The use of LISREL in validating marketing constructs
- 1. 283 The use of LISREL in validating marketing constructs * Jan-Benedict E.M. Steenkamp and Hans C.M. van Trijp Department of Marketing and Marketing Research, Wageningen University, Hollandseweg I, 6706 KN Wageningen, Netherlands ,4n expository overview of the use of LISREL in validating marketing constructs is presented and its advantages over the “traditional approaches” are demonstrated. LISREL’S contribu- tion in all phases of construct validation is discussed. It is shown that LISREL has much to offer in purifying the measure by testing the unidimensionality of the measurement instru- ment, and in cross-validation to investigate the convergent validity (within a method) and reliability. LISREL allows a rigorous assessment of the stability of the construct and its measurement instrument, and it is a powerful methodology for assessing convergent validity across methods, discriminant validity, and nomological validity. The use of LISREL in con- struct validation is empirically illustrated by the analysis of data concerning consumers’ variety seeking tendency with re- spect to foods. 1. Introduction The validity of constructs is a necessary condition for theory development and testing and, therefore, construct validity lies at the very heart of scientific progress in marketing. Construct validity is the degree to which a construct achieves empirical and theoretical * This paper was written while Professor Steenkamp was on sabbatical leave at the Department of Marketing, The Penn- sylvania State University, supported by a fellowship from the Niels Stensen Foundation. The research was partially supported by a grant from ECOZOEK to Mr van Trijp for the proJect “Variety Seeking in Consumer Behavior”. The authors thank Professors Richard P. Bagozzi (University of Michigan), Hans Baumgartner (The Pennsylvania State Uni- versity), and James C. Anderson (Northwestern University), and two anonymous reviewers for their valuable comments on earlier drafts of the paper. The usual disclaimers apply. meaning (Bagozzi, 1980; Peter, 1981). In the literature, the following criteria have been proposed that should be satisfied for con- struct validity to be achieved: (1) unidimen- sionality, (2) within-method convergent valid- ity, (3) reliability, (4) stability, (5) across- method convergent validity and discriminant validity, and (6) nomological validity (Nunn- ally, 1978; Churchill, 1979; Bagozzi, 1980, 1981a,b; Judd et al., 1986; Gerbing and Anderson, 1988). There is an implied hierarchy among the construct validation criteria from the easiest to attain to the more complex and difficult to satisfy. Earlier criteria should be satisfied before going to later criteria. Convergent validity is men- tioned twice, first for multiple applications of the same method, and subsequently for in- struments using dissimilar methods (cf. Bagozzi, 1981a; Phillips and Bagozzi, 1986). In order to draw meaningful conclusions about the convergent validity across methods, the convergent validity of a set of measures using the same method should first be estab- lished. * Many researchers still use rather straight- forward techniques such as coefficient (Y,ex- ploratory factor analysis and bivariate corre- lations to assess the criteria for construct validity (see, e.g., Seymour and Lessne, 1984; Zaichkowsky, 1985; Parasuraman et al., 1988). While these traditional techniques are val- uable, the emergence of covariance structure Intern. J. of Research in Marketing 8 (1991) 283-299 North-Holland ’ A case in point is “key informant” research where multiple informants (serving as methods) rate multiple items. It makes only sense to assess the extent to which the key informants agree when it has first been established that the set of items the informant has rated converge to a common construct (Phillips and Bagozzi, 1986). 0167-8116/91/$03.50 0 1991 - Elsevier Science Publishers B.V. All rights reserved
- 2. 284 J.-B. E. M. Steenkump, H. C.M. uan Trijp / Vuhdating marketing constructs models and the widespread availability of accompanying computer programs such as LISREL (Jijreskog and Siirbom, 1988) provide the researcher with a powerful tool for more detailed assessment and refinement of the construct validity of marketing measurement instruments. Basically, there are two primary advantages of LISREL over the traditional methods, pertaining to the construct’s em- pirical and theoretical meaning. 2 First, it provides a test of the theoretical structure of the measurement instrument, i.e., the rela- tionship of the construct with its measures. Second, the relationships between the con- struct and other constructs can be tested without the bias that measurement error in- troduces. Both advantages are relevant for theory building in marketing science as well as in applied settings where unbiased esti- mates of the measure’s reliability, stability, and validity are also of great importance. In the last decade, a considerable number of studies have been published, dealing with the use of LISREL in construct validation. These studies usually concentrate on one is- sue, are often highly technical, and have ap- peared scattered through the psychological, sociological, marketing, educational, and eco- nomic literature. Thus, the literature is rather fragmented. The purpose of this paper is to present an overview of the use of LISREL in validating marketing constructs and to il- lustrate its application empirically. The ad- vantages of the “LISREL approach” over the “ traditional approaches” will be discussed. It should be noted beforehand that the analysis of multitrait-multimethod (MTMM) matrices with LISREL will not be explored in great z In this paper, “LISREL" and “covariance structure model” are used interchangeably. Although other programs exist for parameterizing covariance structure models (e.g., EQS, Bent- ler, 1985), and some limited tests in confirmatory factor analysis can be conducted with computer packages such as SAS or SPSSX, LISREIL appears to be by far the most widely adopted program in marketing and the social and managerial sciences. detail, and no empirical illustration is pro- vided. This would increase the length of the paper substantially while excellent expository papers on this subject have recently appeared in the marketing literature (Lastovicka et al., 1990; Bagozzi and Yi, 1991). The following section briefly discusses the method employed in the empirical study to illustrate the role of LISFEL in construct vali- dation. The empirical illustration concerns the development of a measurement instrument for consumers’ variety seeking tendency with respect to foods. In Sections 3 through 7, the use of LIsRH_ for assessing various aspects of construct validity is reviewed. In these sec- tions, first the traditional approach is briefly described, next it is shown how LISFLEL yields additional insights, and finally its application is demonstrated empirically. Section 8 con- tains the conclusions. 