# Four Methodological Problems in Multi-Attribute Attitude Models

^{[ to cite ]:}

Michel Laroche (1978) ,"Four Methodological Problems in Multi-Attribute Attitude Models", in NA - Advances in Consumer Research Volume 05, eds. Kent Hunt, Ann Abor, MI : Association for Consumer Research, Pages: 175-179.

^{[ direct url ]:}

http://acrwebsite.org/volumes/9420/volumes/v05/NA-05

[This research is part of a project supported by the Laboratoire de Recherche of the FacultT des Sciences de l'Administration of the UniversitT Laval, Quebec.]

Four methodological problems are identified: two dealing with the scaling decision, i.e., origin and range; and two dealing with the relation among attributes, i.e., interaction and halo effects. Two procedures are proposed in order to improve the specification of the multi-attribute attitude models and our understanding of the process of attitude formation, as well as their predictive abilities.

IDENTIFICATION OF THE PROBLEMS

There has been a great amount of research in marketing on multi-attribute attitude models inspired by the work in social psychology of Rosenberg (1956) and Fishbein (1967). Basically, consumers evaluate competing brands on a certain number n of attributes according to the following multiplicative rule:

where:

"

_{j}is the consumer's attitude toward brand j;B

_{ij}is the strength of belief i about brand j, i.e., the probability that brand j is associated with attribute i;a

_{i}is the evaluation of attribute i.

Some problems appeared, as researchers tried to implement the previous model or to compare its performance with additive or other nonlinear models. Excellent reviews of these attempts are available in Wilkie and Pessemier (1973) and in Einhorn and Gonedes (1971). The four major problems could be described as follows:

1. The problem of the

originof the scales used in measuring B_{ij}and a_{i}. As it was correctly pointed out by Schmidt and Wilson (1975), by choosing between uni-polar (for example, from 1 to 5) and bipolar (from -2 to +2) scales for each concept, the researcher is able to manipulate the correlation between A_{j}and the summation of a_{i}B_{ij}'s. This is so because (1) is basically anonlinearmodel, and a transformation of its variables by manipulation of the scales is likely to modify the functional form by which it is represented. If we note that the coefficient of correlation between two entities is unaffected by linear transformation of these entities, we can see that this problem of the origin of the scales will not affect the performance of linear models of attitude formation.2. The problem of the

rangeof the scales used in measuring B_{ij}and a_{i}. Most of the published studies have used the same range for all the concepts, usually scales with 5 or 7 points. As Etter (1975) correctly remarked, the model (1) will be sensitive to variations in the range of these scales, and the introduction of scale transformation parameters could improve its performance. This is so for the same reason as before, i.e., (1) is basically a nonlinear model.3. The model (1) does not take into account the

interactionamong the different attributes. In effect, the algebraic rule contained in (1) is equivalent to assuming independence of the different effects. It is evident that this is very often not the case. Sheth (1974) proposed a two-step procedure: a reduction of the dimensions by using a decomposition procedure of the different beliefs followed by a regression analysis in order to determine the weights of the underlying independent beliefs. But this method assumes homogeneity among the respondents and does not solve the problem of the origin. Besides, the derived dimensions are often difficult to interpret.4. It has been observed that respondents tend to indicate higher beliefs about a brand according to the general attitude toward this brand. This phenomenon is the

halo effect, and it represents a serious methodological problem in multi-attribute attitude models (see Beckwith and Lehmann, 1975).

This paper will attempt to provide some alternatives in order to obviate some of the problems which have just been identified.

THE PROBLEM OF THE ORIGIN

When studying consumer behavior, the researcher selects a scale in order to measure a given phenomenon, such as the strength of a belief or the evaluation of an attribute. The phenomenon is assumed to exist independently of the type of scale used. For example, we feel the same way today, whether the temperature is expressed in Celsius or Fahrenheit. Faced with bipolar adjectives, the respondent indicates his position by checking one of the possible alternatives. Then, the researcher attributes numbers to these alternatives. As long as this measure is used in an additive way, no problem arises. But in multi-attribute attitude models, researchers are trying to multiply such measures and in order to do so ratio scales are needed. In physics, absolute temperatures had to be introduced when temperature was one of the multiplying variables in a given law. Similarly, it is necessary here to determine the position of the origin of the scale for each concept. It becomes a parameter to be estimated when applying the model (1), in the same way as regression parameters are obtained. That is, the origins for the a_{i}'s and the B_{ij}'s are the ones which maximize the correlation coefficient between the calculated and the measured attitudes.

