categorization scheme is briefly outlined below. For more detail see Bettman, Capon. and Lutz (1974).

Category 1 - No Significant Effects - "No Effects"

Subjects falling into this category have no significant effects for either the treatments or the interaction.

Category 2 - Significant Main Effects - "Adding Model"

Subjects in this category exhibit at least one significant main effect, but have no significant interaction effects. Their data plots correspond to Figure 1(a) -- i.e., a set of parallel lines. The underlying theoretical model implied is addition, rather than multiplication, of the components of the model. This is in contrast to both the Fishbein and adequacy-importance models.

Category 3 - Significant Main Effects, Significant Interaction Concentrated in the Bilinear Term - "Unipolar Multiplying Model"

Subjects in this category exhibit two significant main effects and a significant interaction concentrated in the linear x linear (bilinear) component of the interaction (Anderson, 1970).

The data correspond to the plot in Figure 1(c) -- i.e., a diverging fan of straight lines in the upper right quadrant. The underlying theoretical model is multiplication of components coded in a unipolar fashion, which corresponds to the assumptions of the adequacy-importance model.

Category 4 - Major Portion of Explained Variance in Interaction - "Bipolar Multiplying Model"

The criteria which had to be met for inclusion in this category were as follows: the amount of explained variance in the interaction, as measured by w2, had to be at least 35%, and in addition, had to be at least three times greater than the explained variance for each main effect taken separately. The underlying theoretical model is multiplication of components coded in a bipolar fashion, which corresponds to the assumptions of the Fishbein model.

Category 5 - Major Portion of Explained Variance in One Main Effect and the Interaction - "Asymmetric Multiplying Model"

Subjects in this category have one strong main effect which explains roughly the same proportion of the variance as does the interaction. The specific criteria formulated were that w2 for one main effect was less than ten percent of the total w2, and further, was less than twenty-five percent of the S for the other main effect. Such data was not predicted for the simple rules discussed earlier. Plotted in Figure 2(a), it corresponds to a diverging fan of straight lines, symmetrical about the horizontal axis. One interpretation of this category is that it represents multiplication of components in which the horizontal axis is coded unipolar and the vertical axis bipolar.

Category 6 - Significant Main Effects, Significant Interaction Not Concentrated in the Bilinear Term - "Curvilinear Multiplying Model"

Subjects in this category have two significant main effects, but tests of the interaction show a significant residual interaction after the bilinear term is extracted. This category, shown graphically in Figure 2(b), is clearly related to Category 3 (Figure 1(c)). The major distinction between them is a nonlinearity which is present in this model but not in the unipolar multiplying model.

Category 7 - "Unclassified"

Subjects in this category have data which do not meet the criteria of any of the categories discovered yet. Essentially they have relatively low total explained variance, yet they also have effects which reach significance.

Results

The results of the study are displayed in Table 1. For the adequacy-importance task only fourteen of the eighty-five subjects (16%) obeyed the assumptions of the adequacy-importance model, whereas forty-four of seventy-seven subjects (57%) obeyed the assumptions of the Fishbein model. This difference is significant (X = 29.1, d.f. = 1, 2 <.001): Even under the conservative assumption of ordinal equivalence, which requires the adding model subjects of Category 2 to be combined with the unipolar multiplying models for the adequacy-importance task only [Green (1973) has shown that an interaction of the form shown in Figure l(c) can be transformed through ANOVA to additivity, represented by Figure l(a). Hence, the two patterns are "ordinally equivalent."], the Fishbein model still performs significantly better (x2 = 5.4, d.f. = 1, p < .05).

Subjects who performed the adequacy-importance task were more widely distributed over categories than those performing the Fishbein task, and particular interest settles upon the asymmetric multiplying and curvilinear multiplying model types. As discussed elsewhere (Bettman, Capon and Lutz, 1974) the curvilinear multiplying model results from subjects treating the importance component in a manner not indicated by the model. At low levels of belief, the affect value was initially low, rose, and then fell again as importance increased. There was no such effect at low levels of importance, indicating a possible ambiguity in the importance component. (Bettman. Canon. and Lutz. 1974. p. 17).

TABLE 1

RESULTS OF PREVIOUS STUDY COMPARING THE FISHBEIN AND ADEQUACY-IMPORTANCE MODELS

The asymmetric model category is particularly interesting. One strong main effect and a strong interaction are required for inclusion, but the component which produces the main effect differs in type for the two tasks. For the adequacy-importance task, the adequacy component (Bij) demonstrates the strong main effect, while for the Fishbein task, the evaluation component (ai) exhibits the effect. (Within each task all subjects in the category, 13 for adequacy-importance, and 6 for Fishbein, had the same strong main effect).