2. Method 2.1. Vuriety seeking tendency The issue of variety seeking has recently gained more widespread attention among marketers (see, e.g., McAlister and Pessemier, 1982; Givon, 1984, 1985; Lattin and McAlis- ter, 1985; Kahn et al., 1986). In studying variety seeking in the consumption context, the distinction between the trait of con- sumers’ variety seeking tendency and variety seeking behavior is of great importance (cf. Midgley and Dowling, 1978). Variety seeking behavior refers to those observable aspects of consumer behavior that are motivated by the desire for change itself and reflects the ob- servation that consumers derive utility from the consumption of many different items per se, in addition to the characteristics levels provided by these items (Givon, 1984; Wierenga, 1984). The underlying trait of consumers’ variety seeking tendency has been related to a more
- 3. J. -B. E. M. Steenkamp, H. C. M. van Trgp / Validating marketing constructs 285 global concept, known as Optimal Stimula- tion Level (OSL) to explain why consumers derive utility from variation per se (see, e.g., Berlyne, 1960, 1963; Fiske and Maddi, 1961; Raju, 1980). The concept of OSL states that individuals have an idiosyncratic intermediate level of stimulation that is most preferred by them. Several measurement instruments have been proposed for this personality character- istic, Zuckerman’s (1979) Sensation Seeking Scale being the best known among them. Be- havior aimed at modifying stimulation from the environment into correspondence with the optimal level is termed exploratory behavior. Variation in behavior is one of the sources that contributes to the actual level of stimula- tion consumers are experiencing (Fiske and Maddi, 1961). As such, variety seeking behav- ior is conceived of as a specific manifestation of exploratory behavior (see, e.g., Raju, 1980) in that it may serve as a means of bringing a suboptimal level of actual stimulation into closer correspondence with the optimal level. Utility derived from variety seeking behavior is due to the behavior’s contribution to the actual level of stimulation. Consumer’s variety seeking tendency is re- lated to OSL but differs from it in that it only refers to stimulation regulation through varied product consumption. Variety seeking tend- ency is not regarded as a generalized per- sonality trait such as OSL, but as a domain- specific concept. A consumer might be a variety seeker with respect to foods but not with respect to vacations. This view on variety seeking tendency accords with current psy- chological literature suggesting that attitudes, values, and personality variables should be operationalized within a limited domain in order to be related to specific behavior (Ajzen and Fishbein, 1980; Verhallen and Pieters, 1984). The use of LISREL in the validation of marketing constructs will be empirically il- lustrated on data collected for developing a measurement instrument for variety seeking within the domain of foods. Foods is one of the product categories for which variety seek- ing may be especially important (Hoyer and Ridgway, 1984). We define the construct of variety seeking tendency with respect to foods as “the motivational factor that aims at pro- viding variation in stimulation through varied food consumption, irrespective of the instru- mental or functional value of the product alternatives”. It is hypothesized to be a one- dimensional construct that influences varia- tion in food consumption behavior. It is out- side the scope of this paper to present a comprehensive treatment of the literature on variety seeking tendency and related con- structs (see, e.g., van Trijp, 1989). In this paper, the discussion of the empirical results is focused on LIsmL-related issues and not on variety seeking tendency. 2.2. Analysis Details of the data collection will be dis- cussed in subsequent sections of the paper. LISREL 7 (Joreskog and S&born, 1988) was used to analyze the data, where the analyses were conducted on the covariance matrix of the variables. The maximum likelihood esti- mation procedure was used, unless otherwise indicated. ML parameter estimates are rather robust against moderate violations of the multivariate normality assumption, provided that the sample size exceeds about 100 (Boomsma, 1982; Gerbing and Anderson, 1985), but this is not the case for the overall x2 test statistic and the asymptotic standard errors (Browne, 1982, 1984a). Browne (1984a) proposed an estimation procedure which is asymptotically insensitive to the distribution of the observations. How- ever, the computational requirements of this procedure, called Weighted Least Squares (WLS) in LISREL7, are formidable and a large sample size is required to estimate the asymptotic covariance matrix accurately. Joreskog and SBrbom (1986) propose the fol-
- 4. 286 J.-B. E. M. Steenkamp, H.C. M. uan Trijp / Validating marketing constructs lowing rule of thumb: the sample size should be at least 200 if q < 12, and at least 1_5q(q + 1) if q > 12, where q is the number of items. 3 When the sample size does not meet this requirement, as will often be the case in construct validation studies, ML is to be pre- ferred to WLS (Jiireskog and S&born, 1988). Another approach is to use ML, and to correct the overall x2 value for deviations from multivariate normality with respect to kurtosis. The x2 value tends to be overesti- mated when the data are leptokurtically dis- tributed, and underestimated when the data are platykurtic. A corrected x2 value can be obtained by dividing the x2, as estimated with ML, by the multivariate coefficient of relative kurtosis (Browne, 1984a). 4 This coef- ficient can be computed with PRELIS (Jbre- skog and SBrbom, 1986). 5 If the kurtosis is substantial, estimates of the standard errors should be approached with caution, and t- values should be considerably greater than 12.0 ) before it can be concluded with confi- dence that a coefficient is significant. In the present empirical illustration, the multivariate coefficient of relative kurtosis was computed for each set of data, but the basic conclusions remained unaltered. There- fore, the uncorrected x2 values are reported in this paper, unless indicated otherwise. 3 In this paper, “item” and “measure” are used interchangea- bly to denote any type of response that is employed as an operational measure of the construct. 