ESSCA: A multidimensional analysis tool for marketing research

ESSCA: A Multidimensional Analysis Tool for Marketing Research

George M. Zinkhan University of Houston

William B. Locander University of Tennessee

Multidimensional analysis techniques such as ESSCA (External Single-set Components Analysis) are useful for marketing researchers who want to estimate the dimensionality o f a group o f related measurement instruments. Here, the advantages and disadvantages of this procedure are illustrated through an investigation of four advertising recall measures. The ESSCA solution suggests that two dimensions of recall are actually being measured:favorable recall o f stimulus features and brand name recall.

INTRODUCTION

Examining the dimensionality of stimulus items (ads, products, concepts) is one important application of marketing research tools. However, our understanding of multivariate tools is critical when addressing various dimensionality problems. Exploratory factor analysis or principal component analyses are most commonly used in situations where there are no specific hypotheses about the structure of the data set. In cases where there is strong a priori knowledge, confirmatory factor analysis or structural covariance analysis would be more appropriate. When the analysis task falls somewhere in between exploratory and confirmatory analysis, then other procedures may be considered, such as canonical correlation, redundancy analysis, or External Single-Set Components Analysis (ESSCA). All three techniques

�9 1988, Academy of Marketing Science Journal of the Academy of Marketing Science Spring, 1988, Vol. 16, No. 1,036-046 0092-0703/88 / 1601-0036

involve multiple criterion variables and multiple predictor variables. The purpose of this paper is to discuss marketing applications of the most sophisticated of these procedures: ESSCA. By way of contrast, all three multiple criterion/ multiple predictor (MCMP) techniques are discussed. Then, with this background, the use and limitations of ESSCA are illustrated through an example drawn from an advertising research problem.

MULTIPLE CRITERION/MULTIPLE PREDICTOR TECHNIQUES

Canonical correlation, redundancy analysis, and ESSCA represent advances over more traditional techniques such as multiple regression since the former are not merely simultaneous forms of analysis but are truly multidimensional in nature. Under the multiple criterion/multiple predictor techniques, theoretical constructs (or variates) are explicitly modeled; multiple indicators (or measures) are allowed for each construct. Thus, there is a more sophisticated interplay between data and theory when compared with more traditional analysis procedures. In addition, all three MCMP techniques provide statistics which can be used to test the overall fit of a model as well as the significance of individual parameter estimates. A brief description of each of the MCMP techniques follows.

Canonical Correlation Analysis Given two sets of variables, canonical correlation forms

variates which maximally correlate. This is shown graphically in Figure 1. Once this first set of variates is obtained, a second set of variates can be extracted- orthogonal to the first. In order to test hypotheses, metric data are assumed. Canonical analysis creates variates through a formative and additive process; and in this way assumes a linear and additive relationship between two sets of variables. The estimation procedure is non-

JAMS 36 SPRING, t988

ESSCA: A MULTIDIMENSIONAL ANALYSIS TOOL FOR MARKETING RESEARCH ZINKHAN & LOCANDER

FIGURE 1 Canonical Correlation

First Set of Variates:

Yl If Y2 FI xl Ii x2 ff x3

rl Y2

Second Set of Variates: (Orthogonal to the first set):

Xi x2 II x3

statistical in that it is not necessary to make assumptions regarding error disturbance to estimate the model; however, to test hypotheses, an assumption of normality is required (Fornell and Zinkhan t982). Canonical correlation can be viewed as a principal components analysis followed by a simple regression. A few of the recent applications in the marketing literature include: Alpert and Peterson (1972); Etgar (1976); and Westbrook and Fornell (1979).

