Developing a Bayesian Measure of Brand Loyalty: a Second Look


James W. Gentry and Thomas L. Brown (1980) ,"Developing a Bayesian Measure of Brand Loyalty: a Second Look", in NA - Advances in Consumer Research Volume 07, eds. Jerry C. Olson, Ann Abor, MI : Association for Consumer Research, Pages: 713-716.

Advances in Consumer Research Volume 7, 1980     Pages 713-716


James W. Gentry, Oklahoma State University

Thomas L. Brown, Kansas State University


This paper reports the results of a study replicating the Lutz and Winn (1974) study, in which a Bayesian measure of brand loyalty was introduced and its validity investigated. The Bayesian measure includes both a behavioral and an attitudinal component of brand loyalty; the weights of the two components are determined by their relative precision (the reciprocal of the sample variance).

This study used different behavioral measures (time and dollars spent as opposed to the number of trips), different stimuli (fast food restaurants rather than grocery stores), more stimuli (four restaurants versus two grocery stores), and a slightly longer data collection period (14 weeks as opposed to 12 weeks). As in the initial study, the Bayesian loyalty measure was found to have convergent and discriminant validity. However, a more simply computed summative measure was found to be just as valid, if not more so, than the Bayesian loyalty measure.

Further the store loyalty measures were related to a construct (location) that should be expected to have a strong relationship with store patronage. Few of the relationships were significant, thus raising question as to the value of the loyalty measures used in this study.


The concept of brand loyalty has been of considerable interest and importance to marketing academicians (as indicated by the attention devoted it in the literature--for a good summary of this literature, see Jacoby and Kyner 1973) and to marketing practitioners (as evidenced by the large amount of money spent to encourage brand loyalty). [An example of the importance of brand loyalty is that the oil companies continue to encourage the distribution of their credit cards (as positive incentive in the establishment of brand loyalty) although the costs of operating the systems (estimated to be about 24 per gallon sold) have reached the level that credit cards are labeled "burden" a "burden" (Business Week 1978).] One serious problem with the concept is that there is a wide range of operational definitions available, most of which have both strong supporters and strong detractors. The early operational definitions were based on repeat purchase behavior in the form of brand choice sequences, proportion of purchases, or re-peat-purchase probabilities. More recently, a distinction has been drawn between repeat purchase behavior and "true" brand loyalty by Jacoby and his colleagues (Jacoby 1971; Jacoby and Kyner 1973; Jacoby and Olson 1970). While in one instance repeat purchase behavior may he the result of a psychological commitment to the brand, in another instance it may be a function of situational factors that serve to inhibit purchase of the brand to which one is actually committed or "loyal." Thus, factors like non-availability or high price relative to income may prevent one from purchasing "his" truly favored brand. Consequently, analysis of that individual's repeat purchase behavior would omit the favored brand from consideration.

Recent studies have been broadened to include attitudinal, behavioral, and combination measures of the brand loyalty concept rather than behavioral measures alone. One approach (Bennett and Kassarjian 1972; Jacoby 1971; Jacoby, Chestnut, and Fisher 1978; Jacoby and Kyner 1973; Jacoby and Olson 1970; Jarvis and Wilcox 1976) is based on the Sherifs' (Sherif, Sherif, and Nebergall 1965) concepts of latitudes of acceptance, rejection, and non-commitment as applied to brand choice. In this approach subjects label familiar brands as acceptable (A) or unacceptable (R). The noncommitment region (NC) includes any familiar brands that the subject cannot classify into those two groups plus any unfamiliar brands. The attitudinal loyalty measure is then defined as


where TOTAL is the total number of brands available.