4 This correction is based on the assumption of a multivariate elliptical distribution of which the multivariate normal dis- tribution is a special case. The proposed correction has been found to perform well, even when the distribution of the data diverges substantially from an elliptical distribution (Browne, 1984a). 5 The formula for the multivariate coefficient of relative kurtosis is: N II= c {(X~--)‘W-‘(X,--f)}2/{Nq(q+2)}, r=l where x, is a q X 1 vector of values for subject r, X is the corresponding q X 1 vector of sample means, q is the num- ber of items, W= ((N -l)/N)S, S is the sample covari- ante matrix, and N is the sample size (Browne, 1984a). 3. Unidimensionality Unidimensionality can be defined as the existence of one construct underlying a set of items and has been recognized as “one of the most critical and basic assumptions of mea- surement theory” (Hattie, 1985, p. 139). 6 The point of departure is a pool of items, based on review of the literature, focus group dis- cussions, etc., that all purportedly relate to the construct under investigation. These items are administered to subjects for scoring, and subsequently the pool of items is purified, using item-total correlations, corrected for the item in question, in order to obtain a unidi- mensional measurement instrument. When the construct is hypothesized to consist of several subconstructs (or dimensions), item-total cor- relations should be computed for each sub- construct separately. ’ The dimensionality of the reduced set of items (if applicable: per subconstruct) may be explored with explora- tory factor analysis. The number of items can be further reduced by selecting only high 6If a construct is hypothesized to consist of several subcon- structs or factors, unidimensionality refers to each of the factors separately, i.e., each item is related only to one subconstruct. The construct itself is multidimensional at the first-order level. ’ One reviewer noted that by using the item-total correlation criterion one could omit important items that for some reason become surpressed and include irrelevant items that somehow become inflated, as reflected in the correlations. Further, meaningful items might be eliminated when (1) the construct consists of several subfactors, (2) some subfactors have only one or two items and these subfactors are weakly correlated with the other subfactors, and (3) the researcher is not aware of what the subfactors might be. When the researcher is not certain about what the subfactors might be it is prudent to apply exploratory factor analysis to the total pool of items in order to investigate whether meaningful subfactors are present in the data before computing item- total correlations. One should guard, however, against re- taining factors that have no substantive interpretation. These issues emphasize that it is crucial to carefully delineate the domain of the construct and to assess its operational meaningfulness prior to the empirical investigation of a measurement instrument. Admittedly, this is a subjective undertaking and probably represents the weakest link in the construct validation process (cf. Cracker and Algina, 1986).
- 5. J.-B.E.M. Steenkamp, H.C.M. uan TrQp / Validating marketing constructs 287 loading items. Depending on the results, one or more scales are usually constructed as an unweighted sum of the scores on these high loading items. When coefficient (Y of this scale(s) is adequate, it is concluded that a reliable, unidimensional measurement instru- ment is obtained. However, coefficient cxis a measure of reliability and cannot be used to infer unidimensionality (see Hattie, 1985, for an extensive discussion). 3.1. The use of LISREL in assessing unidimen- sionality LISRELcan add to the results of the tradi- tional techniques by testing the unidimen- sionality of a scale, and, if necessary, refining the factor structure found in exploratory fac- tor analysis in order to ensure unidimen- sionality. Although LISREL could also be ap- plied to the complete pool of data, the use of item-total correlations and exploratory factor analysis to reduce the set of items and to provide preliminary scales that can subse- quently be tested and refined with LISREL makes the LISREL analysis more manageable (Gerbing and Anderson, 1988). The confirma- tory factor analysis model on which the analyses are based is where x is the q X 1 vector of the n sets of observed variables (items), 6 is the n x 1 vec- tor of the underlying factors, A is the q x n matrix of regression coefficients relating the items to the underlying factors, and S is the q X 1 vector of error terms of the items. Re- strictions are placed on various parameters for theory testing (and for identification pur- poses). A common situation is when n = 1, i.e., the construct is hypothesized to consist only of a single factor. Unidimensionality im- plies that in equation (1) A has only one column and n = 1 (or, in case the construct is multidimensional, and unidimensionality re- fers to each subconstruct, only one element per row of the matrix A is different from zero). ’ The overall fit of the model provides the necessary and sufficient information to determine whether a set of items is unidimen- sional (Kumar and Dillon, 1987). If LISREL shows a bad fit of the model, respecification is necessary. Examination of standardized residuals can assist the re- searcher in identifying items that cause the unacceptable fit of the initial model. Stan- dardized residuals are the residuals from the observed and reproduced covariance matrix divided by their asymptotic standard errors, and values exceeding 12.58 1 indicate mis- specification (Jdreskog and Sorbom, 1988). The pattern of standardized residuals is infor- mative for respecification. When a subset of items has large negative standardized residu- als (representing overfitting) with the other items pertaining to the same factor, and large positive residuals among each other (repre- senting underfitting), this suggests that the subset constitutes a separate factor. Further, an item that is related to the wrong factor will usually have large negative residuals with the other items of that factor and large positive residuals with the items of the “correct” fac- tor. When an item has many large standar- dized residuals (in absolute value) but no clear pattern emerges, it appears best to delete the item. However, standardized residuals should be used with caution. They are calcu- lated under the assumption of multivariate normality, and will be be biased when the data violate this assumption. With large sam- ples, standardized residuals could become sig- 8When the construct consists of four or more subconstructs, higher-order unidimensionality of the construct can be tested by performing a second-order confirmatory factor analysis on the covariances among the subconstructs.