Redundancy Analysis

Redundancy Analysis (van den Wollenberg 1977), like canonical analysis, applies to situations in which there are two sets of variables and the researcher is interested

in the resemblance of the two sets. Also, as in canonical correlation, redundancy analysis is similar in focus to the linear regression model (Stewart and Love 1968). Under redundancy analysis, one set of variables is arbitrarily fixed as the predictor set. This is shown graphically in Figure 2. Thus, in redundancy analysis, the objective is to construct variates that explain a maximum amount of variance of that variable set on another variable set. In contrast to canonical analysis, redundancy analysis maximizes the amount of variance explained in the original variables rather than maximizing the amount of variance explained in the variates. This is equivalent to maximizing the product of the squared correlation between x and y-variables and the mean squared loading of the y- variables (Fornell and Zinkhan 1982). To date, there have

JA MS 37 SPRING, 1988


FIGURE 2 Redundancy Model

Yi II Y Y3

Subsequent variates can be extracted; rotation is possible to enhance interpretation.

been relatively few applications of redundancy analysis in marketing (see Zinkhan 1982).

ESSCA

ESSCA (Fornell 1979) also maximizes redundancy. Contrary to van den Wollenberg's technique, ESSCA is clearly unidirectional; and variates are formed for x- variables only. There is no need to extract y-variates. In addition, ESSCA facilitates interpretation through redistributing intra- and inter-set loadings in an orthogonal fashion. Figure 3 represents the basic ESSCA model.

Comparison of MCMP Techniques

One of the drawbacks of canonical analysis is that canonical correlations show relations between composites of variables but give no indication about direct associations between obsrved variables (Zinkhan 1982). Estimates of explained variance which are based on the size of the canonical correlation coefficient ignore the original

variance that was lost as a result of the extraction of variates; thus, these estimates tend to be overly optimistic. Since this is so, significant canonical correlation coefficients have little practical significance (Fornell 1978). As a solution to this problem, Stewart and Love (1968) have proposed a redundancy index which examines the proportion of redundant variation associated with a given relationship. The redundancy between the variable sets can be obtained by multiplying the squared canonical correlation by the mean loading on the criterion side. In other words, the redundancy index is a-measure of the mean variance of the variables of one set that is explained by the canonical variate of the other set (Zinkhan 1982).

Redundancy analysis is different from canonical correlation in that the purpose of the former is to maximize redundancy instead of maximizing the correlation between two variates (van den Wallenberg 1977). A squared canonical correlation coefficient represents the variance shared by linear composites of two sets of variables. In contrast, the redundancy index represents the proportion of criterion variance predicted by the optimal linear combination of predictors. Thus, the redundancy index

JAMS 38 SPRING, 1988


FIGURE 3 ESSCA Model

/

/ / ; g

As in canonical correlation, subsequent variates -- orthogonal to the previous variates -- can be extracted.

Solid lines represent loadings

. . . . . . . . . . . Dotted lines represent cross loadings

can be interpreted in much the same manner as a squared multiple correlation coefficient (R2), whereas the canonical correlation coefficient reflects the correlation between two linear composites and this presents some interpretative problem (Stewart and Love 1968).

ESSCA is similar to canonical correlation except that, instead of maximizing the correlation between unobserved variates, the sum of squared interset loadings is maximized. Cont rary to the canonical correlation solutions, this method insures that the shared variance between predictor variates and criterion variables is maximal.

ESSCA is similar to redundancy analysis except that an ESSCA model implies directionality. Instead of extracting variates from both criterion and predictor variables, only one set of components (from the predictor variables) is constructed. Without loss of common variance, an orthogonal rotation can be applied to the resulting loadings in order to simplify structure (Fornell 1979). One set of variables can be identified as predictors, and a second set can be clearly identified as criterion variables. As such, ESSCA is more theory driven than is redundancy analysis and provides for more flexible rotation.

Summary of MCMP Techniques

From the above discussion, it is apparent that MCMP techniques are appropriate for marketing researchers when there is a multidimensional analysis problem with at least two measures for each theoretical construct of interest. Of the three alternatives discussed, ESSCA is the most sophisticated in that the ESSCA model implies directionality (with respect to hypotheses about structural relationships between constructs) and allows for more flexible rotation (which leads to enhanced interpretation). In the following sections, ESSCA is applied to an advertising research problem, and the strengths and weaknesses of the procedure are illustrated. In addition, an empirical comparison with redundancy analysis is included so as to highlight the differences between these two data analysis procedures.