This data pattern would be expected if, for each task, one of the two types of information was coded unipolar and the other bipolar, before multiplying. The unipolar dimensions from the two models were importance (Ii) and likelihood (bij), the bipolar dimensions being adequacy (Bij) and evaluation (ai). This bipolar coding for one component and unipolar coding for the other is contrary to the assumptions of both the adequacy-importance and Fishbein models.

Other "incorrect" coding occurred in the adequacy-importance task for eleven subjects who were classified as bipolar multiplying. Thus a total of 24 (11 + 13), or 28% of the subjects, treated the adequacy-importance data in a manner different from that assumed by the model on the coding dimension.

A NEW MODEL

The ambiguity of the importance component in the adequacy-importance model and the indication of possible ambiguity in the likelihood component of the Fishbein model suggest that a new model which is a hybrid of the two models may be superior to both of them.

This new model may be formulated as:

EQUATION    (4)

where Aj = Attitude toward the brand; Bij = Belief as to the extent to which attribute i is offered by brand j; ai = Evaluative aspect of attribute i, its goodness or badness; and n = the number of attributes. Both the evaluative and belief (adequacy) components are assumed to be coded in a bipolar manner and then multiplied. For purposes of further discussion, this new model will be referred to as the adequacy-evaluation model. [Strictly speaking, this "new" model is not really a new model so much as it is a new operationalization of the Fishbein model. Fishbein and Ajzen (1974) have suggested previously that a scale very similar to the adequacy measure used in this study may be a satisfactory operationalization of the bij construct.]

The development of this model and the overall concern with validation of multi-attribute attitude models led to a second study, in which the aim was to test the adequacy-evaluation model by an ANOVA approach and to compare the results with those of the Fishbein and adequacy-importance tasks highlighted above. In addition, all three models were tested by both the individual correlation analysis approach and by cross-sectional correlation. It was hoped that the use of these three alternative validation procedures would result in greater insight into attitude structure than the single method approach employed in past studies.

A MULTIMETHOD APPROACH

Method

Sixty subjects from an undergraduate psychology class were each required to complete two tasks. In the first task, they were presented with a series of scales relating to different brands and attributes of toothpaste. They were asked to evaluate a series of attributes of toothpaste (on a good-bad scale) and then rate their beliefs as to the adequacy of certain brands in offering each attribute (on a very high-very low scale). Finally, they responded to an overall affect measure for each toothpaste brand (very favorable-very unfavorable). This data would be input into correlational tests of the adequacy-evaluation model.

The second task was identical to the ANOVA task described for the previous study. Subjects were presented with a series of profiles of the form:

You believe that Brand X is: very high :_:_X:_:_: very low in possessing a quality which you personally believe is: very good :_:_:_:_:X: very bad. To you, using Brand X would be: very favorable :_:_:_:_:_:_:_:_:_:_:_: very unfavorable.

A total of fifty profiles of the hypothetical brand were rated, two replications each of the 5x5 factorial design. The instructions for the profile rating task emphasized that subJects were to rate a hypothetical product, Brand X, and not toothpaste; i.e., they were asked to consider how they would use information on attributes for products in general. Also, subjects were told that they should evaluate Brand X assuming that they had information only on the single attribute in the profile, and that the two pieces of information in the profile were intended to represent their own feelings about the attribute, not someone else's. The response scale used for the profiles was anchored (Anderson, 1974), by presenting subjects with "extreme" profiles first. For example:

Very high :X:_:_:_:_: very low -- Very good :X:_:_:_:_: very bad.

Order of the other profiles was randomized.

Data for input into the correlation analyses for the Fishbein and adequacy-importance models had been previously gathered in a similar manner from the subJects whose data were presented above in the discussion of the ANOVA results in the first studY.

Results

Three sets of results will be presented in this section. First, the adequacy-evaluation model is compared with the Fishbein and adequacy-importance models in the ANOVA framework; then the results from the individual correlation analyses and the cross-sectional correlation analyses are discussed.

ANOVA. Detailed results for the adequacy-evaluation model are shown in Table 2. [Two measures of reliability of subjects' ratings are presented in Table 2; Ew2, the total variance accounted for by the ANOVA, and r, the product-moment correlation between the two sets of twenty-five ratings.] Comparison with similar data for the other two models (Bettman, Capon, and Lutz, 1974, p. 31) indicates a similar pattern of explained variance (U2)for each category. A comparison of how subjects are classified by the three models is presented in Table 3.

