Effects of the Number and Type of Attributes Included in an Attitude Model: More Is Not Better

Citation:

William L. Wilkie and Rolf P. Weinreich (1972) ,"Effects of the Number and Type of Attributes Included in an Attitude Model: More Is Not Better", in SV - Proceedings of the Third Annual Conference of the Association for Consumer Research, eds. M. Venkatesan, Chicago, IL : Association for Consumer Research, Pages: 325-340.

Proceedings of the Third Annual Conference of the Association for Consumer Research, 1972      Pages 325-340

EFFECTS OF THE NUMBER AND TYPE OF ATTRIBUTES INCLUDED IN AN ATTITUDE MODEL: MORE IS NOT BETTER

William L. Wilkie, Purdue University

Rolf P. Weinreich, Purdue University

[William L. Wilkie, Assistant Professor; and Rolf P. Weinreich, Doctoral Candidate, Krannert Graduate School, Purdue University.]

In recent years, there has been a growing interest in marketing applications of multi-attribute attitude models of the form originally proposed by Rosenberg and Fishbein [7,2]. In behavioral theory, an attitude is defined as the evaluative dimension of a concept - a relatively stable affective response to an object [3,6]. Specifically, in Fishbein's formulation, attitude formation is viewed as a process of cognitive summation. Essentially, the principle leads to the prediction that an individual's attitude toward any object is a function of his beliefs (i.e., perceptual or cognitive constructs) about the object, and the evaluative aspects of those beliefs:

(1)   EQUATION

where, for each individual,

"_o = the attitude toward object "o"

B_k = the strength of belief k about o

a_k = the evaluative aspect of B_k

s = the number of beliefs

As can be seen from the formula, an attitude is the weighted sum of beliefs about an object, the weights representing the relative contribution of each belief in forming an attitude. Typically, model performance is tested by correlating the derived attitude scores with an independent measure of affect.

In the marketing context, this approach has been extended to postulate that attitudes toward brands are governed by a consumer'S beliefs about the ability of different brands to satisfy specific product attribute intensities he desires Although the situation is somewhat different, in that several "attitude objects" are evaluated, a similar model structure has been proposed to operationally determine an individual's attitudes toward each of 1 brands.

(2)   EQUATION

where, for each individual,

"_j = the attitude toward brand j

B_jk = the rating of brand j on attribute k

I_k = the importance of attribute k in forming an overall attitude toward brands

Instead of predicting affect for a single concept, the model is used to predict the preference orderings (or other external criteria) for competing brands. Thus, model performance is tested by correlating a set of attitude and preference ratings:

(3)   P_j = f(A_j) = f(_k I_k ^. B_jk)

where for each respondent,

P_j = the preference for brand j

"_j = the attitude toward brand j

Some thirty marketing studies related to this basic model have been reported in the past three years, reflecting the natural appeal of the multiattribute notion to marketers. If attitudes are intervening, evaluative responses - indeed removed from, but closely associated with choice - then the model might provide operational measures of how a brand is being perceived and evaluated vis a vis its competitors. This information might then be useful for brand positioning decisions.

While considerable testing of the predictive and diagnostic power of this approach has been undertaken by marketing, several issues clouding its practical application remain unresolved [8]. One important issue area concerns the nature and handling of attributes themselves. Attributes ("k" in formula 2) are used as basic dimensions of the model; respondent ratings of the importance of each attribute and brand possessions of the attribute then provide the raw data for calculations of brand attitude scores for each individual. There are two broad decisions involved in the model's use of attributes:

(1) initial specification

(2) inclusion in the calculations of brand attitude

Initial specification concerns the manner in which a candidate list of product attributes - typically representing perceptual rather than concrete product characteristics - is generated by the research. Marketing applications have usually utilized some form of unstructured pretests to generate lists of 5 - 30 attributes which are then presented to respondents for brand belief and importance ratings.

"Inclusion in the model" refers to the manner in which the raw data is used by the researcher. In particular, are all attributes in the initial list applicable to all respondents? If not, how many and which attributes should be used for each respondent? Typical marketing studies have used all attributes for every individual and have thus assumed that the same belief structure holds for all consumers.