THE ANALYSIS PROBLEM: THE DIMENSIONALITY OF MEMORY

It has been proposed that memory is a multidimensional construct (Bagozzi and Silk 1983). However, little is known about the character of these separate dimensions and how they may be related. Many different memory measures have been proposed, and it is not clear that they all tap the same psychological processes (Zinkhan et al. 1986). Recognition of a brand name is sometimes employed as a memory measure, as in the Starch noted score (Hanssens and Weitz 1980). Other times, recognition of advertising facts is employed (e.g., Claycamp and Liddy 1969). Buchanan (1964) combines several dichotomous recall measures to form an interval scale, although the theoretical justification for doing so is unclear. Often, there are no theoretical guidelines to indicate how these various measures might be combined into a single memory construct (Zinkhan 1982). When multiple memory measures are used, it is sometimes difficult to know whether or not it is appropriate to collapse these measures into a single scale.

One possible way of clearing up this confusion is by examining the relationship between the measures of memory and predictors of memory. These predictors may be able to sort out which advertising recall measures belong together and which do not. The dimensionality of recall may well depend on the particular predictor variables selected for investigation (Zinkhan 1982). Thus, one of the purposes of this study is to demonstrate, empirically, that advertising recall is a multidimensional construct and that predictors of ad recall do not bear identical relationships to the various dimensions of recall. One way to examine similarities and differences in recall measures is to analyze their structures and determinants.

This sort of analysis can be implemented through an application of ESSCA. Thus, ESSCA is used to examine various memory measures and to determine how these measures are related to a set of predictor variables.



The Study

Four memory measures were administered following an advertising exposure. The purpose of the study was to examine the relationship between the four memory measures and six candidate predictor variables. The study was guided by the global hypothesis that the predictors would differentially impact the four memory measures.

The four memory measures include:

1. Brand Name Recognition - - basically a measure of brand awareness. In a brand name recall test, respondents are asked to indicate which products out of a list of both fictitious and real products they recall.

2. Recognition of facts in the Advertisement - - concern with the ability to recall a number of facts about the advertised product. Claycamp and Liddy (1969) used this method to develop their Ayer Model of New Products.

3. Favorable Recall Associated with the Advertisement - - recently employed as a measure of effectiveness (Goodwin and Etgar 1980) and similar to the notion of attitude toward the advertisement (Shimp 1981).

4. Favorable Recall Associated with the Advertised Brand - - concerned with positive associations for the brand itself and is akin to belief measures. Previous research suggests that at least six predictor

variables might be related to advertising recall. The very nature of these six and their theoretical underpinnings suggest that although they seem to be related to advertising recall, their relationship to each other and the four measures of recall is not at all clear. The six predictor variables include: (1) Product Interest (Greenberg and Garfinkle 1962; Claycamp and Liddy 1969; Bower and Chaffee 1974); (2) Motivation to read the ad (Janis 1978; Zinkhan 1982); (3) Enjoyment of the ad (Shimp 1981; Bartos 1981); (4) Information contained in the ad (Silk and Vavra 1974); (5) Cognitive Differentiation (Saliagas 1985; Zinkhan and Martin 1983); and (6) Ability topredict the structure of an advertisement (Abruzzini 1967; Holbrook 1975; Holbrook and Hirschman 1982).

Procedures

Two hundred and sixty student subjects were shown a 250 word long print advertisement for a fictitious calculator brand - - the Computron R-55. The stimulus advertisement was created by copy, creative, and production advertising professionals from various firms. The study was run in five different sessions. In the first session, cognitive differentiation was measured. During the second and third sessions, product interest measures and the Cloze procedure were administered. In the fourth session, respondents were exposed to the target ad which was for an electronic calculator. Following exposure, respondents answered questions concerning the design of the ad in order to assess motivation, enjoyment and information. During the fifth and last session, the four

measures of advertising recall were taken. This session occurred one day after the fourth, whereas the time interval between the other sessions was one week in duration.

Operational Measures

Table I includes the four measures used to operationalize the advertising recall construct. Brand name recognition was measured by having the respondent pick the target name from a list of brand names. Fact recognition was tested by a series of True/False questions. Favorable recall associated with the ad and brand were operationalized by coding respondents' free elicitations.