- 6. 288 J. -B.E.M. Steenkamp, H. C. M. oan Trijp / Validating marketing constructs nificant, simply because of the power of the test. 9 3.2. Application: assessing the unidimensional- ity of the VST-SC& Preliminary item tryouts resulted in a set of 42 items all purportedly representing the un- derlying construct of consumers’ variety seek- ing tendency with respect to foods (hereafter called VST).The items were personally admin- istered to a random sample of 159 female purchasers of foods, living in two large cities. In all phases of measurement development, the items were scored on five-point labeled Likert scales ranging from “completely dis- agree” ( = 1) to “completely agree” ( = 5). Seventeen items were selected on the basis of a corrected item-total correlation exceed- ing 0.60. Principal axis factoring of these 17 items yielded the following eigenvalues for the first three factors: 9.57, 1.24, and 0.95. The results strongly suggested a single un- derlying factor as the first factor explained more than 50% of the variation in the data, 16 items had loadings exceeding 0.60 on this factor (the 17th item had a loading of 0.58), and the plot of eigenvalues showed a distinct scree at two factors (Cattell, 1966). The num- ber of items was further reduced by selecting the 11 items that had a factor loading exceed- ing 0.70 on the first factor (cf. Armor, 1974). Purification of the measure usually stops here. Coefficient (Y would be computed (0.95 in this case) and one would conclude that a reliable and unidimensional ll-item measure of VST is obtained. However, contrary to LISREL,these techniques do not test the factor structure of the construct. It will be shown that the ll-item scale is not unidimensional, despite its high reliability. LISREL was applied to the covariance ma- trix of the 11 items to test the unidimen- yWe thank a reviewer for bringing our attention to this point. sionality of the scale. The fit of the (one-con- struct) model was unacceptable: x2(44) = 167.49 (p -CO.OOl), x2/df ratio = 3.81, good- ness-of-fit index (GFI)= 0.82, Tucker-Lewis index (TLI)= 0.89.lo The standardized resid- uals indicated that the problems were caused by three items. Nine standardized residuals, all involving one or two of these three items, were greater than 12.58 1, and most of the other standardized residuals involving these items were also considerable. Further, no con- sistent pattern emerged (e.g., high negative standardized residuals with the other eight items and high positive values among them- selves). These findings suggest that these items are not unidimensional with respect to the other items, but also do not constitute a sep- arate factor. The measurement model was respecified by eliminating the three items. The resulting 8-item model yielded a good fit, indicating that a unidimensional measure for VST was obtained: x2(20) = 27.06 (p = 0.13) x’/df ratio = 1.35, GFI = 0.96, TLI = 0.99. ” 4. Cross-validation, within-method convergent validity, and reliability Cross-validation of the unidimensional measurement instrument on new data is re- commended because there is the possibility ‘” The Tucker-Lewis index (Tucker and Lewis, 1973) is less frequently applied in marketing than the Bender-Bonett incremental index of fit (BBI) (Bentler and Bonett, 1980). However, TLI is relatively independent from sample size and incorporates a penalty function against “overfitting”, both of which are not the case for BBI (Marsh et al., 1988; McDonald and Marsh, 1990). The eight items constituting the vsr-scale are: (1) “When I eat out I like to try the most unusual items, even if I am not sure I would like them”; (2) “While preparing food or snacks, I like to try out new recipes”; (3) “I think it is fun to try out food items one is not familiar with”; (4) “I am eager to know what kind of foods people from other countries eat”; (5) “I like to eat exotic foods”; (6) “Items on the menu that I am unfamiliar with make me curious”; (7) “I prefer to eat food products I am used to” (reversed); and (8) “I am curious about food products I am not familiar with”.
- 7. .I.-B.E.M. Steenkamp, H. C.M. van Trap / Validatingmarketq constructs 289 that one has capitalized on chance (Cudeck and Browne, 1983). These data may also be used to test the within-method convergent validity and reliability of the measurement instrument. Churchill (1979) implicitly sug- gests that the new data should only be used to cross-validate the reliability of the scale. It is thus assumed that a set of items having a high reliability also possesses within-method con- vergent validity, as no separate investigation of convergent validity is proposed. However, a set of items can be reliable without exhibit- ing within-method convergent validity. By in- creasing the number of items, one can nearly always increase reliability, even when these items have very low and nonsignificant factor regression coefficients. Gerbing and Ander- son (1988) showed empirically that a mea- surement instrument that has unacceptable within-method convergent validity may still be highly reliable. Thus, within-method con- vergent validity should be achieved before reliability is estimated (see also Bagozzi, 198lb; Bagozzi et al., 1990). ‘* 4.1. The use of LISREL in assessing within- method convergent validity and reliability A weak condition for convergent validity is that the factor regression coefficient on a particular item is statistically significant. A stronger condition is that the factor regres- sion coefficient is substantial. Hildebrandt (1987) suggests with respect to the latter crite- rion that the correlation between the item and the construct should exceed 0.50. These con- ditions should be evaluated, provided that a I2Within-method convergent validity deals with the extent to which multiple applications of the same method are in agreement, while reliability is the degree to which measures are free from random error. Thus, as one reviewer pointed out. the two concepts are closely related. Fulfillment of the criteria of convergent validity virtually guarantees that the measurement instrument is reliable. However, Gerbing and Anderson (1988) have shown that the reverse need not be the case. third requirement of convergent validity is met, i.e., that the overall fit of the model is acceptable. Subjects’ scores on the construct are usu- ally estimated as a weighted or unweighted linear composite of the item scores. The relia- bility of the composite, pg, is given by (Jore- skog, 1971a; Alwin and Jackson, 1979) p6 = l/{ 1 + l/( X’&iA Var(t))}, (2) where X is the p x 1 vector of factor regres- sion coefficients, 9 is a p X p diagonal matrix with error variances in the diagonal, and p refers to the items pertaining to the same construct (p G q). The most reliable com- posite has item weights proportional to X,/Var(&) (i = 1, 2,. . . , p). It is common practice in marketing to use the unweighted sum of the item scores as estimate of the construct scores, but this will only maximize construct reliability in case of equal lambda’s and error variances (implying that each item reflects the underlying construct to the same extent and has the same amount of measure- ment error). In that case, equation (2) can be reduced to the formula for coefficient (Y.When these conditions are not met, coefficient (Y underestimates construct reliability, but the extent of underestimation is usually slight (Armor, 1974). 4.2. Application: cross-validation and assess- ment of within-method convergent validity and reliability of the VST-SC& The eight-item measure for VST together with the three items that were deleted in the previous phase were administered to a new random sample of 151 female purchasers of foods, living in a large metropolitan area. The a priori hypothesis that the three “offending” items should be deleted was confirmed. The fit of the 11-item model was again unaccepta- ble: x*(44) = 240.96 (p -CO.OOl), x*/df ratio = 5.48, GFI = 0.76, TLI = 0.76, while the fit of the eight-item model was good: x*(20) =
