An Investigation of Some Alternatives to the Linear Attitude Model


Bobby J. Calder and Richard J. Lutz (1972) ,"An Investigation of Some Alternatives to the Linear Attitude Model", in SV - Proceedings of the Third Annual Conference of the Association for Consumer Research, eds. M. Venkatesan, Chicago, IL : Association for Consumer Research, Pages: 812-815.

Proceedings of the Third Annual Conference of the Association for Consumer Research, 1972      Pages 812-815


Bobby J. Calder, University of Illinois at Urbana-Champaign

Richard J. Lutz, University of Illinois at Urbana-Champaign

The concept of attitude has been of central interest to both researchers and practitioners interested in consumer behavior. Investigations of attitudes offer the possibility both of understanding the cognitive processes of consumers and of predicting their future behavior. Recently, many researchers in this area have been especially attracted to a class of attitude models known as the expectancy-value approach. In contrast to the more traditional cognitive-affective-conative approach to the organization of attitudes, these models employ two elements, the likelihood (expectancy) of each belief making up an attitude and the worth (value or affect) associated with each belief (see Calder and Ross, 1972). If products are conceived of as bundles of attributes about which consumers may have a variety of beliefs, the expectancy value approach seems well suited to the analysis of consumer behavior.

Perhaps the most influential expectancy-value model has been proposed by Fishbein (1963, 1965, 1967). His model is given by the equation

A = Ei=1 Biai   [1]

where A is an attitude toward an object or action, B is the strength of belief i about the object or action, and a is the evaluative aspect of belief i. These components are usually assessed by semantic differential rating scales (Fishbein and Raven, 1962). Notice that this model postulates that beliefs are processed as the summation of the multiplicative combination of belief strength and affect. A similar expectancy-value model of this form has been presented by Rosenberg (1956, 1960) in which the expectancy component is treated as the "perceived instrumentality" of a value and the value component is represented by the "importance" of the value. These models have received the most empirical attention in the consumer behavior area (e.g., Bass and Talarzyk, 1972; Cohen, Fishbein, and Ahtola, 1972; Sheth and Talarzyk, 1972).

Other models within the same expectancy-value approach are certainly possible, however, Anderson (1971), for instance, has argued for the extension of his information integration model to attitude change. This model is written as

R = Ei=o wisi  [2]

where R may be considered the attitude response, s is the scale value of source-communication i (which could be a belief) on the attitude dimension, and w is a weight reflecting the importance of i (woso represents an initial attitude). Though clearly an expectancy-value approach, this model calls for averaging rather than summation (Ew = 1).

Indeed, one problem with the expectancy-value approach is that there exists a large number of possible composition rules for combining the two components, of which summation and averaging are just two instances. Consequently, in order not to be arbitrary, an expectancy-value model must be directly based on theoretical considerations regarding the cognitive structure from which the composition or cognitive processing rule may be derived. But this is precisely where current expectancy-value models are weakest. Fishbein offers an account of his model in terms of classical conditioning and generalization; Rosenberg relies simply on a general functionalist point of view; and Anderson employs only mathematical considerations. None of these rationales are sufficient to justify a particular form of the expectancy-value model. The purpose of this paper is to describe a new expectancy-value model developed by Calder and Lutz (1972) which does have an explicit basis in a representation of cognitive structure.


Cognitive structure is represented in this approach as a two-dimensional metric space. One dimension represents an affective component (liking or favorableness) and the other represents a cognitive component (likely or probable). Any belief an individual possesses about a product is characterized by a value on each of these dimensions, i.e., as a set of coordinates in the cognitive space.

Our model is stated in terms of vector forms. The points representing beliefs in the cognitive space may be considered as vectors from the origin of the cognitive space. In terms of a model of cognitive process, the question now concerns how these belief vectors combine to determine attitude. An obvious structural solution is to think of attitude as a resultant vector whose coordinates are the sum of the affective coordinates (Ea) and the sum of the cognitive components (Eb) of the beliefs.