Table 2 presents the six predictor variables used in the study along with the estimates of coefficient alpha where appropriate. Product interest was measured on 8 point Likert-type scales with subjects indicating their level of interest and involvement in the product class. Motivation measured the subjects' motive strength toward reading the advertisement itself. Cognitive differentiation was operationalized using Scott's (1962) R measure which is a relative measure of entropy. The ability to predict structure was measured by the Cloze procedure (Taylor 1953). This Cloze procedure was administered by asking respondents to read through a version of the target ad which had every sixth word systematically deleted. Subjects then tried to "close up" the gaps by supplying the missing word. There were a total of 43 such blanks, and subjects' Cloze scores were calculated by counting the number of times that each subject could exactly supply the missing word. For more details concerning the implementation and interpretation of this Cloze procedure see Zinkhan and Martin (1983).

Analysis Method

The analysis objective faced here falls somewhere in between exploratory and confirmatory. One might expect directional relationships between certain predictors and several measures of recall, but there is little work to support theoretical hypotheses regarding the number and structure of the dimensions involved. As a result, this research used a form of analysis that is confirmatory in the sense that several predictors should be related to several criterion variables and exploratory in the sense that structure and dimensionality are not a priori specified.

Since the various measures of recall cannot be assumed to be independent of one another (i.e.,Ryy ~- 1), a technique that does not require this assumption was used. Since the purpose of the study was to identify dimensions of recall based on predictor variable relationships and at the same time account for maximal variance in the criterion variables, some form of multivariate multiple regression is appropriate. External Single-Set Components Analysis (ESSCA) developed by Fornell (1979) is such a regression.

In its general form, the model is

y = B X + e

where y is a vector of criterion variables, B is a matrix

JAMS 40 SPRING. 1988


TABLE 1 Operational Definitions of Recall Measures

1) Brand name recognition Brand awareness Awareness of test brand from prompt list of fictitious and real products

2) Recognition of facts from the ad

3) Favorable recall about the ad itself

Number of facts correctly identified using True/False questions

How effective an impression the ad made on the receiver one day after exposure

T / F items tested for the Computron R-55: a) programmability b) price c) scientific functions d) data retaining ability e) country of manufacture f) retail availability g) guarantee

In a free response format, respondents were asked to write down their thoughts about the ad. The total number of positive thoughts about the ad itself were later counted up

4) Favorable recall about the advertised brand

Positive feeling that respondents had toward the brand one day after advertising exposure

The elicitations described in 3) above were coded for positive associations with the advertised brand

of regression coefficients, X is a vector of ESSCA variates, and e is a residual vector. The ESSCA variates are estimated as:

where n- is a matrix of regression coefficients and x a vector of predictor variables. The ESSCA variates are chosen such that they explain a maximal amount of variance in the set of y-variables (Fornell 1979). The maximum number of (X) variates which can be extracted is equal to the number of predictor variables. See the Appendix for more details concerning ESSCA estimation and interpretation.

RESULTS

Just as the case with factor analysis or canonical correlation, a key issue in ESSCA involves determining the dimensionality of the solution. It is, for example, possible to retain all those dimensions which are interpretable. Here, we choose to retain those variables which explain a significant (alpha = .01) portion of criterion variance. Specifically, the significance of redundancy in ESSCA variates may be tested by using Miller's (1975) analogue to the F-test in regression. Using this test, the two dimensional solution appeared optimum for this data set. Figure 4 presents a visual representation of the ESSCA model postulated here.

Table 3 shows the two dimensional ESSCA solution obtained using Kaiser's varimax rotation. The variance

of the y-variables accounted for by the X-variates is .28 (. 19+.09). As mentioned above, both variates represented in Table 3 are statistically significant (p < .01) in terms of redundancy.

That is, both X variates account for a significant portion of the variance in the original y-variables. The proportion of redundant variance associated with a given relationship is a useful overall measure for interpreting ESSCA results, just as it is a useful measure for assessing the output of canonical correlation. In the present case, a sizable relationship is found between the hypothesized predictors and the recall measures.

