Testing Consumer Behavior Theories: Lisrel Is Not a Panacea

ABSTRACT - In the consumer research literature, LISREL (a procedure to estimate structural equations with latent or manifest variables) has been frequently used to estimate causal models. It is argued here that LISREL cannot distinguish between a correlational link between two given variables and a causal link between those variables. Although LISREL has some desirable features over the more conventional multi-variate techniques such as regression analyses, when it comes to resolving questions of causality, it is shown that LISREL is just as unhelpful as the conventional procedures are.

Citation:

Banwari Mittal (1993) ,"Testing Consumer Behavior Theories: Lisrel Is Not a Panacea", in NA - Advances in Consumer Research Volume 20, eds. Leigh McAlister and Michael L. Rothschild, Provo, UT : Association for Consumer Research, Pages: 647-653.

Advances in Consumer Research Volume 20, 1993      Pages 647-653

TESTING CONSUMER BEHAVIOR THEORIES: LISREL IS NOT A PANACEA

Banwari Mittal, Northern Kentucky University

ABSTRACT -

In the consumer research literature, LISREL (a procedure to estimate structural equations with latent or manifest variables) has been frequently used to estimate causal models. It is argued here that LISREL cannot distinguish between a correlational link between two given variables and a causal link between those variables. Although LISREL has some desirable features over the more conventional multi-variate techniques such as regression analyses, when it comes to resolving questions of causality, it is shown that LISREL is just as unhelpful as the conventional procedures are.

INTRODUCTION

The use of causal modeling for testing theoretical relationships is increasing in consumer research. Since the publication of Bagozzi's seminal book on causal modeling (Bagozzi 1980), marketing and consumer researchers have increasingly cast their theories as networks of variables interconnected by causal paths. LISREL (Joreskog and Sorbom 1984) has been a popular procedure to estimate such network models. Increasingly one sees use of LISREL modeling even for uncomplicated regression models (for example those involving 1 criterion and 2 or 3 predictor variables). Furthermore, use of LISREL modeling is increasing to test alternative causal models. Some of these alternative models test the alternative causal direction between two variables (i.e., a¦b versus b¦a). An assumption is unwittingly made that LISREL modeling can settle the issue of which direction of causality is the right one. This assumption and model testing strategy are both wrong. The purpose of this paper is to illuminate some of the issues concerning LISREL's ability to test causality in correlational data.

Background

The practice of marketing rests crucially on assumptions of cause and effect. Marketing managers assume that certain salesperson compensation schemes will improve sales productivity, certain price deals will lure brand-switchers, certain product claim messages will induce favorable brand pre-dispositions, and certain combination of after-sale service attributes will yield high customer satisfaction. Correspondingly, marketing theories in the academic literature are increasingly being cast in causal terms. Causal Models have been advanced and tested for such diverse marketing phenomena as salesman satisfaction with pay (Churchill and Pecotich 1982), customer satisfaction (Churchill and Suprenant 1982), intra-channel reward and power relations (Gaski 1986), Hierarchy of Communication Effects (Zinkhan and Fornell 1989), Theory of Reasoned Action (Burnkrant and Page 1982; Bagozzi 1982; Shimp and Kavas 1984), and brand- and ad-attitude relationship (e.g., Mackenzie, Lutz, and Belch 1986).

Bagozzi (1980) enumerates some benefits of casting one's theories in causal terms. These include: (a) explicit documentation of assumptions, variables, and hypothesized relationships; (b) precision in the specification of operationalizations and functional relationships; and (c) better representation of complex social and psychological processes. The overall benefit is that "the causal model provides a framework for constructing and testing the internal consistency of one's theories and measurements as well as the degree of correspondence between theory and observation" (Bagozzi 1980, p. 75). These benefits legitimize the use of causal modeling for testing the hypothesized causal paths, i.e., for testing the significance of paths which are a priori posited to play a causal role. What the causal modeling does not do, however, is to confirm that the variable assumed to be a cause is indeed a cause rather than an effect or rather than a mere correlate. We illustrate this point below by an empirical analysis.

We define as cause an event which necessitates a subsequent event. This is the second type of cause in Aristotle (1930), as described in Bagozzi (1980, p. 2). In Bollen's (1989) terms, this concept of causality entails the three conditions of isolation, association, and temporal priority. Given this definition, causality can be empirically tested by (i) experimental manipulation of the causal variable and subsequent observation of the ensuing effect, and (ii) by time-separated measures of the causal and consequent variables. A majority of the causal models in the consumer research literature are however tested on correlational data. Because the models are depicted as causal diagrams and because LISREL is employed to estimate the path coefficients, LISREL-unfamiliar readers run the risk of inadvertently assuming that somehow causality is being tested. The empirical example below is designed to illuminate the fallacy of this assumption.