Several researchers have used this broadened definition of brand loyalty in studies relating brand loyalty to consumer information processing. Jarvis and Wilcox (1976) related both a cognitive loyalty measure and a self-report behavioral loyalty measure with marketing-related dependent variables such as price sensitivity, purchase intentions for a new product, and message evaluation. They found the dependent variables more strongly related to the cognitive loyalty measure than to the behavioral loyalty measure. Jacoby, Chestnut, and Fisher (1978) found attitudinal brand loyalty to be only marginally related to the amount of information search exhibited by subjects, while there was no relationship between the amount of information search and a self-report of the purchase share devoted to the most preferred brand.

A second approach to broadening the concept of brand loyalty involves integrating attitude and behavior into a single index of brand loyalty. This approach was proposed by Day (1969) and expanded by Lutz and Winn (1974), and includes a measure of attitude toward a particular brand rather than a measure based on the Sherifs' concept of a more general attitude toward brands in a product class. Using the multitrait-multimethod framework, Lutz and Winn (1974) compared the validity of five different operational measures of loyalty (store rather than brand) by investigating attitudes and behavior toward two grocery stores over a twelve-week period.


Lutz and Winn (1974) introduced a Bayesian measure of brand loyalty as well as investigating an attitudinal measure, a behavioral measure, a summative measure combining those two, and a measure based on the average run length (the average number of consecutive shopping trips to a store). The Bayesian measure is similar to the summative measure except that the relative weights of the two components are determined by their relative precision (the reciprocal of the sample variance). The logic behind this approach is given in Tiao and Zellner (1964).

The approach taken by Lutz and Winn, and the one taken in this study, involved the collection of multiple measures of attitude and behavior. The measures used in the Lutz and Winn study were

1.  ZAX--the mean attitude toward shopping in store j, as measured on a seven-point scale ranging from "dislike" to "like," converted to a Z-score.

2.  ZBX--the proportion of shopping trips devoted to store j, converted to a Z-score.

3.  ZAX + ZBX - the sum of the first two measures.

4.  BLM--the Bayesian Loyalty Measure, which weights the two components by their relative precisions (the reciprocals of their sample variances).

5.  ARL--average run length, the average number of consecutive shopping trips to store j, as calculated by the algorithm presented by Massy, Frank, and Lodahl (1968).

A thorough description of the procedures used to develop these measures is available in Lutz and Winn (1974).

The measures used in this study are similar to those used by Lutz and Winn. However, while the number of trips to a given store in a given period of time was used as the behavioral measure in the earlier study, the present study uses amounts of time and money spent at a given store, as reported by the respondents, as separate behavior measures. These measures of behavior provide insight into the "quality" of the store visits, as well as the frequency. Dollar purchases are clearly more informative measures of "purchase behavior" than store visits. The time spent at a restaurant may have some attitudinal linkages, as a relaxed atmosphere in a fast food restaurant may or may not contribute to more time being spent there and/or to the development of store preference. The use of two behavioral measures resulted in eight measures of loyalty in this study:

ZAX -- attitude measure as defined in Lutz and Winn.

ZBXT  -- behavior measure based on amount of time spent.

ZBX$  -- behavior measure based on amount o dollars spent.

ZAX + ZBXT -- summative measure, including time spent.

ZAX +  ZBX$ -- summative measure, including dollars spent.

BLMT -- Bayesian loyalty measure, including time spent.

BLMS -- Bayesian loyalty measure, including dollars spent.

ARL -- average run length, based on frequency of trips (as in the Lutz and Winn study) rather than amount of time or money spent.


The intent of this paper is to replicate and extend the Lutz and Winn study using 1) different measures of behavior, 2) different types of stores, and 3) more stores. In addition, the measures of loyalty are related to another construct, distance. Whereas the multitrait-multi-method framework allows checks on internal consistency (i.e., are all methods measuring the same construct?), there is no assurance that the construct in question is loyalty. Churchill (1979) suggests observation of how the measure (loyalty) behaves in relation to other constructs known to be related to the construct. This study related store location (in terms of distance between the store and the respondent's home) to store loyalty. The retailing literature has long recognized the strong relationship between patronage and location. There is evidence that this relationship exists even when consumers fail to recognize it. Gentry and Burns (1978) found that consumers rated the importance of location 11th out of 17 criteria used in selecting a shopping center. However, a location variable was the single best predictor of where the same consumers shopped. Further, "marketing research" to many retailers means "site location." Consequently, one would expect a good measure of loyalty to be inversely related to the distance to the store. Bellinger, Steinberg, and Stanton (1976) found the distance to the store most frequently patronized to be negatively related to their multivariate measure of store loyalty.