This approach is superior to the arbitrary determination of these parameters which has been found in the literature. For example, completely different predictions could result from such an initial choice, as is illustrated in Table 1 with an hypothetical example. As is evident in this case, the determination of the origin is not only a question of calibrating a tool; it is essentially a very important element of model specification.

WITH THE SAME DATA, DIFFERENT PREDICTIONS ARE MADE ACCORDING TO THE SCALES CHOSEN.

In order to illustrate one of the procedures proposed in this paper, a set of data was collected for 75 persons selected in a shopping center of Quebec. The questionnaire used dealt with the choice between two competing brands of cola in the large size category: the 53 oz. bottle of Pepsi and the 40 oz. bottle of Coke. Four criteria were used: economy, ease of manipulation, brand reputation and ease of storage in the refrigerator. The bipolar adjectives used were "bad description good/description" for the strengths of beliefs and "not important at all/very important" for the evaluations. Both were collected on a 5-points scale. The raw data were then transformed by varying the origin for each set of scales, and the transformed data were used in (1) in order to obtain the predicted attitude which was correlated with the measured overall attitude. The correlation coefficients thus obtained are presented in Table 2. The results illustrate dramatically the effect of changing the codifications of the data used in (1).

In effect, the model (1) should be rewritten as

where a and B are constants to be determined.

In Table 2, one can find the correlation for the bipolar model (a = 3, B = 3), the mixed models (a = 0, B = 3; a = 3, B = 0) and the unipolar model (a = 0, B = 0). Further analysis leads to the following conclusions:

1. The best model for Pepsi alone is a = 0, B = 4.4 for which the correlation coefficient is equal to .6450;

2. The best model for Coke alone is a = 2.1, B = 3.5 for which the correlation coefficient is equal to .6188;

3. The best model for both is a = 1.1, B = 3.8 for which the coefficients of correlation are respectively .6277 and .5942. This was obtained by maximizing the sum of both correlation coefficients.

Finally, it can be shown that Anderson's averaging model is relatively unaffected by the problem of the origin. This would explain why this model performs in a more consistent manner than the model (1). Basically, one can generally describe the averaging model as follows (Anderson, 1970):

The evaluation scale is a weight variable w_{i}, which one can define as

which leads to

These weights then combine in a multiplicative fashion with the strength of belief in order to yield the attitude A'_{j}

By decomposing (4) and rearranging terms, one finds:

This last expression shows that the coefficient of correlation between A'_{j} and the measured attitude would be independent of B, which is the origin of the belief scale. But the correlation coefficient is still dependent upon a, which is the origin of the evaluation scale. Intuitively, one would expect a to be the lowest value of that scale. This was borne out experimentally on the same set of data as before. The procedure was the same as before: a was varied, and for each value of a the correlation coefficient between predicted and measured attitudes was computed. The origin a was determined to be equal to 1, and the corresponding coefficients of correlation were respectively for Pepsi and for Coke equal to .6436 and .6114. It is worth noting here that these coefficients are very close to the ones obtained previously for Fishbein's model. This might suggest that, with proper adjustment of the scales, their predictive abilities are similar.

Limitation of the method

This procedure for determining the origin of each type of scale, i.e., a_{i} and B_{ij}, suffers from one implicit assumption: that all attributes have the same origin on the same scale. Although this is intuitively appealing, it should be tested, and the previous method could be adapted in order to fit the following model:

This would necessitate the estimation of 2n parameters instead of 2.

THE PROBLEM OF THE RANGE OF THE SCALES

The same arguments as for the origin can be used to defend the need for a determination, at least implicitly, of the range of the scales used to measure a_{i} and B_{ij}. But there is one major exception for which this problem does not arise. If one assumes that all the a_{i} scales have the same range r_{1}, and that all the B_{ij} scales have the same range r_{2}, then the analysis of the behavior of the correlation coefficient shows that any uniform change of range for each group would not affect it. This result is a major difference with the previous problem.

