An Approach to the Resolution of Multicolinearity in the Attribute Structure of Attitudes

Citation:

Reza Moinpour and James B. Wiles (1972) ,"An Approach to the Resolution of Multicolinearity in the Attribute Structure of Attitudes", in SV - Proceedings of the Third Annual Conference of the Association for Consumer Research, eds. M. Venkatesan, Chicago, IL : Association for Consumer Research, Pages: 341-348.

Proceedings of the Third Annual Conference of the Association for Consumer Research, 1972      Pages 341-348

AN APPROACH TO THE RESOLUTION OF MULTICOLINEARITY IN THE ATTRIBUTE STRUCTURE OF ATTITUDES

Reza Moinpour, University of Washington

James B. Wiles, University of British Columbia

[The research was supported by the Office of Publications and Research, Graduate School of Business Administration, University of Washington.]

[Reza Moinpour is Assistant Professor of Marketing, Graduate School of Business Administration, University of Washington, Seattle, Washington. James B. Wiley is Acting Assistant Professor of Marketing, Faculty of Commerce and Business Administration, The University of British Columbia, Vancouver, British Columbia, Canada.]

Recently, a number of market researchers have proposed that the consumer's preference for a product can be accounted for by a weighted, additive utility (WAU) model (Bass and Talarzyk, 1969; Cohen and Ahtola, 1971; Cohen and Houston, 1971; Hughes, 1970; Moinpour and MacLachlan, 1971; Sheth, 1970; Sheth and Talarzyk, 1970). The WAU motel is derived from attitude theories formulated by Rosenberg (1956) and Fishbein (1965).

Such models postulate that the individual's preference for a product is a function of a) the degree to which the product possesses certain attributes, and b) the importance of the attributes. One example of such a construct is the following (Moinpour and MacLachlan. 19715:

(1)    EQUATION

where

"_x = a consumer's attitude toward a particular product or brand X.

W_i = the importance or weight of attribute i.

B_ix = the product's satisfaction score on attribute i; subject's belief about attribute i for product X.

n = the number of product attributes.

A review of the literature reveals some important issues which market researchers have encountered in applications of WAU model in consumer behavior!

1. The use of separate or disaggregative rather than the summed-score form of the model.

2. The application of individual vs. group analysis as methodological procedures.

3. The extent of the contributions of the two components of the model (Wi and BiX) to its predictive power.

4. The existence of collinearity amongst individual's evaluative beliefs.

There appears to be agreement among researchers that the disaggregative form of the model is the more appropriate one for the investigation of consumer attitude (Cohen and Ahtola, 1971; Cohen and Houston, 1971; Sheth, 1970). In this form, the model allows for further evaluation of the relative contributions of underlying attributes.

Most of the studies in this area have used regression as their method of analysis. Recently, applications of multidimensional scaling (Hansen and Bolland, 1971; Moinpour and MacLachlan, 1971) and canonical analysis (Lutz and Howard, 1971; Sheth, 1971) have also been reported. However, the generalization across subjects that takes place when a group is used as the experimental unit may lead to confounded response circumstances. This problem can be attacked by carrying out regression on groups of subjects with homogeneity of response sets (Scott and Bennett, 1971). It has been correctly pointed out, however, that the theory underlying the WAU model depicts an individual construct; thus, individual analysis is conceptually the proper one to use (Moinpour and MacLachlan, 1971).

There has been some controversy surrounding the question of the extent of the contributions of the two components of the attitude model. Several researchers have suggested that "weights" incorporated into the WAU model contribute little to its predictive power (Cohen and Houston, 1971; Moinpour and MacLachlan, 1971; Sheth and Talarzyk, 1970). The unimpressiveness of respondent-provided "weights" to the model's predictive power has been a factor in the decision of a number of researchers to use regression analysis to estimate weights rather than use "weights" supplied by respondents (Cohen and Ahtola, 1971; Sheth, 1970). We argue that, given the theory underlying the model (1), the lack of contribution of weights to the predictive power may be due to the fact that because of measurement problems the attribute scores may in fact already reflect the "weighting" criterion. In other words, they may in fact be-"weighted judgments;" consequently, multiplying by independently derived "weights" would serve only to doubly weight the attribute scores. It has been suggested, as an alternative approach, that the attribute importance component of the model can best serve as criteria for the selection of attributes (Moinpour and MacLachlan, 1971).

A final problem, which infrequently has been considered, is the existence of intercorrelation between individuals' expressed, evaluative beliefs concerning brands' possession of "salient" product attributes. One might expect this problem to arise in the case of unplanned data. However, the results of a number of studies using factor analysis (Moinpour and MacLachlan, 1971) and canonical correlation (Sheth, 1971) suggest that the phenomenon may occur even when care is taken in the original selection of "salient" product attributes. Inasmuch as the model (1) prescribes an independent structure, we feel that an effort should be made to satisfy this requirement. This is particularly true when regression techniques are used, since estimates of regression weights are notoriously unstable when collinearity exists among the explanatory variables (Kendall, 1957).

