Application of Discriminant Analysis in Formulating Promotional Strategy For Bank Credit Cards

James B. Wiley, Wayne State University
Lawrence M. Richard, Wayne State University
[ to cite ]:
James B. Wiley and Lawrence M. Richard (1975) ,"Application of Discriminant Analysis in Formulating Promotional Strategy For Bank Credit Cards", in NA - Advances in Consumer Research Volume 02, eds. Mary Jane Schlinger, Ann Abor, MI : Association for Consumer Research, Pages: 535-544.

Advances in Consumer Research Volume 2, 1975      Pages 535-544


James B. Wiley, Wayne State University

Lawrence M. Richard, Wayne State University

The objectives of this research are threefold: to present the complete analysis of psychographic data as suggested by Wells and Tigert, that is to go beyond reporting percentage figures on item responses; to extend the current research methodology by using generated factor scores as input to discriminant analysis for purposes of predicting user categories; and to examine the extent of concordance between this research and previously cited efforts. Factor analysis is used with linear discriminant analysis based on factor scores. The results suggest the following: Psychographics effectively can predict usage patterns for bank credit card users. As does multiple regression analysis, multiple discriminant analysis offers a diagnostic capability. It can serve as a guide to answering such questions as which set of variables are "important" from the standpoint of prediction. Finally, the results are suggestive of the explanatory potential of psychographic variables incorporated in predictive models.

Since 1963, marketing researchers have been exploring various market related measures of consumers' activities, interests, and opinions. These explorations represent what Edgar Pessemier and Albert Bruno have described as "the conscious attempts of researchers to expand the set of descriptors of consumer characteristics to fill the existent void between the economists' demographics and the psychologists' personality inventories" [Pessemier and Bruno 19711.

Generally referred to as "life style research," such efforts have been conducted across a wide range of consumer activities. The most notable work has been carried out by Joseph Plummer [1971b, 1974], William Wells and Douglas Tigert [1971], Tigert [1966, 1969], Pessemier, F. S. DeBruicker, and Thomas Hustad [1968], Bruno [1971], and Pessemier and Bruno [1971].

Life style research most recently has been applied in the bank services area. Plummer [1971a] presented a psychographic profile of the users of bank credit cards, while Albert Pool [1974] extended Plummer's methodology somewhat through the application of discriminant analysis in examining cash dispensing machine users. This article represents an extension of both of these previous works.


One objective of this paper is to examine the extent of concordance between this research and previously cited efforts [1971a]. The primary objectives. however, are (1) to present a complete analysis of psychographic data as suggested by Wells and Tigert [1971], that is, to go beyond reporting percentage figures on item responses, and (2) to extend the current research methodology by using generated factor scores as input to discriminant analysis for purposes of prediction. Pool [1974] attempted to move in this direction, but he used only a limited number of psychographic items. This restriction was probably a function of instrument length prior to inclusion of the psychographic items. This study includes 53 items selected from several available item banks.

We believed it would be more meaningful for decision making to categorize users according to level of usage, rather than in a purely dichotomous fashion. For this reason, we have avoided the user versus nonuser categorization and have chosen to examine heavy versus light patterns. Accordingly, each card holder is classified as either (1) a "heavy" user (more than once a week), (2) a "medium" user (once a fortnight to once a week), or (3) a "light" user (less than once every two weeks). These categories correspond to usage categories adopted by the firm in related research.


The respondents participating in this study were randomly selected from a list of applicants for cash dispensing machine cards. This sample is to be utilized in a study of cash dispensing machine as well as bank credit card users, but the results here pertain only to the latter category.

Standard demographics (Table 1) in conjunction with selected psychographic items (Table 2) were gathered. The latter were selected from previously utilized items [Plummer, 1971b; Pool, 1974] which have demonstrated reliability over time and stability across populations [Pessemier and Bruno, 1971]. One thousand applicants were sampled, with 35 percent responding to the questionnaire. Of the 350 respondents, 233 held bank credit cards.

Table 1 presents the demographic description of the credit card users surveyed. The heavy users, as opposed to light users, both male and female, tend to be younger (25-34), relatively highly educated (college graduate), employed in managerial and/or professional occupations, and have higher mean incomes. These results tend to conform to previous research [1971a]. Our objectives here are to go beyond such descriptive characterization of the data. A sequential analysis was adopted for this purpose.


The data are analyzed using factor and linear discriminant analysis. Results of the former are based on all respondents. Results for credit card usage, of course, refer to the sample of card holders. This latter sample proved to be sufficiently large for the "best" stepwise discriminant model to yield encouragingly stable results under double cross-validation procedures.

In utilizing factor analysis, the task is to reduce the large number of explanatory variables (AIO items) to a smaller number of presumably underlying variables or factors which then can be used as independent variables in subsequent analysis. This study follows a method proposed by Kendall [1957] which bases analysis upon the principal components of R, the correlation matrix of the total pool of AIO items. The components then summarize the "shared" variance in the explanatory pool and, by definition, provide an orthogonal set of predictors for subsequent analysis. The basic factor analysis model is

Zi = ail + ... + aij Fj + aiK FK + ei   (1)


Zi = variable i in standardized form;

Fj = hypothetical factor j;

aij = standardized multiple regression coefficient of variable i on factor j (factor loading);

K = number of factors; and

ei = error term.