On the other hand, if the ranges of, say, the a_{i} scales depend on the nature of the attribute, they become parameters to be estimated. This is what was done implicitly in the second phase of Sheth's method, and his regression coefficients represent the product of the average evaluation by a range adjustment factor (Sheth, 1974). One can say that, in general, one of the main advantages of multiple regression in this context is its ability to adjust for the misspecification of the range of each scale. This property will be used later in conjunction with the method of orthogonal polynomials.

INTERACTIONS AMONG ATTRIBUTES AND THE HALO EFFECT

The model represented in (1) assumes that each attribute is processed by the consumer independently of the other ones. This would justify the manipulation of a selected attribute in order to improve the attitude toward a given brand. However, this is not often the case. For most products it is likely to find high correlations among attributes on the ai and Bij dimensions. For example, in the case of these soft drinks, we should expect an interaction between the manipulation and the storage criteria. Then, the question in terms of attitude change becomes one of direction and degree of modification of the related components of (1). If an induced variation in one of the attributes produces changes in the same direction on all the related attributes, then there will be some positive attitude change. But, if the induced variation produces opposite changes, then it will be necessary to determine, if possible and if desirable, the approximate amount of stimulation that would lead to positive attitude change.

A particular case of interaction effects among attributes is due to the halo effect (Beckwith and Lehmann, 1975). In their paper, Beckwith and Lehmann suggest the introduction in the application of the model (1) of the average attitude A as a proxy variable for this effect. It can be argued that a better proxy variable for the halo effect is the attribute of brand reputation. The higher the reputation of the brand, the more likely it will be overvalued on certain attributes. The main advantage of using this variable is that in doing so we better capture individual differences. In addition, it is possible to study the interactions involving the halo effect as will be shown in the next section.

APPLICATION OF THE METHOD OF ORTHOGONAL POLYNOMIALS

Methodology

The method of orthogonal polynomials developed by Laroche (1974) from the work of Fisher (1958) is particularly useful in the context of empirically determining the consumer's decision rules. Its major advantages are as follows:

1. It adapts itself to the two problems associated with the scales, i.e., origin and range.

2. It decomposes the effects into independent entities: main and interaction.

3. All interactions can be introduced into the analysis.

4. The halo effect can be determined more precisely.

The same data as before are used in this application. For each attribute, the main effects are calculated (linear, quadratic and cubic). To summarize, the method consists of decomposing the effect of x on y into a trend or linear component, a quadratic component uncorrelated with the trend, and a cubic component uncorrelated with the previous two. On the interaction side, and this is the important part, the effects of x and z on y are decomposed into two main effects or trends and an interaction component uncorrelated with the trends of x and z. Thus, for each set of attributes, an interaction component is calculated. All of these components are then entered into a stepwise regression, and the resulting coefficients are presented in Table 3.

REGRESSION RESULTS FOR PEPSI AND COKE USING THE METHOD OF ORTHOGONAL POLYNOMIALS

Major findings

1. The criterion of economy is independent of the other criteria, including the halo effect. It is significant only for the most economical brand, i.e., the 53 oz. bottle of Pepsi. On that dimension, since the only significant terms are the strength of belief (main) and the interaction (bipolar), the model used by the consumers is a mixed one: roughly bipolar on the evaluation (a

_{1}) and roughly unipolar on the strength of belief (P_{1}). This is consistent with the previous overall result.2. The previous finding for a

_{1}is also true for a_{2}and a_{4}for both brands.3. For both brands, the reputation of each one on the main effect is the most important criterion. The halo effect is apparent by the significant interaction of brand reputation with manipulation in the case of Coke and with manipulation and storage in the case of Pepsi. In particular, for Coke the more important the criterion of manipulation is, the lower the attitude toward Coke is. Similarly for Pepsi, the more important to the consumer both attributes of manipulation and storage are, the lower the attitude toward Pepsi will be.