METHOD

Data

We use a research setting where consumers are exposed to an advertisement for an unfamiliar brand. Post exposure measures assess consumer ratings on brand attitudes, attitude toward the advertisement, utilitarian brand beliefs, and image brand beliefs. Brand attitudes are hypothesized to be caused by attitude toward the advertisement, and by brand beliefs (both utilitarian and image beliefs). This research setting and the hypothesis is described in Mittal (1990). The research hypothesis is intended to show that inclusion of image beliefs as predictors reduces the independent contribution of attitude toward the advertisement. Four regression equations needed to test this hypothesis are presented in Table 1. In Mittal (1990), these four regression equations are represented as Models 1, 2, 3, and 4. We use this research paradigm here to explore as to what happens when certain variables are connected by a correlational linkage versus when they are connected by a causal path. Using the same shampoo ad as in Mittal (1990), we obtained post-exposure ratings from a group of 80 students. These data are utilized to estimate the four regression equations of Table 1 via LISREL, and then subsequently explore alternative models.

Analysis

The solutions to the four regression equations (estimated via LISREL) are presented here as Models 'A', 'B', 'C', and 'D' in Figure 1. In Model 'A', utilitarian beliefs, image beliefs, and ad-attitude are shown as antecedents to brand-attitude. In all the models discussed in this paper, ad-attitude and brand-attitude are measured with multiple indicators (three indicators for each), while for image beliefs, and likewise for utilitarian beliefs, an index is computed by a weighted summation of individual beliefs as in multi-attribute models. For simplicity in presentation, the measurement model for the ad-attitude and brand-attitude is not shown in figures. In Model 'B', ad-attitude is omitted as a predictor; in model 'C', image beliefs are omitted; and in Model 'D' both image beliefs and ad-attitude are omitted as predictors. In all four models, only correlational linkages are modeled among the 3 antecedents. Both models 'B' and 'C' fit better than model 'D', based on a chi-square difference test (for one degree of freedom difference, the chi-square difference exceeds the critical value of 3.84, at p<.05). The R-Squared is also substantially more for models 'B' and 'C' than in model 'D'. On similar grounds, model 'A' is superior to all 3 models. This establishes the non-redundant contributions of all 3 antecedents.

TABLE 1

A regression procedure would yield similar findings. When all 3 predictors are in the regression, the total explained variance would be exactly the same as in Model 'A'. The beta coefficients of the three predictors would also be exactly the same as in the LISREL solution. This identity of results between the LISREL and regression solutions is observed for the other 3 models as well. Furthermore, nested models comparison test for two hierarchical regression models (such as between models 'A' and 'B') will yield the same conclusion (as do the LISREL models) about the significance of the incremental or non-redundant contribution of any of the predictors.

The Effect of Causal Relations Among the Predictors

Figure 2 shows Models 'A1' and 'A2' which are modifications of Model 'A'. The modification is that among the three antecedents to brand-attitude, causal rather than correlational paths are modeled. Note that (a) the overall model fit (i.e., chi-square statistic), (b) the R-squared value for brand-attitude, and (c) the causal coefficients of the 3 antecedents are exactly the same as they were in Model 'A'. The only difference is that some of the estimates of the paths among the three predictors themselves are different between models 'A', 'A1', and 'A2'. We shall return to this finding shortly. The important result for now is that prediction of brand-attitude is not affected at all. Recall that this prediction was also the same as in the regression models. Thus, just because LISREL simultaneously allows modeling of causal linkages among the predictors of a criterion variable, it is no reason to expect that LISREL modeling (with or without such causal paths among predictors) will yield additional insight about the regression-estimatable predictor-criterion relationships themselves. This is not an isolated finding. The modification of model 'B' into Model 'B1' and Model 'B2' also yields similar findings (see Figure 3). (Note that in Model 'B2' we incorporate mutual causation between two of the antecedents of brand-attitude.) These results are not mere coincidence. The fact is that as long as the same predictors remain connected to a criterion or endogenous construct, and as long as each antecedent or predictor remains either connected or unconnected with any other antecedents in any two models being compared, the overall model fit and criterion-predictor coefficient estimates will remain unaltered.

WHEN ARE CAUSAL PATHS DIFFERENT FROM CORRELATIONAL PATHS?

Let us return to Models 'A', 'A1' and 'A2' (Figure 2)- this time to examine the estimates of the paths among the 3 predictors themselves. For convenience, we shall abbreviate utilitarian beliefs as UB, image beliefs as IB, and ad-attitude as AAD. In Model 'A1' (compared to Model 'A'), only the path between UB and IB remains unaltered (0.19). In Model 'A2' (compared to model 'A'), only the path between UB and AAD remains unaltered (0.27). What happens is this. In Model 'A1', IB is the only construct with single path terminating into it. That is, it has only one antecedent. Since it has only one antecedent, its linkage with that antecedent is same whether we make that linkage a causal or a correlational one. Since AAD has two paths terminating in it, each of these paths will be lower than their value in the correlational model (unless of course if the two antecedents to AAD in Model 'A1' were totally uncorrelated, in which case the causal and correlational paths would have been identical). This explains why UB=>AAD path in Model 'A2' is same as the correlational path between UB and AAD in model 'A'. Since the overall fits of the models 'A', 'A1', and 'A2' are the same, this sort of model fitting will not enable us to resolve the choice between correlational and causal linkages. Indeed, if we rerun Model 'A' as a four-factorial model (with all 4 constructs mutually correlated among one another), its overall chi-square fit statistic will still be 32.94 (with same degrees of freedom). The fact is that LISREL modeling cannot distinguish between causal and a correlational linkage.