The principle factor loading matrix, A, for the ten principle components with eigenvalues greater than 1.00 was calculated and rotated according to the varimax criterion across all psychographic items. An element of this matrix, aij indicates the correlation between attribute Zi and factor Fj. The varimax rotation tends to maximize the correlation between an attribute and a single factor. An abbreviated version of A is presented in Table 2. The number and nature of factors recovered and the patterns of factor loadings appear to correspond closely with the experience of previous research. Many of the common variables identified here parallel those identified in Plummers' work [1971a] as well as in the more general study of Pool [1974]. These variables also closely correspond to those described by Pessemier and Bruno as exhibiting considerable stability and reliability over several previous studies. The factor names in Table 2 are the same as those which appeared in these previous studies.



As a result of the factor analysis, respondents are characterized not only by a demographic profile, but also by a profile of scores that presumably summarize their attitudes, interests, and opinions in selected areas. Furthermore, each card holder can be classified as (1) a "heavy" user (more than once a week), (2) a "medium" user (once a fortnight to once a week), or (3) a "light" user (less than once every two weeks). Can this information be used to predict card holders' usage patterns? If so, which type of information is most useful?

Multiple discriminant analysis can be used to answer such questions. [An alternative approach could be based on canonical discriminant analysis. Use of factor scores, however, appears to offer the advantages of canonical analysis while retaining the explanatory potentiality of AIO analysis.] The basic idea is simple; linear combinations of variables are sought that will maximize differences between the classes relative to differences within the classes. In order to do this, we calculate a vector of weights, w1, for each of the classifications entering analysis:

w1 = V-1m1   (2)


w1 = a vector of weights;

V = pooled dispersion matrix; and

m1 = mean scores for each class, 1 = 1, K. [The analogy with the multiple regression equation b = R-1 K is evident. Both w (Equation 2) and b are vectors of weights. The vector of differences between group means of the variables (d) is analogous to the vector of correlations between the predictor variables and the criterion variable (K).]

In addition, we calculate a constant for each class, c1:

c1 = m1'. w1/2.   (3)

Let us suppose we wish to decide which usage pattern characterizes a given card holder and that the card holder is characterized by the vector of scores Si. In order to do this, we compute a score for class:

Sil = Si'. w1 - c1.   (4)

We assign the individual to the class for which he obtains the highest score.

This procedure assumes the a priori probability of a card holder falling into a class (usage pattern) is equal to 1/K for every class. If we can assign differential probabilities to classes, we can refine the classification procedure. We add to a person's score for each class the value loge P1, where P1 is the a priori likelihood of a card holder having adopted the 1(th) Usage pattern. That is

S(adj)il = Si1 + loge P1.   (5)

The result of applying a variety of multiple linear discriminant functions to card holders characterized in terms of psychographic and demographic variables is summarized in Tables 3, 4, and 5. Results for four models are reported. The first consists of the "best" stepwise model. That is, predictions are based on variables selected through stepwise procedures. Psychographic factor scores provide the input for the second model, demographic variables for the third model. [Sex and occupation were coded as dummy variables.] The input for the fourth model consisted of all (53) AIO items plus all demographics. Table 3 results using discriminant functions derived from scores of the classified individuals. Tables 4 and 5 report results using discriminant functions derived from scores of one half of the sample to classify the other half, and vice versa. Comparison of the results in Table 3 with those in Tables 4 or 5 shows the considerable "shrinkage" that can occur when discrimination functions derived from one sample are used to classify individuals drawn from another sample.








In reviewing the results of the analyses, several points should be made. Our first objective was to report the complete results of a factor analysis of psychographic items. As shown in Table 2, our findings tend to be supportive of previous ones. The common variables in this analysis have tended to appear in previous works [Plummer, 1971a; Pool, 1974], implying that they do exhibit relative stability and reliability over time [Pessemier and Bruno. 1971].

Our second objective was to extend the current methodology through the use of discriminant analysis with generated factor scores being used as input. Table 3 presents the two-way classification of observations according to usage patterns. More important, Tables 4 and 5 present double cross validations based on equal and proportional prior probabilities for assignment. An examination of these tables supports the following positions:

(1) Psychographics effectively can predict usage patterns for bank credit card users. For example, when using the best stepwise model, 55 percent of the observation are correctly classified, which is better than the number expected by chance with equal a priori assignment (33 percent), better than with proportional a priori assignment (37 percent), and better than the number expected with assignment of everyone to the most frequent class (43 percent). The second criteria corresponds to Morrison's [1969] Cmax criteria. The latter corresponds to his Cpro criteria.

(2) Psychographics do a better job than demographics alone.

(3) The critical variables that seem to do the best job of predicting usage categories are factors 1 (Dynamic Leader), 3 (Price Conscious), 4 (Fashion Conscious), 6 (Credit User), 7 (Community Minded), 8 (Financially Satisfied), and income.

Table 6 presents the mean scores for the factor scores on these factors, plus income. The table suggests that the observed income difference between heavy and light users of bank credit cards is a significant one.

It should be pointed out that due to the sample utilized, these results are not intended to be generalizable to the population of all bank credit card users. However, these data can and should be treated as inputs to further study as they illustrate how relatively stable consumer characteristics may be linked to an indicant of service usage. As Frank et. al [1972] point out, such links can serve a dual purpose:

1. To facilitate reaching the attitudinal segments via media

2. To better understand the nature of this segment and hence better design promotional messages aimed at its members

In more specific terms, these are data that can provide guidance for the promotional strategist who is concerned with constructing a tentative answer to the following questions: "Who are the users of these services, and how can the bank most effectively promote continued and/or expanded use of the services?" For example, these results (Table 6) suggest Heavy users tend to have significantly higher incomes. They also tend to exhibit significant differences in individual self-confidence; that is, they tend to be more competent than Light users. Heavy users of bank credit cards also tend to be both significantly more price and fashion conscious. They tend to be more community minded or community oriented. These individuals also tend to be financially satisfied. This is, at least intuitively, in line with the point that they fall in the high income categories.




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