- 8. 290 J. -B.E.M. Sieenkamp, H.C.M. uan Trijp / Validating marketing constructs 53.18 (p < O.OOl), X*/df ratio = 2.66, GFI = 0.92, TLI = 0.93. As might be expected, the fit indices were somewhat lower than in the previous phase but the amount of shrinkage is small. The value of GFI compares favorably with simula- tion results (Anderson and Gerbing, 1984) and TLI is above 0.90 (Bentler and Bonett, 1980). The data tended to be leptokurtic, the multivariate coefficient of relative kurtosis being 1.50. The corrected x2(20) is 35.48 (p = 0.02), and the corrected x’/df ratio is 1.77. Confidence in the model is further enhanced by an analysis in which the meaning of the construct is kept invariant by constraining the h’s in the cross-validation sample to be equal to the h’s found in the first sample (cf. Cudeck and Browne, 1983). The following values for the indices of fit were obtained: x2(27) = 69.75 (p < O.OOl), x2/df ratio = 2.58, GFI = 0.90, TLI = 0.93, corrected x2(27) = 46.53 (p = 0.012), corrected x*/df ratio = 1.72. The difference in x2 between the unconstrained and constrained model after correction for kurtosis was a nonsignificant 11.05 (df = 7, p = 0.132). Thus, it can be concluded that the eight- item instrument is acceptably unidimensional. Within-method convergent validity is also achieved as the overall fit of the model was good, all factor regression coefficients were highly significant ( p -c O.OOl), and the corre- lation of each item with the construct ex- ceeded 0.50. The reliability of the construct is an adequate 0.92, using equation (2) (coeffi- cient (Y= 0.90). 5. Stability Probably the most widely used method for assessing the stability of a construct is to compute the correlation between the (un- weighted) composite scores from two admin- istrations of the same test to the same sub- jects. However, random measurement error attenuates the test-retest correlation, while on the other hand systematic error, due to mem- ory effects and other possible causes, may inflate the stability estimate. Sources of insta- bility cannot be located with the test-retest correlation method as it does not distinguish between the construct and its measurement instrument. 5.1. The use of LISREL in stability assessment LISREL enables the researcher to estimate the stability coefficient, i.e., the correlation between the scores on the construct at two points in time, corrected for random and sys- tematic error in the items, and to test a num- ber of aspects of the factorial invariance of the construct through a sequence of tests (Al- win and Jackson, 1981; Marsh and Hocevar, 1985). Testing of aspects of factorial invari- ance yields insight into possible causes of construct instability. As an important preliminary step, the re- searcher should test for the existence of sys- tematic error in the items by comparing the fit of the unrestricted factor model, that al- lows for correlated errors between the same items over time, with the fit of the restricted model that does not allow for correlated er- rors. When the difference in x2 is significant, subsequent analyses should be performed on the correlated-errors-model. Otherwise one can proceed with the model of no correlations between errors. Subsequent analyses take the form of testing the difference in fit of a sequence of four nested models. First, one should test for invariance of the factor regression coefficients. This test is of central importance to stability assessment be- cause it tests the stability of the meaning of the construct. If the fundamental relation- ships between the measures and the construct are not stable, it can hardly be argued that the construct is stable (Alwin and Jackson, 1981). Second, test for the simultaneous in- variance of factor regression coefficients and
- 9. .J-B.E.M. Steenkamp, H.C.M. van Trijp / Validating marketing constructs 291 error variances. Third, test for the simulta- neous invariance of factor regression coeffi- cients, error variances, and variances of the latent variables. l3 This amounts to testing whether the reliability of the individual items and the reliability of the construct are in- variant over time. Fourth, test for the simul- taneous invariance of factor regression coeffi- cients, error variances, variances of the latent variables, and for a stability coefficient equal to unity. Joreskog (1971b) suggests that one should support earlier steps before going to later steps. In each step, the model in ques- tion is tested against the model of the im- mediately preceding step. 5.2. Application: assessment of the stability of VST To examine the stability of VST, the eight items were administered to 96 students during class time. Two weeks later the eight items were administered to the same subjects, again during class time. Thirty-two students were lost to attrition, leaving 59 students for stabil- ity assessment. While this number is not large, and a longer period between test and retest might be preferable, the data are sufficient for illustrative purposes. LISREL was applied to the covariance matrix of the 16 items. The model contained two scores for VST, one for t, and one for t,. Due to the small number of observations, the models were estimated using U nweighted Least Squares (ULS) (Jiireskog and S&born, 1988). The asymptotic proper- ties of ML only apply with large numbers, and ML is not robust in small samples (Boomsma, 1982; Gerbing and Anderson, 1985). No dis- tributional assumptions are necessary with ULS, and ULS estimates seem to be more robust against small sample sizes. The fit of the model that allows for the existence of systematic error was significantly better than the fit of the model with uncorre- lated errors across time (x:(8) = 42.62, p < 0.001). Thus, the hypothesis that item errors are independent from t, to t, should be re- jected. In this case, the upward bias in the stability coefficient due to systematic error was small (0.03), but may be more substantial in other studies. The other analyses were con- ducted with the correlated-errors-model. The hypothesis that factor regression coefficients are invariant could not be rejected (x:(7) = 7.71, p = 0.37). This means that the meaning of VST is stable. Neither the hypothesis of invariance of the factor regression coefficients as well as the error variances, nor the hy- pothesis of invariance of regression coeffi- cients, error variances, and factor variances could be rejected (x:(8) = 3.84, p = 0.87, and xi(l) = 0.96, p = 0.34, respectively). Thus, the reliability of the individual items and the reliability of the construct are invariant over time. The estimated reliability of the con- struct for this sample of students was 0.92, which is the same as reported earlier for the cross-validation sample. The final hypothesis stating that, in addition to the other aspects mentioned earlier, the stability coefficient equals unity was rejected (xi(l) = 9.55, p < 0.01). The best estimate of VST’S stability, using the model with correlated errors, and lambda’s, error variances, and factor vari- ances invariant, was a high 0.93. l4 The simple test-retest correlation between the composite scores was 0.81, which under- estimates the “true” stability of VST. In this case the attenuation, due to random measure- ment error, exceeds the upward bias in the l3When the construct consists of more than one factor, one I4 The fit indices also indicate that the model has a satisfactory should not only test for invariance in variances between fit: x2(111) =149.86, p < 0.01; x’/df =1.35; GFI = 0.98; corresponding factors over time but also for invariance in TLI = 0.98. The x2 value, corrected for kurtosis, was 137.49 covariances between factors. ( p = 0.05).