THE OBJECTIVE

This study is concerned with the resolution of the collinearity problem in the attribute structure. In this paper, we describe a method for selecting a subset of "salient" product attributes which minimizes overlapping of information supplied by explanatory variables in regressions. Factor analysis is employed to summarize a set of potential explanatory variables to one with a few variables with a little loss of information. It can be used to identify and to extract a relatively uncorrelated-subset of independent variables to be included in regressions. In this study, predictions of brand preferences (for soft drinks) made from an uncorrelated subset of three product attributes were often better, and never significantly worse than, predictions made using the entire set of ten product attributes. Furthermore, in light of previous findings, it was encouraging that those attributes selected for the model happened also to be those indicated by the respondents to be "important."

THE DATA

Data was collected from 35 University of Washington students. The following information for 10 brands of soft drinks were collected:

Part 1. Each student was asked to rate each brand on 10 attributes using a 6-point scale, ranging from l--satisfactory to 6--unsatisfactory. The list of brands and product attributes appears in Table 1.

Part 2. Each respondent was asked to evaluate these product attributes in terms of importance on a 6-point scale, ranging from l--important to 6 unimportant.

Part 3. The participant was also asked to rate the 10 brands in terms of preference using a 10-point scale, ranging from 1 most prefer to 10--least Prefer.

TABLE 1

LIST OF BRANDS AND ATTRIBUTES

METHOD OF ANALYSIS

The objective is to minimize the intercorrelation between explanatory variables in a regression equation. One method suggested by Kendall (1957) is to regress the dependent variable (preference) on the principle components of Rii, the correlation matrix of the total pool of explanatory variables (product attributes). The result, by definition, is orthogonal regression. We adopt an approach based on the one proposed by Kendall (1957) and previously utilized by Twedt (1952) and Daling and Tamura (1970). The aim of this latter approach is to select a set of relatively uncorrelated variables, using the extracted factors as guidelines, that retain most of the predictive power of the original pool of potential explanatory variables. The basic factor analysis model is of the following form:

(2)  EQUATION

where

X_i = value of an observed explanatory variable

f_j = common factors

a_ij = factor loadings, indicates the correlation between X_i and f_j

e_i = an error term

The principle factor loading matrix, A, for the first three principle components of Ri was calculated and rotated according to the varimax criterion. An element of this matrix, aij, indicates the correlation between attribute Xi and factor f . The varimax rotation tends to maximize the correlation between an attribute and a single factor. If an attribute is highly correlated with a factor and the factor is highly correlated with preference, then, in turn, the attribute should also be correlated with preference. Similarly, if an attribute is highly correlated with a factor it cannot be highly correlated with another factor and, in turn, cannot be highly correlated with attributes having high loadings on that factor. Thus, by selecting attributes having maximum loadings on the rotated factors, a set of relatively uncorrelated explanatory variables were obtained.

The success of this procedure can be evaluated by performing two sets of regressions for each product (across subjects). One regression incorporates the entire pool of potential explanatory variables (product attributes), the other includes only the three attributes selected in the manner described above. That is, for each brand we fit the following model:

(3)    EQUATION

where

Y - stated preference ratings

X_i = the attribute scores

e = an error term

The results appear in Table 2.

DISCUSSION OF RESULTS

For each of the ten brands separate regressions were performed of preference rating on attribute scores across subjects, using all attributes. Next, the subject by attribute matrix of each of the previous regressions was factor analyzed. The first three factors extracted accounted for most of the variance of the explanatory variables. Following a procedure adopted by Twedt (1952) and by Daling and Tamura (1970), the product attributes with the highest loading on each of the rotated factors were selected for inclusion in a second set of regressions. These variables offer most promise for prediction of preference.

Adjusted R2 values for both sets of regressions are given in Table 2. (Adjusted coefficients of determination are presented to allow comparison with other studies.) For six of the ten brands. the reduced attribute set explained more of the variation in the preference ratings than did the complete attribute set. For the remaining four brands the results of the two regressions were comparable. We infer from these results that reduction of variables in the regression does not lead to significant reduction in R2 when the reduced variable set is free from the interdependency which may have existed in the original variable set. We may add that most of the variables selected on the basis of the factor analysis were indicated, a priori, by the respondents as being important product attributes.

TABLE 2

SUMMARY OF REGRESSION RESULTS

CONCLUDING REMARKS

It appears that the major issues confronting the researchers in this area relate to the specification of the variables and their measurement and the specification of the WAU model itself. A critical aspect of the first problem is the existence of intercorrelation among variables even when care is taken in the original selection of "salient" product attributes (Lehmann, 1971). Since the model (1) prescribes an independent structure, attempt should be made to satisfy this requirement especially when regression is used since the net regression coefficients tend to be unstable when collinearity exists among the explanatory variables (Kendall, 1957). An approach to this problem is the use of orthogonal factor analysis for selection of variables. This technique provides the experimenter with an orthogonal subset of explanatory variables to be used in regressions. The results of this study indicate that significant prediction of brand preference can be made from an uncorrelated subset of explanatory variables (product attributes).

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