In the rotated ESSCA solution, the predictor variables seem to divide into two distinct groups defined by the predictor variates. Motivation, enjoyment, information, and product interest load on the first variate, while cognitive differentiation and ability to predict structure load highly on the second variate. As for the criterion variables, brand name recognition displays a high cross loading on the second variate. Recognition of facts loads moderately on the first variate along with high loadings for favorable ad recall and favorable product recall.

The multidimensional nature of the recall construct can be seen by examining the two ESSCA variates. The first variate indicates that motivation to read the ad and enjoyment of the ad are strongly related to favorable recall of both ad and product. The first ESSCA variate appears to be strongly related to the stimulus properties of the ad itself. That is, respondents' feelings of enjoyment in reading the ad and their motivation to read it are a function of the nature of the ad itself. Product interest also loads



TABLE 2 Measuring the Predictor Variables

1.

.

.

.

.

.

Product Interest

On 8 point Likert-type scales, respondents indicate how much they: use calculators are involved with calculators are calculator experts are interested in calculators, relative to other products

Coefficient Alpha - - .873

Motivation

On an 8 point Likert-type scale, respondents indicate how motivated they are to read the ad.

Ability to Predict Structure

The Cloze procedure is used so that every sixth word is deleted; in total there are 43 blanks which the respondent attempts to "close up" by filling in the missing word.


Cognitive Differentiation

Cognitive Differentiation is measured in two stages (Scott 1962). First, in a free format, respondents list all of the important attributes that they can think of associated with a product class. Second, respondents put these attributes into groups that are similar. A respondent can make as many or as few groups as seem appropriate. A measure of cognitive differentiation can be obtained according to a formula derived from information theory:

n R = [log2 (n) 1/n E ni log2 (ni)]/log2(n),

i=l

where n is the total number of attributes and ni is the number that appears in a particular combination of groups.

Informativeness of the ad

On 8 point Likert-type scales, respondents indicate: how much information is in the ad how confusing the ad is how understandable the ad is


Advertising Enjoyment

On 8 point Likert-type scales, respondents indicate how much they: liked the ad enjoyed the ad found the ad to be good


JAMS 42 SPRING, I988


FIGURE 4 Pictorial Representation of the ESSCA Model

+. .. \ \ ~ " -

Solid lines represent loadings . . . . . . . . . . . Dotted lines represent cross loadings

moderately on the first variate. To the extent that the reader was interested in the product class, the ad and product were viewed positively. To the extent that the advertisement was seen as informative and understandable, it and the product were viewed favorably. The fact that information loads highly on this first dimension indicates that this first variate does not reflect merely affective elements; there is also a cognitive component. This finding supports Zajonc and Marcus' (1982) contention that cognitive and affective processing may overlap or else intersect under particular circumstances.

Thus, this first ESSCA variate indicates that certain advertisement properties can produce a motivation to read an enjoyable and informative ad that will result in favorable attitudes toward the ad itself and the product being promoted. This finding is consistent with the latest thinking in the area of cognition and affect. It has been shown that subjects who find a situation pleasing also rate their experience with products more favorably (Clark and Isen 1982). Thus, it is consistent to find in this study a strong relationship of the stimulus properties that created the motivation to read and enjoy the ad with a positive feeling toward both the ad and the product being promoted. Mitchell and Olson (1981) had a similar finding

in a study that varied the advertisement. Attitude toward the advertisement partially mediated brand attitudes.

The second ESSCA variate implies more about the cognitive structure of the individual. Cognitive differentiation and the ability to predict structure load very strongly on the second variate, implying that the more differentiated a person is with respect to calculators and the more a person can predict the ad structure, the higher the likelihood that the brand name will be remembered. To the extent that the receiver is interested in the product class and sees the ad as understandable, there is some moderate contribution by these variables to the second ESSCA variate. Thus, the second variate relates to the individual's cognitive information processing ability as explaining brand name recall.