As in the Lutz and Winn study, this study applies to the loyalty measures to stores rather than brands. The measures seem equally applicable to both concepts of loyalty.

Lutz and Winn instructed a student panel to record their grocery purchases for 12 weeks at two different stores, Eisners (E) and IGA (I). Since the respondents in the present study were not likely to be regular grocery store shoppers, the panel, made up of undergraduate consumer behavior students, was asked to record the following information about patronage of ten fast food restaurants each week: date of visit, length of visit, and approximate amount spent. Each week the panel members were also asked to indicate their attitudes toward the ten restaurants using a seven point "like-dislike" scale. The analysis reported here is limited to the four most frequented (among the panel) restaurants: Hardees (H), McDonalds (M), Vista (V--a regional franchise), and Dairy Queen (D). The data set consists of the information supplied by the 85 panel members who completed the semester and turned in diaries each week (for a total of 14 weeks). Analysis consists of constructing the multi-trait-multimethod matrix and making the proper cell comparisons to establish the validity of the eight brand loyalty measures (methods) across the four traits (loyalties toward the four restaurants).


The correlation matrix from the Lutz and Winn paper (five loyalty measures and two stores) is shown in Table 1 and the corresponding matrix for this study (eight loyalty measures and four stores) is shown in Table 2.



Both matrices are similar to the multitrait-multimethod matrix proposed by Campbell and Fisk (1959). Although Lutz and Winn refer to theirs as a multitrait-multistore matrix, it, like the one in Table 2, is more properly termed a multistore-multimeasure matrix. In both cases the "traits" are loyalties toward different stores and the "methods" are the different measures of loyalty. Thus, the Lutz and Winn matrix has two traits measured five ways and this study's matrix has four traits measured eight ways.

Convergent validation is established if alternative measures of the same trait (store) correlate strongly with one another. These correlations are termed convergent validities. [The convergent validities are circled in Tables 1 and 2.] For discriminant validity to exist, the convergent validities must exceed 1) the correlations between different traits (stores) measured by different methods, and 2) the correlations between different traits (stores) measured by the same method. In addition to measure validation, the matrix has implications for the validity of the loyalty construct itself. Construct validity is indicated if, regardless of method, the correlations between traits exhibit the same pattern.

Lutz and Winn concluded that the behavior related measures had greater convergent validity than did the attitude measure. Further, they found that their proposed Bayesian loyalty measure (BLM) had convergent validity. Present results concerning convergent validity support their findings. While the majority (21 of 28) of the convergent validities involving the attitude measure (ZAX) are significant at the .0001 level, the absolute levels of these correlations are lower than the levels of the convergent validities for the other loyalty measures. The convergent validity of the BLM measures in this study is also quite strong, as 50 out of 52 of the convergent validity correlations involving one of the BLM measures are significant at the .0001 level. All convergent validities for the summative measures are significant at the .0001 level.

It is not clear that the use of two definitions of behavior (time spent and money spent) added greatly to the study. The convergent validities between comparable "time" and "money" measures (i.e., rZBXT, ZBX$, rBLMT, BLM$, and rZAX + ZBXT, + ZBX$) are for the most part close to 1.0. Also, the patterns of convergent validities involving the two different behavior definitions are fairly consistent. Apparently time spent and dollars spent do not represent different behavioral patterns for fast food restaurants.