- 10. 292 J. -B.E.M. Steenkamp,H.C.M. uanTri~p/ Validatingmarketingcanstracts test-retest correlation, due to systematic error in the items. 6. Across-method convergent validity and dis- criminant validity Across-method convergent validity may be investigated with the multitrait-multimethod (MTMM) matrix (Campbell and Fiske, 1959), where each trait or construct is measured by two or more (maximally) different methods. Assessment of convergent validity across methods is highly desirable since high conver- gent validity within a method may be due to all items converging on a method factor in- stead of loading on the construct in question. The MTMM matrix can also be used for explor- ing discriminant validity, although a more limited investigation of this criterion can also be carried out when the various constructs are operationalized with a single method only. Campbell and Fiske (1959) developed four criteria that should be met to achieve conver- gent validity (across methods) and discrimi- nant validity in a MTMM framework. These criteria are based on the pattern of correla- tions between the scores on the various meth- ods for the constructs, have been extensively discussed in the marketing literature (see, e.g., Bagozzi, 1980; Lastovicka et al., 1990), and will not be repeated here. Several problems with the Campbell-Fiske criteria may be noted. There is a lack of quantitative specifi- cation as to what constitutes satisfactory re- sults. Item variance cannot be separated into the contributions of constructs, methods, and error. The criteria are based on observed cor- relations, and hence it is assumed that each measurement instrument is equally reliable. It is implicitly assumed that there are no corre- lations between method factors and construct factors, that all constructs are influenced to the same extent by method factors, and that method factors are uncorrelated (Marsh and Hocevar, 1983; Schmitt and Stults, 1986). 6.1. The use of LISREL in assessing across- method convergent validity and discrimi- nant validity MTMM matrices can also be analyzed with LISREL. The scores on each observed variable can be considered to be a function of three components: a trait or construct component, a method component, and a random error component. Constructs and methods are rep- resented by latent variables, and the (sum- mated) scores on the different measurement instruments, each purporting to measure a construct with a certain method, are used as indicators. The most widely applied LISREL approach to the analysis of MTMM matrices is the con- firmatory factor analysis model (CFA) (Marsh and Hocevar, 1983; Widaman, 1985). Wida- man (1985) outlined a procedure, involving four nested models, to test hypotheses about construct and method factors. Briefly, model 1 (null model) explains the variance in the measures by random error; model 2 (con- struct-only model) explains the variance in the measures by the construct factors and random error; model 3 (method-only model) explains the variance in the measures by the method factors and random error; and model 4 (construct-method model) explains the vari- ance in the measures by construct factors, method factors, and random error. x2 dif- ference tests are used to test for the presence of construct and/or method factors. If con- struct factors are present, model 2 should have a significantly better fit than model 1, and model 4 should have a significantly bet- ter fit than model 3. If method factors are present, model 3 should have a significantly better fit than model 1, and model 4 should have a significantly better fit than model 2. If the test procedure indicates the presence of construct and/or method variance in the data, their magnitude in each measure can be estimated using the factor regression coeffi- cients (Widaman, 1985).