For purposes of comparison, Table 4 presents a redundancy analysis solution for the criterion variate, using the same data set. In this case, the total redundancy of the predictors is lower (.22 + .02 = .24) than the total redundancy reported for the ESSCA solution (.28). In fact, as shown in Table 4, the second dimension is not significant in terms of redundancy and explains only two percent of the variance. In general, the redundancy analysis solution seems a little bit more difficult to interpret. All


ESSCA: A MULTIDIMENSIONAL ANALYSIS TOOL FOR MARKETING RESEARCH ZINKHAN & LQCANDER

TABLE 3 Rotated ESSCA Solutions Kaiser's Varimax Rotation

Criterion Variables ESSCA

BRAND NAME RECOGNITION .20

FACT RECOGNITION .35

FAVORABLE AD Recall .65

FAVORABLE PRODUCT Recall .41

Predictor Variables ESSCA

Product Interest .38

Motivation .73

Ad Enjoyment .78

Information .57

Cognitive Differentiation .03

Ability to Predict Structure of an Ad .23

Redundancy .19

Significance (Miller's Test) p<.001

(Cross) Loadings

.50

.23

.18

.10

Loadings

.29

.06

.07

.24

.83

.57

.09

p<.01

2 X L 2 y/Xi

i=l

.29

.18

.46

.18

.23

.53

.61

.38

.68

.38

TABLE 4 Redundancy Analysis Solution: Crltedon Variates

Criterion Variables

BRAND NAME RECOGNITION

FACT RECOGNITION

FAVORABLE AD Recall

FAVORABLE PRODUCT Recall

Predictor Variables

Product Interest

Motivation

Ad Enjoyment

Information

Cognitive Differentiation

Ability to Predict Structure of an Ad

Redundancy of Predictors

Significance (Miller's Test)

Redundancy Loadings

2 X L 2 y/Xi

i=l

.52 .81 .93

.51 .01 .26

.80 .33 .75

.49 .45 .44

Redundancy (Cross) Loadings

.37 .00

.55 .11

.60 .11

.48 .07

.34 .31

.39 .14

.22 .02

p<.001 N.S.

.14

.31

.37

.24

.21

.17



of the predictors and criteria have moderate to high loadings (and cross-loadings) in this first dimension. In contrast, only one of the predictors has a moderately high cross-loading on the second dimension (cognitive differentiation loading = .31). The remaining cross- loadings on the second dimension are all below .2. In summary, for this particular data set, the ESSCA solution seems more readily interpretable than the redundancy solution. It must be emphasized, however, that both redundancy analysis and ESSCA involve an exploratory component; thus interpretation of their respective output is somewhat subjective in nature.

DISCUSSION

The results of the study suggest two dimensions that have an impact on the recall measurement area. Those interested in the communication process should be mindful of the impact of these two aspects of memory. To the extent that viewing the ad represents a short mood state, positive or negative, the experience can have an impact on recall of brand name. To the extent that the ad reader is "in tune" with the language of the copywriter (as measured by cognitive differentiation and Cloze procedure), the experience of reading the ad can influence recall of advertising claims.

The major purpose of this study has been to illustrate the usefulness of ESSCA for advertising research applications. More and more, advertising researchers are drawn to second generation analysis techniques, such as ESSCA, since functional multivariate techniques, such as regression and discriminant analysis, are incapable of simultaneously handling more than one criterion variable. Structural techniques such as factor or cluster analysis do not discriminate between criteria and predictors. As a solution, marketing researchers turn to such methods as canonical correlation analysis which allow for simultaneous analysis of both structural and functional relationships. These techniques allow for the investigation of multidimensional phenomena, such as advertising recall.

However, canonical analysis can suffer from substantial interpretive problems. Numerically large canonical correlations may lead to exaggerated interpretations since these correlations do not reflect the variance of observed variables, but rather the variance of derived canonical scores, which themselves are subject to interpretation. ESSCA, as described in this paper, addresses both the problem of explained variance and the problem of substantive inference. Instead of maximizing the correlation between unobserved variates (as does canonical), the ESSCA solution ensures that explanatory capability is optimal according to Stewart and Love's (1968) redundancy criterion. This makes sense since the redundancy criterion is now the recommended method for interpreting canonical results (van den Wollenberg 1977), so ESSCA sets out to maximize this criterion from the outset.