This paper reports the results of a study comparing the efficacy of this common assumption versus analyses which explicitly manipulate the number and type of attributes included so as to better reflect individual differences in attitude structures. A brief review of relevant literature on this question is followed by descriptions of the data, methodology, and results of this study. It is argued that neither theory nor prior research support the practice of including all attributes for every respondent; this paper demonstrates the magnitude of some drawbacks inherent in this practice and offers feasible procedures which allow for idiosyncratic attitude structures within the framework of a multi-attribute model.

DISCUSSION OF PAST RESEARCH

There is little explicit argument of this matter to be found in the literature, but a careful reading of several prominent papers can shed some light on the issue.

One of the earliest accounts of the summative model was presented in social psychology by Rosenberg [7]. His model structure is similar to formula (1), although its theoretical underpinnings are somewhat different to those later postulated by Fishbein. Rosenberg tested his model by using the summative form on 35 value items related to "whether or not members of the Communist Party should be allowed to address the public." He concluded that "beliefs associated with an (independent) attitudinal affect tend to be congruent with it, i.e., that there exists within the individual an 'organization' of the affective and cognitive properties of his total pattern of response to what, for him, is an 'attitude object."'

This statement bears the clear implication that individual differences in the type and number of beliefs should be recognized. Although Rosenberg tests the effect of utilizing different numbers of values in the summation model, it is not clear in his report whether the composition of values was allowed to vary for each individual. In a second test using only idiosyncratic "salient" beliefs, however, Rosenberg notes that predictive power increased as compared to using all thirty-five values.

Fishbein defined salient beliefs to be "those present in the individual's response hierarchy" [2] and noted that inclusion of nonsalient beliefs will tend to reduce the precision of attitude measurement. Again, the implication is that individual differences in the number and type of "salient" attributes should be recognized. However, a later model test [1] uses a common number and types of beliefs for each respondent - a seeming contradiction with Fishbein's original postulates about individual differences in attitude structure.

Since the context for marketing differs from the concerns of social psychology, it is possible that the proposals of Rosenberg and Fishbein might not be of pragmatic value for the attribute issue. In marketing, there seems to be agreement that attributes are likely to be product-specific, that reasonable attributes will generally be small. But the marketing literature also lacks discussion about the issue of idiosyncratic attribute inclusion. Following Fishbein's position, the virtually unanimous stand taken is that only "salient" attributes should be included in the model. Most papers assume, however, that the original list of attributes (generally 5-7) is sufficiently and exhaustively "salient" for all respondents. Operational definitions of salience are rarely undertaken. Equating salience with "importance," Hansen [4] presents one of the few evidences of the effect of attribute types included in the model. He chose the three most important attributes for each respondent, compared model performance against utilizing all attributes, and noted that predictive power was not diminished by using fewer attributes. However, no test on the effects of varying attribute numbers was mentioned.

This paper moves beyond traditional testing of the model by systematically looking at the effect of attribute inclusion in the basic summative model. The hypothesis advanced is that gains can be achieved when individual differences are allowed in the number and type of dimensions utilized in computing a respondent's attitude toward brands. Results of using varying numbers of attributes from a common list, of allowing the types of attributes included to vary (holding their number constant), and of permitting both type and number to differ from respondent to respondent are compared against the traditional approach of utilizing all ratings for each individual.

METHODOLOGY

The Data

A convenience sample of twenty-nine housewives living in a small Eastern town were asked to rate seven supermarkets on seven store attributes (using seven-point bipolar scales): location, prices, quality, variety, closeness to other services, shopping climate, and "other shoppers." The attribute set was generated from a more extended list, used in preliminary interviews. In addition, subjects were also asked to rate the importance of the attributes in making a choice of a shopping place, as well as to rank preferences for the seven stores in the area.

Analysis

The traditional approach to these data is represented by applying the seven store attributes to all subjects, computing an attitude score for each respondent using formula (2), ranking the derived scores, and correlating attitudes with preferences using Spearman's Rho index to determine the degree of association of the two measures.

The approach in this paper is methodologically different in that attributes are entered into the summation in stages. According to some criterion or entry rule (to be discussed shortly), one additional attribute is entered at a time, until all seven have been included. At each summation stage, the basic formula is applied to compute attitude scores for each brand and each individual. These are then correlated with stated rank preferences. Figure 1 shows in flow-chart form the procedure used.

FIGURE 1

DESCRIPTION OF THE STAGED ENTRY APPROACH

Spearman Rho correlations between ranked attitudes and preferences are used to measure performance of the model. Thus, by comparing correlations at each stage with correlations represented by the traditional approach, changes in model performance can be analyzed with respect to changes in inferred attitude dimensionality.