Lutz and Winn argued that the high negative correlations between traits for the same measure were evidence of discriminant validity for their behavior related loyalty measures. The similar correlations in this study are much lower than the convergent validities and in most cases (30 out of 42 at the .1 level), nonsignificant. These results are consistent with the second condition for discriminant validity described earlier. Further, the convergent validities are much higher than the correlations between different traits measured by different methods, thus meeting the first condition necessary for discriminant validity.

The size of the present matrix makes the search for consistent patterns of trait relationships across measures somewhat difficult, especially since the majority of correlations are nonsignificant and thus provide "noise." For the most part, the correlations involving Dairy Queen loyalty (D) are smaller than the other correlations. Thus, significant relationships between Hardees and

McDonalds, Hardees and Vista, and Vista and McDonalds are more likely than significant relationships between Dairy Queen and one of the other stores. This pattern is intuitive since Dairy Queen's product assortment differs from the other three stores.

In summary, the results of the present study strongly support the Lutz and Winn (1974) findings. Evidence exists that the Bayesian loyalty measure has convergent and discriminant validity. Moreover, all of the loyalty measures (attitude, behavioral, summative, and average run length as well as the Bayesian loyalty measure) had both convergent and discriminant validity. In fact, the summative measure was found to be just as valid, if not more so, than the Bayesian loyalty measure.


North-south and east-west coordinates of each respondent's residence were compared to the coordinates of the four stores to obtain distance measures. There is a hypothesized inverse relationship between store loyalty and distance.

Simple correlations between the store loyalty measures and distance are shown in Table 3. The correlations between distance and store loyalty were, except in three cases, negative as hypothesized; all but three, however, were nonsignificant. Three of the eight negative correlations between distance from residence to Vista were significant (p < .05). One may have expected the attitude measure of loyalty (ZAX) to have been more weakly related to distance since inhibitors such as unavailability of an automobile might mean choosing a restaurant more on accessibility than preference. However, this is not the case since correlations involving ZAX measures and distance appear no lower than correlations involving another loyalty measure and distance.


The purpose of this paper is to test the validity of eight measures of the store loyalty construct. Using the multitrait-multimethod framework, the measures were found to demonstrate convergent validity. Evaluation of the measures' discriminant ability is less conclusive. Although the data presented meet the first two criteria for discriminant validity, the third criterion of a consistent pattern of correlations between stores within and across methods was not met. Validity of the loyalty construct itself was assessed by relating the eight measures of loyalty to distance from residence to store. Only in three cases out of a possible 32, however, were the negative relationships between loyalty and distance significant.

It seems clear that more work is needed on the validation of store loyalty measures. It is especially important to relate the loyalty measures to other constructs known or thought to be conceptually related to store loyalty. In this manner, one may help to discern whether or not the loyalty measures, no matter how internally consistent, are measuring the construct they are intended to measure. The mixed results for the measures used here provide some support for questioning the value of a simple index of loyalty. The approach used by Jacoby and others which treats the attitudinal and behavioral measures as independent indicants would seam to be more promising.






Bellinger, Danny N., Earl Steinberg, and Wilbur W. Stanton (1976), "The Congruence of Store Image and Self Image," Journal of Retailing, 52 (Spring) 17-32.

Bennett, Peter D. and Harold H. Kassarjian (1972), Consumer Behavior, Englewood Cliffs, New Jersey: Prentice-Hall, 42.

Campbell, Donald T. and Donald W. Fiske (March, 1959), "Convergent and Discriminant Validity by the Multitrait-Multimethod Matrix," Psychological Bulletin, 56, 81-105.

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Tiao, G. C. and A. Zellner (1964) "Bayes' Theorem and Use of Prior Knowledge in Regression Analysis," Biometrika, 51, 219-230.



James W. Gentry, Oklahoma State University
Thomas L. Brown, Kansas State University


NA - Advances in Consumer Research Volume 07 | 1980

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