ESSCA is also superior to canonical in that it is more theory-driven. Specifically, pairs of variates are not extracted; only predictor variates are extracted. This

requires that the researcher specify a priori which set of variables is dependent on the remaining set. Canonical correlation analysis does not have this restriction since its solution is symmetrical.

ESSCA is superior to canonical in that more flexible rotation is possible. By rotating the resulting structure in an orthogonal fashion, interpretability can be enhanced without loss of variance. For example, in the analysis of recall data presented here, Kaiser's varimax rotation was able to facilitate the task of interpretation by separating high versus low loadings on a variate.

One of the major drawbacks associated with ESSCA is that it is not a pure confirmatory technique. For example, it is not as sophisticated as LISREL which combines path analysis with confirmatory factor analysis using maximum likelihood estimation (Joreskog 1969; Bagozzi 1980). However, there are times when marketing theory may not be advanced enough to specify all of the relationships which must be identified to implement the LISREL analysis procedure. In these instances, ESSCA provides an important bridge between purely exploratory analysis methods (such as principal components analysis) and purely confirmatory procedures (such as LISREL). Thus, a data-driven analysis such as ESSCA may be useful in developing working hypotheses which can later be more rigorously tested using a confirmatory data analysis procedure.

In sum, ESSCA may be useful to marketing researchers when there are multiple criterion variables and multiple predictors. If there are precise hypotheses which specify exactly how each predictor should be related to each criterion, then LISREL may be the appropriate analysis method. Otherwise, ESSCA provides an alternative which offers most of the advantages of canonical correlation analysis but shares few of its drawbacks. More and more we are beginning to realize that crucial and interesting marketing phenomena are multidimensional in nature. Given that there is an increasing interest in examining the relationships between groups of predictors and groups of criterion variables, ESSCA represents a promising new technique for marketing researchers.

APPENDIX

External Single-Set Components Analysis (ESSCA) starts with one set of standardized y-variables and another set of standardized x-variables. The objective is to find a linear combination (X) of the x-variables that maximizes the common variance between the y-variables and the X- variate. It is possible to estimate a second X-variate (orthogonal to the first) using the remaining variance and following the same principle. Thus if there are Mequations, p predictors, and q criterion variables where x and y are two sets of measures:

~(l = W X l l + W X l 2 + . . . + W X l p

X2 = WX21 + WX22 + . . . + WX2p

'^

X m = W X m l + WXm2 + . . . + W X m p



ESSCA finds the vectors of the weights w which maximize the summed squared correlation between x and the y- variables. In matrix notation, this can be written in characteristic equation form:

(RxyRyx- h Rxx) w = 0 where h is the eigenvalue and w the weight vector. The eigenvalue divided by the number of criterion variables is equal to the redundancy associated with a particular variate (Stewart and Love 1968). See Fornell (1979) for more details concerning ESSCA estimation and interpretation.

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ABOUT THE AUTHORS

GEORGE M. ZINKHAN is Associate Professor of Marketing at the University of Houston. He has published over 50 articles in the areas of advertising and knowledge development. He received a Ph.D. from the University of Michigan in 1981 and is currently a Visiting Associate Professor at the University of Pittsburgh, Graduate School of Business.

WILLIAM B. LOCANDER received his Ph.D. from the University of Illinois in 1973. He was on the faculty at The University of Houston for 10 years. While at Houston, he served as Chairman of the Department of Marketing and Associate Dean of The College of Business Administration. In 1983, Dr. Locander took the Distinguished Professorship in Marketing at The University of Tennessee and now is the North American Philips Faculty Scholar. In 1982-83, Dr. Locander was elected Vice-President of The American Marketing Association, Education Division and in 1984-85 and 1986- 87 was elected Vice-President for Finance. He is presently serving as President of the Association.


Documents

ESSCA: A multidimensional analysis tool for marketing research