Criteria for Attribute Entry

Given a list of attributes the traditional approach has introduced all ratings to the model; the order in which attributes enter is of no import. When staged inclusion is attempted, however, the order of entry is of obvious concern, and some rule or criterion is required to ensure that "salience" is represented in entry. As noted, little discussion has been devoted to the definition and operationalization of "salience" in previous marketing studies. Two allied constructs have, however, been advanced: importance and determinism. The study reported here utilized both rules as criteria with which to generate order of 2 attribute entry to the model; results for the determinism criterion are reported. [The importance criterion simply used the magnitudes of respondent's stated importance weights to rank-order attributes for inclusion. Tied ratings were resolved by randomized rank assignments.] Determinant attributes, as proposed by Myers and Alpert [5], are those "which are most closely related to preference or actual purchase decisions." Car safety is an example of a dimension which is probably important, but not determinant for most consumers due to perceptions that brands do not significantly differ on this attribute. Thus, the Determinism concept incorporates both importance weights and the notion of disparity in perceived satisfaction on the attributes through different brands. Operationally:

(4)   D_k = I^*_k ^. o_k

where, for each respondent,

D_k = the determinism score for attribute k

I^*_k = the standardized importance score for attribute k

o_k = the standard deviation (over all stores) of attribute k

Four studies were performed for comparison purposes:

1. The first represents the traditional approach, whereby all attributes (7 here) are included for each individual in the summation formula, and correlations with stated preference are computed.

2. The second study measures the impact on model performance of allowing the number of attributes to vary from 1 to 7, but constraining them, at each stage, to be of the same type. The mean Determinism score for each attribute across the sample was used to order entry. Thus, attitude scores were computed for all individuals after the most determinant attribute; the two most determinant attributes (and so on) had been entered into the summation, until all seven had been included. By comparing correlations at each stage with the traditional approach, the degree to which a smaller set of attributes (<7) performs better, equal or worse can be analyzed.

3. A third study concentrated on the effect of attribute types on model performance. To derive attitude scores at each stage, attribute inclusion was resolved by using each individual's Determinism scores on each attribute as entry criteria. This analysis allows a study of the extent to which individual differences in the type of dimensions (but using the same number) will result in better performance than using a common set (i.e., study 2).

TABLE 1

RESULTS FROM THE STAGING APPROACH FOR TWO SELECTED RESPONDENTS

TABLE 2

RESULTS FOR THE TRADITIONAL APPROACH SPEARMAN RHO CORRELATIONS BETWEEN ATTITUDE AND PREFERENCE RANKS (ALL 7 ATTRIBUTES INCLUDED)

TABLE 3

THE EFFECTS OF THE NUMBER OF ATTRIBUTES INCLUDED IN THE MODEL: MEAN CORRELATIONS AT EACH ENTRY STAGE (ATTRIBUTE SEQUENCE CONSTRAINED TO BE THE SAME FOR ALL INDIVIDUALS)

FIGURE 2

MEAN CORRELATIONS PLOTTED AGAINST THE NUMBER OF ATTRIBUTES ENTERED

TABLE 4

THE EFFECT OF THE TYPE OF ATTRIBUTES INCLUDED IN THE MODEL: MEAN CORRELATIONS AT EACH ENTRY STAGE (ATTRIBUTE TYPES PERMITTED TO VARY AT EACH STAGE FOR EACH INDIVIDUAL)

FIGURE 3

MEAN CORRELATIONS PLOTTED AGAINST THE NUMBER OF ATTRIBUTES ENTERED (ATTRIBUTE TYPES PERMITTED TO VARY FOR EACH INDIVIDUAL)

TABLE 5

MAXIMUM OR "PEAK" CORRELATIONS (o max) VS CORRELATIONS AT STAGE 7 (o 7) (BY RESPONDENT AND MODEL FORM)

TABLE 6

MODEL PERFORMANCE AT THE INDIVIDUAL LEVEL - NUMBER OF RESPONDENTS FOR WHICH FEWER ATTRIBUTED INCLUDED (k < 7) RESULTED IN BETTER, EQUAL AND WORSE PERFORMANCE THAN USING k = 7.