TABLE 2

SUMMARY OF ANOVA RESULTS FROM THE ADEQUACY-EVALUATION TASK

Once again a fairly large number of subjects, twenty, is classified into the adding category. However, twenty-three of the sixty subjects (30%) were classified into the "correct" bipolar multiplying category, a result which is inferior to the Fishbein task (57%) yet far superior to the adequacy-importance task (16%). Indeed, the pattern of data-resembles that of the Fishbein task more than that of the adequacy-importance task, in that only a few subjects are classified into the unipolar, asymmetric and curvilinear multiplying categories. The conclusion from the ANOVA analysis is that of the three competing models, the Fishbein model is superior in capturing the judgment process of most subjects for the ANOVA rating task, but that the adequacy-evaluation model clearly outperforms the adequacy-importance model.

TABLE 3

COMPARISON OF ANOVA RESULTS FROM THREE TASKS

Individual level correlation analysis. The results of the individual level correlation analyses are shown in Table 4. They are displayed by constructing a series of interval ranges for the correlation coefficient and placing subjects in the appropriate range. As shown in the table, 54% of the subjects in the adequacy-evaluation task demonstrated statistically significant correlations, while only 35% and 32% of the adequacy-importance and Fishbein task subjects did so. The average values of r, as computed through Fisher's r to z transformation, differed significantly between the adequacy-evaluation model and the Fishbein model (p <.01), with the adequacy importance model differing significantly from neither. Thus, based on the individual level correlation analysis, the Fishbein model appears to be inferior to the other two models.

Cross-sectional correlation analysis. The final set of analyses were cross-sectional correlations performed on the individual toothpaste brands. These results are presented in Table 5.

The first point of interest is the average amount of variance explained by each model, as computed from the adjusted r2 (r2 adj.) values, which indicates that the adequacy-evaluation model outperforms both the adequacy-importance model and the Fishbein model.

Further, for each individual brand, both the adequacy-evaluation and adequacy-importance models outperform the Fishbein model on every comparison.

TABLE 4

INDIVIDUAL LEVEL CORRELATION RESULTS FROM THREE TASKS

The adequacy-evaluation model exhibited higher r than the adequacy-importance model in four out of the six possible comparisons. The low correlations obtained for the Fishbein model in this case are somewhat perplexing; in all of the published work on the model, the relationships have seldom been as small as the ones observed here. Further, Nakanishi and Bettman (1974), in a study utilizing an instrument virtually identical to the one employed here, measured student attitudes toward the same seven brands of toothpaste and obtained an average r2 of .253, more than twice the size of the present findings. Therefore, the poor correlations found for the Fishbein model in this study can be somewhat discounted. This same conclusion can be applied to the results of the individual level correlation analysis as well, where the Fishbein model's performance was substantially weaker than in the Nakanishi and Bettman study. Obviously, the present findings may be more valid than the Nakanishi and Bettman results; however, the weight of other evidence for the Fishbein model dictates against this conclusion.

TABLE 5

CROSS-SECTIONAL CORRELATION RESULTS FROM THREE TASKS

Discussion

This study reports a multimethod validation approach for three different multi-attribute attitude models. Two of the models tested were the Fishbein and adequacy-importance models, the third being a new model -- the adequacy-evaluation model -- whose genesis was suggested by the results obtained from an earlier study.

The three validation procedures employed were the familiar cross-sectional correlation, individual level correlation, and an ANOVA validation procedure new to the field of consumer behavior. The results which were obtained from these procedures were equivocal. From the ANOVA validation methodology, the adequacy-importance model was inferior to the other two models by virtue of the wide classification distribution of subjects. This did not occur to the same degree for the adequacy-evaluation and Fishbein models, but the Fishbein model outperformed the adequacy-evaluation model in terms of correct classifications by a considerable margin.

The individual correlation approach showed the Fishbein model to be inferior to the other two models, the adequacy-evaluation model being marginally superior to the adequacy-importance model by the criterion of r2. The cross-sectional correlation analysis magnified the differences found at the individual level, the adequacy-evaluation model outperforming the adequacy-importance model, and both being superior to the Fishbein model

Taking all of these results into consideration, it appears that the new adequacy-evaluation model is superior overall to both the adequacy-importance and the Fishbein models, for it does not perform badly on any one of the validation tests and is superior on two of the three.

Clearly this is not the last word in validation and multi-attribute models. Other models exist in the literature, and some of these should be subjected to a multimethod validation procedure. It is interesting to note that the genesis of the new model was due to a new validation procedure being applied at the individual level. Cross-sectional analysis modes might not have been able to isolate the possibility of such a model.