Attitude is thus conceived of as the resolution of the forces created by several specific beliefs. The magnitude of the attitude is simply the length of the attitude vector from the origin. Since we know the coordinates involved, it follows from elementary plane geometry that attitude is given by

A = [(Ei=1ai)2 + (Ei=1bi)2]1/2   [3]

where A is analogous to the traditional attitude score, a is the affect associated with belief i, and b is the strength of the belief i. Unlike previous expectancy-value models, the vector model follows directly from our assumptions about cognitive structure.


Two studies (Calder and Lutz, 1972) have been conducted to compare the vector model with direct reports of attitude and with predictions yielded by the Fishbein and Anderson models. Both studies obtained standard semantic differential measures of attitudes toward buying non-phosphate detergents and of the affect and belief strength aspects of several beliefs concerning attributes of non-phosphate detergent. The first study used a sample of ninety-two University of Illinois business students. (For this sample a measure of the importance of each belief was also obtained in order to test Anderson's model.) The results indicated that the vector model correlated .60 with reported attitude, and the Fishbein and Anderson models correlated .60 and .64 respectively.

The second study employed a convenience sample of forty-six women employed in University of Illinois offices. The correlations were, somewhat inexplicably, lower for this sample but still comparable to each other. The vector model correlated .33 with reported attitude and the Fishbein model .37

In general, these results indicate that the predictive validity of the vector model is as strong as that of other expectancy-value models. In fact, it would seem that predictive validity is not an especially satisfactory criteria for evaluating such models. The class of possible composition rules which would sometimes produce high correlations is no doubt extremely large. This is, however, precisely why we believe the vector model and other cognitive structure approaches deserve serious attention. By having a basis in cognitive theory, they may be examined beyond their predictive ability.


In order to suggest some possibilities for research on the vector model, perhaps we should briefly note two other properties of the model. First, the model can be given a much more general form. Consider the Minkowski r-metric for determining distance in a metric space

dij = [Enk=1 |xik-xjk|r]1/r,r>1,

where each difference in coordinates on dimension k is raised to the rth power, these are summed, and finally the rth root is taken. Clearly the vector model, Equation [3], is a special case of this distance function with r = 2. It is thus possible to state a "city-block" (r = 1) version of the vector model. Therefore, r would seem to be an interesting parameter for further research. Likewise, the way in which the components (Ea) and (Eb) are weighted is also of interest. It can be shown (Calder and Lutz, 1972) that these weights may be written as (Ea/A)r-1 and (Eb/A)r-1 respectively.

Another feature of the vector model is that attitudes may be described not only by the property of magnitude but also direction. Some attitudes may be predominantly cognitive oriented whereas others may be more affective. This property suggests a new approach to the old problem of types of attitudes.

To summarize, traditional expectancy-value models are severely limited by the absence of any cognitive theory from which they may be directly derived. The vector model described here does possess a basis in cognitive structure. It appears to have predictive validity comparable to the other models. Moreover, the vector model seems to have several properties worthy of future research.


Anderson, N. H. Integration theory and attitude change. Psychological Review, 1971, 78, 171-206.

Bass, F. M. and Talarzyk, W. W. An attitude model for the study of brand preferences. Journal of Marketing Research, 1972, 9, 93-96.

Calder, B. J. and Lutz, R. J. Cognitive structure and attitude models, manuscript, 1972.

Calder, B. J. and Ross, M. Attitudes and Behavior. New York: General Learning Press, in press, 1972.

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

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. A consideration of beliefs, attitudes, and their relationship. In I. D. Steiner and M. Fishbein (eds.), Current Studies in Social Psychology. New York: Holt, Rinehart and Winston, 1965, pp. 107-120.

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, pp. 389-400.

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

Rosenberg, M. A structural theory of attitude dynamics. Public Opinion Quarterly, 1960, 24, pp. 319-340.

Sheth, J. N. and Talarzyk, W. W. Perceived instrumentality and value importance as determinants of attitudes. Journal of Marketing Research, 1972, 9, pp. 6-9.



Bobby J. Calder, University of Illinois at Urbana-Champaign
Richard J. Lutz, University of Illinois at Urbana-Champaign


SV - Proceedings of the Third Annual Conference of the Association for Consumer Research | 1972

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