TABLE 7

FREQUENCY DISTRIBUTION OF THE NUMBER OF ATTRIBUTES INCLUDED TO ACHIEVE l MAX (BASED ON THE "EARLIEST" MAXIMA FOR EACH RESPONDENT)

TABLE 8

FREQUENCY DISTRIBUTION OF ATTRIBUTE TYPES INCLUDED TO ACHIEVE l max

4. Finally, a fourth analysis allows for complete freedom in the number and type of attributes included for each individual. Using the individual determinism entry criterion, attitude scores and correlations for each respondent were computed each time an additional attribute was entered. As many ratings as necessary to achieve maximum correlation with preference were chosen for each respondent. Table 1 shows staging procedure results for two selected respondents to illustrate this procedure. It displays the entry order of attributes, the attitude scores computed at each stage, their ranks, and the Rho correlations with preference.

The Models

The analytical procedure is not straightforward for this problem. Results can depend upon various forms of the basic summative model used. Therefore, two (pragmatic) versions were included for analysis (a) the traditional I-B model using raw scores (formula 2 - henceforth identified as model I), and (b) a more sensitive version, in which both the belief and importance scores are standardized before multiplication and summation:

(5)    EQUATION

where for each respondent,

"_j = the attitude score for store j

I^*_k = the standardized importance score for attribute k

B^*_jk = the standardized rating (across stores) of j on attribute k

RESULTS

Study 1: The Traditional Approach

Table 2 shows the results of utilizing all seven ratings for each respondent (under the two model forms) and thus the results of a traditional multiattribute analysis. For model I, the mean correlation (after Fisher's Z-transformation) was .60, with individual values ranging from -.30 to .97. For model II, the mean correlation was only .36, with a range of values between -.90 and .97. A Wilcoxon matched-pairs test indicated that the magnitude of correlation differences between the two model forms was statistically significant (p < .001).

Study 2: The Effect of the Number of Attributes

Table 3 and figure 2 summarize the results when the same attributes are included for every individual at each stage. The first attribute entered into the summation-was #3 (quality). Thus, had only this dimension been considered for all respondents, a mean correlation of .40 would have been obtained. Similarly, choosing two common attributes for all individuals resulted in a mean correlation of .54.

Figure 2 plots mean correlations against number of attributes included, for both model forms. It shows that model performance increases asymptotically up to 5 attributes included. For model I, correlations at this level are not statistically different from using all seven attributes. This indicates that the original list could have been safely trimmed to 5 dimensions, without any loss in efficiency. For model II, however, the inclusion of all seven attributes yielded a considerably lower predictive power than the one possible with the selection of fewer attributes (4 or 5. attribute #3, 2, 4, 1, 5). The same pattern for both model forms resulted when Importance scores were used as entry criterion instead of Determinism, so that poor performances seem to be model dependent. [This interesting result is due to the impact of standardization on ratings which have little disparity across stores, such that one store which diverges slightly in either direction is stretched further and often shifts several places in attitude score ratings. Little disparity appears much more frequently in unimportant attributes.]

Study 3: The Effect of Attribute Types

Table 4 and figure 3 show, in turn, the effect of varying the type of attributes included at each stage for each respondent. As will be recalled, idiosyncratic differences were allowed in the types of attributes chosen for each respondent, utilizing the individual Determinism scores to decide order of entry into the summation formula.

The analysis is more meaningful when the results are compared with those from study 2. For example, at stage l (one attribute included) the mean correlations under study 2 assumptions are .40 for both model forms versus .50 in study 3. This difference reflects the effect of utilizing one common attribute for all individuals versus the results of permitting its type to vary from respondent to respondent.

The impact of attribute types on performance is further evidenced by the earlier "peaks" obtained. Only 3 ratings were necessary to achieve maximum correlation when individual differences were allowed, as opposed to 5 in the previous approach.

Study 4: The Effect of Type and Number of Attributes

As explained earlier, the results of this analysis represent the most general approach, in that an optimal number and mix of attributes to achieve best fits is selected, independently for each respondent. Table 5 presents the maximum correlations (p max) for both model forms, as well as the number of attributes that were needed to achieve that "peak". Columns 3 and 4 are the results of using all seven attributes, as in the traditional approach (reproduced from Table 2 for comparison purposes).

Inspection-of the results show that significantly higher correlations are achieved when individual differences are recognized (a mean of .76 versus .60 for model I; .71 versus .36 for model II). Also, the dispersion of values is reduced, compared to the results of the traditional approach.