Finally, a note of caution is appropriate. The current findings are based on a single-attribute version of all three models tested. Thus the results may not be simply extended to encompass the multi-attribute case. Future research should extend the ANOVA approach to an examination of the additive assumption of multi-attribute models. In addition, other validation procedures should be employed and new models tested by a multimethod approach. Had a single approach been taken in this study, quite different conclusions might have been drawn, depending upon the procedure employed. Multimethod validation procedures allow the development of a richness in research findings which single methods cannot hope to achieve.

REFERENCES

Anderson, N.H. Application of an additive model to impression formation. Science, 1962, 138, 817-818.

Anderson, N.H. Partial analysis of high-way factorial designs. Behavior Research Methods and Instrumentation, 1968, 1, 2-7.

Anderson, N.H. Comment on 'An analysis of variance model for the assessment of configural cue utilization in clinical judgment.' Psychological Bulletin, 1969, 72, 63-65.

Anderson, N.H. Functional measurement and psychophysical judgment. Psychological Review, 1970, 77, 153-70.

Anderson, N.H. Algebraic models in perception. In E.C. Carterette ant M. Friedman (Eds.) Handbook of perception. Vol. 2. New York: Academic Press, 1974, in press (a).

Anderson, N.H. Cognitive algebra: Integration theory applied to social attribution. In L. Berkowitz (Ed.), Advances in experimental social psychology. New York: Academic Press, 1974, in press (b).

Anderson, N.H. Information integration theory: A brief survey. In D.H Krantz, R.C. Atkinson, R.D. Luce, and P. Suppes (Eds.), ContemporarY developments in mathematical psychology. Vol. 2. San Francisco: W.H. Freeman, 1974, in press (c).

Bass, F. and Wilkie, W.L. A comparative analysis of attitudinal predictions of brand preference. Journal of Marketing Research, 1973, 10, 235-241.

Bettman, J.R., Capon, N. and Lutz, R.J. Cognitive algebra in multi-attribute attitude models. Working Paper No. 10, Center for Marketing Studies, University of California, Los Angeles, February 1974.

Birnbaum, M.H. The devil rides again: Correlation as an index of fit. Psychological Bulletin, 1973, 74, 239-242.

Bogartz, R.S. and Wackwitz, J.M. Polynomial response scaling and functional measurement. Journal of Mathematical Psychology, 1971, 8, 418-443.

Brunswik, E. The conceptual framework of psychology. Chicago: University of Chicago Press, 1952.

Brunswik, E. Perception and the representative design of experiments. Berkeley: University of California Press. 1956.

Cohen, J.B., Fishbein, M. and Ahtola, O.T. The nature and uses of expectancy-value models in consumer attitude research. Journal of Marketing Research, 1972, 9, 456-60.

Fishbein, M. An investigation of the relationships between beliefs about an object and the attitude toward that object. Human Relations, 1963, 16, 233-240.

Fishbein, M., and Ajzen, I. Beliefs, attitudes, intentions, and behavior: An introduction to theory and research. Manuscript in press, 1974.

Goldberg, L.R. Simple models or simple processes? Some research on clinical judgments. American Psychologist, 1968, 23, 483-496.

Green, P.E. On the analysis of interactions in marketing data. Journal of Marketing Research, 1973, 10, 410-20.

Hays, W.L. Statistics for psychologists. New York: Holt, Rinehart, and Winston, 1963.

Hoffman, P.J. The paramorphic representation of clinical judgment. Psychological Bulletin, 1960, 57, 116-131.

Hoffman, P.J., Slovic, P., Rorer, L.G. An analysis of variance model for the assessment of configural cue utilization in clinical judgment. Psychological Bulletin, 1968, 69, 338-349.

Mazis, M.B., and Klippel, R.E. Instrumentality theories and consumer attitudes: Comparing alternative models. Proceedings. Association for Consumer Research, 1973, 346-7.

Nakanishi, M., and Bettman, J.R. Attitude models revisited: An individual level analysis. Journal of Consumer Research, 1974, forthcoming.

Rosenberg, M.J. Cognitive structure and attitudinal affect. Journal of Abnormal and Social Psychology, 1956, 53, 367-372.

Sidowski, J.B. and Anderson, N.H. Judgments of city-occupation combinations. Psychonomic Science, 1967, 7, 279-280.

Slovic, P. and Lichtenstein, S. Comparison of bayesian and regression approaches to the study of information processing in judgment. Organizational Behavior and Human Performance, 1971, 7, 649-744.

Wilkie, W.L. and Pessemier, E.A. Issues in marketing's use of multi-attribute attitude models. Journal of Marketing Research, 1973, 10, 428-441.

Wright, P. Research orientations for analyzing consumer judgment processes. Proceedings. Association for Consumer Research, 1973, 268-79.

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