4. Among all the nonlinear components introduced in the stepwise regression, the only significant one is a

_{3}(cubic). This last term, coupled with the linear trend a_{3}, shows that there is a complex negative reaction against the brand Pepsi since the more important this criterion is, the lower the attitude toward Pepsi is.5. In the case of Coke, the criterion of storage seems to follow a bipolar model. In fact, for both products and for all the attributes, this is the only case for which the decision rule is close to the one suggested by Fishbein (1967).

Discussion

This last empirical approach to the determination of the process of attitude formation is probably more fruitful than the comparison of several possible models which could be premature. A strategy of accumulating empirical results of the kind presented in this paper would provide researchers the raw material upon which to build better models of attitude formation or to more adequately adapt existing models or formalize existing theories. This task would also require a more explicit elicitation of the basic assumptions upon which models are elaborated. A case in point is the assumptions underlying the scaling decision, the multiplicative rule, and the additivity of the products.

SUMMARY

Four methodological problems were identified in the context of multi-attribute attitude models, more precisely the linear compensatory model. Two were related to the scaling decision, i.e., the origin and the range of the different scales used to measure the evaluations and the strengths of beliefs. A procedure was proposed in order to obviate these problems. It was based upon a numerical search with the correlation coefficient as the objective function. Two other problems were related to the relationship among attributes, i.e., the interaction and the halo effects. It was proposed that the application of the method of orthogonal polynomials would be very useful in order to incorporate and analyze all four issues. The empirical results are very promising, and they suggest that a better understanding of attitude formation would be reached if we accumulated such findings. These would provide the building blocks for constructing better models, both in terms of explanation and prediction.

REFERENCES

Anderson, N. H. "Integration Theory and Attitude Change,", __Psychological Review__, 77 (May 1970), 153-170.

Beckwith, N. E. and D. R. Lehmann, "The Importance of Differential Weight in Multiple Attribute Models of Consumer Attitude", __Journal of Marketing Research__, Vol. X (May 1973), 141-145.

Beckwith, N. E. and D. R. Lehmann, "The Importance of Halo Effects in Multi-Attribute Attitude Models", __Journal of Marketing Research__, Vol. XII (August 1975), 265-275.

Einhorn, H. J. and N. J. Gonedes, "An Exponential Discrepancy Model for Attitude Evaluation", __Behavioral Science__, 16 (March 1971), 152-157.

Etter, W. L., "Attitude Theory and Decision Theory: Where is the Common Ground?" __Journal of Marketing Research__, Vol. XII (November 1975), 481-483.

Fishbein, M., "A Behavior Theory Approach to the Relations Between Beliefs About an Object and the Attitude Toward the Object", in M. Fishbein, ed., __Readings in Attitude Theory and Measurement__ (New York: Wiley, 1967), 389-400.

Fisher, R. A., __Statistical Methods for Research Workers__, 13th ed. (New York: Hefner, 1958).

Laroche, M., "A New Approach to Nonlinear Consumer Behavior and Market Segmentation by the Use of Orthogonal Polynomials", Unpublished Ph.D. Dissertation, Columbia Graduate School of Business, 1974.

Rosenberg, M. J., "Cognitive Structure and Attitudinal Affect", __Journal of Abnormal and Social Psychology__, 53 (November 1956), 367-372.

Sheth, J. N., "A Field Study of Attitude Structure and Attitude-Behavior Relationship", in J. N. Sheth, ed., __Models of Buyer Behavior__ (New York: Harper & Row, 1974).

Wilkie, W. L. and E. A. Pessemier, "Issues in Marketing's Use of Multi-Attribute Attitude Models", __Journal of Marketing Research__, 10 (November 1973), 428-441.

----------------------------------------

Tweet
window.twttr = (function (d, s, id) { var js, fjs = d.getElementsByTagName(s)[0], t = window.twttr || {}; if (d.getElementById(id)) return; js = d.createElement(s); js.id = id; js.src = "https://platform.twitter.com/widgets.js"; fjs.parentNode.insertBefore(js, fjs); t._e = []; t.ready = function (f) { t._e.push(f); }; return t; } (document, "script", "twitter-wjs"));