- 11. J.-B.E.M. Steenkamp, H.C.M. uan Trtjp / Validatmg markettng constructs 293 The criteria for within-method convergent validity can also be employed for assessing the convergent validity across methods. Dis- criminant validity is achieved when the corre- lation among constructs differs significantly from unity or when the x2 difference test indicates that two constructs are not perfectly correlated. The CFA model avoids the prob- lems of the traditional Campbell-Fiske ap- proach. It allows for a test of convergent and discriminant validity. It provides overall in- dices of fit and tests of hypotheses about construct and method factors. The use of latent variables solves the problem of dif- ferential reliability among the measurement instruments. The variance of the measure- ment instruments can be partitioned into the contributions of constructs, methods, and er- ror. The CFA model assumes that the variation in measures is a linear combination of con- structs, methods, and error. However, method factors may interact in a multiplicative way with construct factors. Campbell and O’Con- nell (1967) presented evidence that the higher the basic relationship between two constructs, the more that relationship is increased when the method is shared. They also presented evidence that when two constructs are basi- cally independent their correlation is zero, even when the constructs are measured by the same method. These data can be explained by a multiplicative model but not by an additive model. Lastovicka et al. (1990) pointed out that when the underlying structure of the MTMM data is multiplicative, the CFA model fails to provide valid insights into the conver- gent and discriminant validity of the mea- sures. Browne (1984b) developed the Direct Product Model (DPM) to deal with multiplica- tive effects of constructs and methods. The DPM was recently introduced in the marketing literature by Lastovicka et al. (1990). They discussed and illustrated how convergent and discriminant validity is assessed with the DPM and showed empirically that the DPM could be used to test the convergent and discriminant validity of two two data sets for which the CFA model even failed to converge. Bagozzi and Yi (1990, 1991) applied the CFA model and the DPM to fifteen previously published MTMM matrices (and one new data set) and found support for the DPM in five data sets. Wothke and Browne (1990) have shown that the DPM can be reformulated as a second-order confirmatory factor analysis model, allowing researchers to estimate the DPM with LISRJSL. I5 Sample LIsREL 7 program specifications for the DPM are given by Bagozzi and Yi (1990, 1991). Thus, method effects are hypothesized to be constant in the CFA model, while they are hypothesized to vary with the level of con- struct correlations in the DPM. Often, the re- searcher will not have a clear hypothesis about the structure of the method effects, and for this reason Lastovicka et al. (1990) and Bagozzi and Yi (1990, 1991) recommend that both models be tested in the analysis of MTMM data. The results reported in these three papers indicate that it is unlikely that both models would fit a particular MTMM data set. Despite its great potential, the MTMM de- sign is not often used in marketing (Cote and Buckley, 1987; Bagozzi and Yi, 1991), a main reason being that it is difficult and costly to develop multiple methods. It is more common to use only a single measurement method. Although the MTMM approach cannot be used in this situation, LISREL can still be used in assessing discriminant validity between con- structs measured by the same method. l6 I5 We thank a reviewer for bringing our attention to this point. ” For unambiguous results, the constructs should be measured by the same method. When each construct is measured by a different method. it is unclear whether discriminant validity is due to differences in constructs, differences in methods or both.
- 12. 294 J. -B. E.M. Steenkamp, H. C. M. uan Trijp / Validating marketing constructs 6.2. Application: assessment of the discrimi- nant validity of VST The 8-item scale for VST, a Dutch version of Zuckerman’s (1979) Sensation Seeking Scale (Feij and Van Zuilen, 1984), purporting to measure Optimal Stimulation Level, and four measures for variation in consumption behavior with respect to foods were person- ally administered to 191 male and female purchasers of food living in five small and medium sized cities. All 53 items of sss were measured on five-point Likert scales. SSS con- sists of four subscales, “Thrill and Adventure Seeking”, “Experience Seeking”, “Boredom Susceptibility”, and “ Disinhibition Seeking”. Following Feij and Van Zuilen (1984), the ratings of the items on each subscale were averaged and these average ratings on the four subscales were used as indicators of sss. Variation in consumption behavior with re- spect to foods (VARBEH) is measured by four measures, based on self-reports: number of different types of fresh fruits that the subject consumes at least four times a year, the num- ber of types of sandwich fillings the subject consumes at least once a month, a coefficient of entropy (Theil and Finke, 1983) based on the number and share of different “bases” (carbohydrate deliverers) consumed with hot meals during the last seven days, and a simi- lar entropy measure for vegetables consumed with hot meals during the last week. These measures capture essential characteristics of Dutch food consumption behavior. Data on VARBEH were collected to assess the nomo- logical validity of VST (see below). Gerbing, 1984). The data contained consider- able measurement error (for example, the variance due to VST was only 51.4% versus 60.1% in the cross-validation sample), which is probably due to the fact that the interview took a long time (on average about 45 minutes). The correlation between VST and sss was 0.41 (p -CO.OOl), which is significantly lower than unity (xi(l) = 108.88, p < 0.001). Thus, discriminant validity between VST and sss is supported. The same conclusion would be reached, using the simple correlation be- tween the raw composite scores on VST and sss (r = 0.35, which is significantly lower than unity, p < O.OOl), but this correlation is at- tenuated due to measurement error, thus overstating the degree of discriminant validity achieved. 7. Nomological validity Nomological validity is assessed by testing the relationships with other constructs in a nomological net, usually with correlation or regression analysis (see, e.g., Westbrook, 1980; Peter, 1981; Comer, 1984; Ruekert and Churchill, 1984). Correlation/regression an- alysis does not allow formal testing of the nomological net and does not eliminate the biasing effect of measurement error from the estimates of the relations between the con- structs. 7.1. The use of LISREL in assessing nomological validity These data do not allow us to illustrate the The overall indices of fit of LISREL are analysis of MTMM matrices for VST, but they usually heavily influenced by the goodness- do allow us to illustrate testing of discrimi- of-fit of the measurement part of the model, nant validity with LISREL. Discriminant valid- and to a far lesser extent by the goodness-of- ity of VST was investigated with respect to SSS. fit of the structural relations part. This is The goodness-of-fit indices indicated a rea- because in most situations by far the greater sonable fit for the two construct model: proportion of the parameters to be estimated x2(53) = 144.48 (p < O.OOl), x2/df ratio = belongs to the measurement part (Mulaik et 2.73, GFI = 0.90, TLI = 0.88 (cf. Anderson and al., 1989). However, the goodness-of-fit of the