Tables 6, 7, and 8 summarize the results at the individual level more succinctly. Table 6 shows, for example, that using the traditional I-B model form (model I) 48% of the respondents suffered from having all attributes included, while only 7% (2 respondents) gained. The remaining 455 did not change. More dramatic results are obtained when the standardized model form (model II) is utilized. Here, allowing for individual differences in the number of attributes included, performance increased for more than 76% of the sample.

Considerable individual differences were also found in terms of the order in which attributes should be included, and in the minimum number of attributes required for best fits. Table 7 presents these results. Utilizing model I, 24% achieved maximum rho with only one attribute included; 52% with three or less; while only 7% (2 respondents) with all attributes included. Similar observations also hold for the standardized model.

While Table 6 shows that the staging approach does improve the performance for a considerable number of individuals, it does not disclose the magnitude of these improvements. The Wilcoxon test for matched pairs (on data of Table 5) was used to test for magnitude differences in the correlations for the two model forms against the typical approach. In all cases, the differences were found to be statistically significant beyond the .01% level, thus confirming the hypothesis that the recognition of individual differences will improve over the typical approach.

CONCLUSIONS - IMPLICATIONS

It appears that the underpinnings of marketing's use of the multi-attribute attitude model call for explicit provision for individual differences in attitude dimensionalities, particularly given the acceptance of perceptual attributes rather than controllable product characteristics. Because of a relative lack of research on the issue, however, little empirical work has used this approach. This study compared the use of all 7 available store attributes against staged attribute entries which allow for each respondent's brand attitudes to be represented by some subset of the original 7 attributes. It is clear that the latter approach offers predictions of store preference which are both more efficient and significantly higher. The following conclusions are thus advanced:

1. In accord with related results in choice theory and information processing, it appears that attitudes can be efficiently described (in predictive terms) with fewer attributes than are typically gathered in marketing research.

2. In accord with the theoretical proposals of Rosenberg and Fishbein, incorporation of only "salient" attributes (which may well differ by individual) leads to significantly better results than inclusion of all available ratings, and, following, that the typical practice of using all attributes for every respondent is likely to significantly understate the predictive power of the multi-attribute attitude model in marketing.

At the same time it should be noted that the more flexible approach advanced in the paper has its drawbacks. Cross-sectional analyses aimed at descriptions of variables (attributes) are now much more difficult; summarizing results in any form beyond predictive power is drastically hindered. Similarly, this approach makes cross-validation cumbersome, if not impossible. Methodological questions of the staging approach are by no means settled; "importance" and "determinism" served here as entry criteria, but it is likely that a better measure of "salience" can be developed. A weakness of standardization was apparent in these results. It is not clear how heavily results depend on the initial specification of attributes; this study accepted a list of seven as exhaustive. It does seem, however, that the results of this study provide sufficient evidence to conclude that this aspect of the attitude model warrants further investigation. Future research should benefit from provisions for differences in the number and nature of attributes included in the modeling of each individual's brand attitude structure.

REFERENCES

Anderson, L.R. & Fishbein, M. Prediction of attitude from the number, strength, and evaluative aspect of beliefs about the attitude object: a comparison of summation and congruity theories. In M. Fishbein (Ed.), Readings in attitude theory and measurement. New York: Wiley and Sons, 437-443.

Fishbein, M. A behavior theory approach to the relations between beliefs about an object. In M. Fishbein (Ed.), Readings in attitude theory and measurement. New York: Wiley and Sons, 389-399.

Fishbein, M. A consideration of beliefs, and their role in attitude measurement. In M. Fishbein (Ed.), Readings in attitude theory and measurement. New York: Wiley and Sons, 257-266.

Hansen, F. Consumer choice behavior: an experimental approach. Journal of Marketing Research, 1969, 6, 436-443.

Myers, J.H. & Alpert, M.I. Determinant buying attitudes: meaning and measurement. Journal of Marketing, 1968, 82, 13-20.

Osgood, C.E., Suci, G.J., & Tannenbaum, P.H. The measurement of meaning. University of Illinois Press, 1957.

Rosenberg, M.J. Cognitive structure and attitudinal affect. In M. Fishbein (Ed.), Readings in attitude theory and measurement. New York: Wiley and Sons, 325-331.

Wilkie, W.L. Issues in marketing's use of multi-attribute attitude models. Purdue University, Krannert Graduate School. Institute paper, 1972.

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