- 13. J.-B.E.M. Steenkamp, H.C.M. van Trijp / Validating marketing constructs 295 structural relations part is of central concern in assessing nomological validity. Recently, Anderson and Gerbing (1988) have proposed a sequential testing procedure involving a series of five nested structural models that deals with this problem. The models are: (1) MS, the saturated structural model in which all structural parameters that can pos- sibly be specified are estimated; (2) M,, the null structural model constrain- ing all structural parameters to zero; (3) M,, the theoretical model (nomological net) under investigation; (4) MC, the next most likely constrained alternative to M,; (5) MU, the next most likely unconstrained alternative to Mt. The researcher first conducts a pseudo x2 test in which the x2 for MS (the smallest possible value for a structural model) is tested with the number of degrees of freedom of M, (the largest possible value for a structural model). When this x2 is significant, no struct- ural model will give an acceptable fit, and the problem is centered in the measurement part of the model which may be respecified. Next, the difference in x2 between M, and MS is tested. This test provides “an asymptotic in- dependent assessment of the theoretical model’s explanation of the relations of the estimated constructs to one another. In other words, one can make an asymptotically inde- pendent test of the nomological validity” (Anderson and Gerbing, 1988, p. 419). When the difference in x2 ’is not significant, J4, is tested against MC. When this difference is significant, and the difference in x2 between M, and MU is not significant, i’Ut is accepted and hence nomological validity is supported. In other instances, one might accept either MC, MU, or respecify the model, depending on the results of the x2 difference tests. In the latter case, the analysis becomes increasingly exploratory (see Anderson and Gerbing, 1988, for further details). The sequential testing procedure relies en- tirely on differences in x2, which are in- fluenced by sample size. Anderson and Gerb- ing (1988) therefore recommend that an in- cremental fit index be used in conjunction with the formal statistical tests to assess whether the difference in fit between rival structural models are not only significant but also substantial. The noncentralized relative normed fit index might be used for this pur- pose (Mulaik et al., 1989; McDonald and Marsh, 1990): NRNF = {(x'n - df,) - (x; - df;)} -(df;-df,)}-‘, (3) where x’,, xf, and xf are the fit of M,, MS, and the model under investigation ( M,, MC, Mu, or a respecified version of MC or Mu), respectively, and df,, df,, and df, are the degrees of freedom of the null model, the model under investigation, and of the saturated model, respectively. When NRNF is high, the structural part of the model is sup- ported, although the traditional goodness-of- fit indices for the complete model may indi- cate mediocre fit (or worse). Differences in NRNF can be used to compare different for- mulations of the nomological net. 7.2. Application: assessment of nomological validity of VST A nomological net consisting of the con- structs VST, sss, and VARBEH was developed. It was hypothesized that VST affects VARBEH and is correlated with sss, and that sss has no significant effect on VARBEH, given findings in the literature that generalized personality constructs are usually not related to specific behavior (Ajzen and Fishbein, 1980; Verhal- len and Pieters, 1984). Although the nomo- logical net is relatively simple, it is sufficient to illustrate the basic principles of LISREL in nomological validity assessment.
- 14. 296 J.-B.E. M. Steenkamp, H.C.M. oan Trgp / Validating marketing constructs The pseudo x2 value was significant (~‘(104) = 249.87, p < O.OOl), indicating problems in the measurement model which were largely due to the measurement error in the data. The sequential test procedure, how- ever, allows the assessment of the nomologi- cal validity despite the significant pseudo x2 value. The difference in x2 between the hy- pothesized model, M,, and the saturated model, MS, was not significant (x:(l) = 2.48, p = 0.12). Further, M, had a significantly better fit than MC, i.c., the model in which the effect of VST on VARBEH is constrained to be zero (x:(l) = 32.77, p -c O.OOl), and the dif- ference in fit between M, and MU (which in this case is the same as MS) was not signifi- cant. The findings of the x2 difference tests were supported by the values of NRNF: 0.41 (MC), 0.99 (M,), and 1.00 (MU). The explana- tion of the structural part of the model im- proved dramatically by specifying a relation- ship between VST and VARBEH, but there was little room for further improvement by speci- fying a causal effect of sss on VARBEH. Note that these conclusions are not apparent from the usual goodness-of-fit indices, which are predominantly affected by the fit of the mea- surement model (e.g., GFI was already a rather high 0.83 for M,). Thus, although the overall fit of the hy- pothesized model was not so good [x2(102) = 252.35 (p c O.OOl), x2/df ratio = 2.47, GFI = 0.86, TLI = 0.841, the nomological validity of VST was supported by the sequential x2 dif- ference tests, the NRNF value of the model, and by the differences in NRNF values with the next most likely unconstrained and con- strained model. The effect of VST on VARBEH is large and highly significant, the path coeffi- cient being 0.63 (p < 0.001). As was found earlier, VST and sss are positively correlated (r = 0.42, p < 0.001). The simple correlations of the four mea- sures of variation in consumption with VST and sss also supported the nomological valid- ity of vsr. Vsr’s correlations were signifi- cantly higher than sss’s for three out of four measures ( p < 0.05, one-sided, after Fisher Y- z transformation). For the number of sandwich fillings, sss had a slightly higher correlation, but the difference was not signifi- cant. However, the measurement part and the structural part of the model are not sep- arated, and the nomological net is not for- mally tested. These drawbacks are solved in the LISREL approach. 8. Conclusions This paper presented an expository over- view of the use of LISREL in validating marketing constructs. Its purpose was not to imply that “ traditional” techniques are not valuable. Preliminary screening of items can be carried out with item-total correlations and exploratory factor analysis, and simple correlations provide valuable information in other phases of construct validation as well. There are also some advantages of the “ tradi- tional” approaches relative to LISREL. For ex- ample, in the “ traditional” approaches it is very easy to obtain observation-by-observa- tion composite scores, while with LISFEL, scores on the construct are indeterminate. No specialized computer programs are required for the “ traditional” approaches. It should also be noted that LISREL and the “tradi- tional” approaches may not always yield sub- stantially different conclusions. However, as has been shown and il- lustrated in the paper, LISREL provides the researcher with a more powerful and versatile tool for a detailed and critical examination of various aspects of construct validity. In puri- fying the measure, LISREL allows for testing the unidimensionality of the measurement in- strument. In cross-validation, LISREL'S contri- bution is in the investigation of the conver- gent validity (within-a-method) and in obtain- ing more accurate estimates of reliability. LISREL allows in-depth assessment of the sta-
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