Can Direction of Causality be Tested?

Models 'A3' and 'A4' are further modifications of Model 'A' (see Figure 4). These two models are identical except that the direction of causality between IB and AAd has been reversed. Again, every parameter estimate in Models 'A3' and 'A4' is identical. Furthermore, the estimate for the IB-AAD link in Models 'A3' and 'A4' (which is 0.56 in magnitude) is the same as that of the same link in the correlational model 'A'. The point is that the zero order correlation between IB and AAD is 0.56 (see Model 'A'), and this magnitude of relationship cannot change no matter how we link these two variables.

They cannot change, that is, as long as in the causal model the linkage is an exclusive one. Add another linkage terminating in either of the variables, and the picture would of necessity change. This is what happens in Models 'A1' versus 'A2' (see Figure 2). There, in Model 'A1', IB=>AAD link is 0.528, but in Model 'A2', the reverse link, AAD=>IB, is 0.549. This is because in Model 'A1', another path terminates in AAD (namely, UB=>AAD path), and likewise, an additional path terminates in IB in Model 'A2' (namely, UB=>IB path). Because all constructs are interconnected in both models 'A1' and 'A2', the overall model fit is same, and this overall model fit cannot serve us in choosing between IB=>AAD versus AAD=>IB direction of causality. One may think that because AAD=>IB link in Model 'A2' is greater than IB=>AAD link in Model 'A1' (0.549 versus 0.528), the former causal link is stronger than the latter; this inference will in our opinion be wrong. The link between them is basically 0.56, and its value changes depending upon what other co-predictor the link happens to have in a particular model. For example, in Model 'A1', remove the UB=>AAd link, and the value of IB=>AAD link will become 0.56 (thus exceeding its present value in Model 'A2').

FIGURE 1

FOUR NESTED LISREL MODELS

FIGURE 2

TWO LISREL MODELS: CORRELATIONAL PATHS AMONG THE 3 EXOGENOUS CONSTRUCTS IN MODEL "A" REPLACED HERE BY ALTERNATIVE CAUSAL PATHS

Discussion

LISREL is an efficient technique for testing causal models, but it cannot establish causality. The question of causality can be addressed only by (i) experimental manipulation of causal variables, (ii) time-separated measures of variables (as in multi-wave data), (iii) by open-ended protocols in qualitative studies, and (iv) by a priori theoretical reasoning (this last one, Bollen 1989 views as a sort of "mental experiment" to assess temporal priority).

Both LISREL and conventional regression procedures can alike estimate causal models. However if the data are merely correlational (and one can fit causal models on correlational data), neither Regression nor indeed LISREL procedures provide evidence of causality. In this respect, contrary to what may be inadvertently assumed, LISREL modeling offers no advantage over the regression modeling. The advantages of LISREL modeling reside elsewhere, and they are these: (1) LISREL modeling allows incorporation of measurement errors, and (2) It allows modeling of causal rather than merely correlational paths among the predictors themselves. The latter feature can raise two false hopes. First, it may be thought that somehow the predictor-criterion coefficients will change (and be more valid) if inter-predictor linkages are properly modeled; of course they cannot. Second, one may think that this would establish causality between any two constructs against the rival correlational hypothesis. This hope too is misfounded.

The ability to model measurement errors is and should be a major motivation for use of LISREL modeling. And, efficiency in estimating a complex network of simultaneous equations (which can also be estimated via several separate regression analyses) is of great value. LISREL is useful for certain other applications as well; for example: (i) Confirmatory factor analysis (e.g., Anderson 1987), (ii) testing a scale for its claimed unidimensionality (Gerbing and Anderson 1988), and, more generally, testing the dimensionality underlying a scale (see Shimp and Sharma 1983, for an application), (iii) for construct validation (e.g., see Peter 1981, for concept discussion, and Hunter, Gerbing, and Boster 1982, for an application), and (iv) second order factor model fitting (Kumar and Dillon 1990, Hunter and Gerbing 1982). These advantages and applications (and other features, such as simultaneous estimation of models for multiple groups) should deservedly make LISREL the preferred method in many research applications. At the same time, when LISREL is used to estimate causal models, researchers should be careful in implying any "proof' of causality, just because the estimation procedure was LISREL.

FIGURE 3

TWO LISREL MODELS: CORRELATIONAL PATHS AMONG THE 3 EXOGENOUS CONSTRUCTS IN MODEL "B" REPLACED HERE BY ALTERNATIVE CAUSAL PATHS

FIGURE 4

TWO LISREL MODELS WITH DIRECTION OF CAUSALITY REVERSED

We do not believe that in the consumer behavior literature, researchers have used LISREL wrongly to estimate causal models. These researchers have first grounded their causal models in a priori theory, and then employed LISREL to estimate the parameters of what on a priori grounds is a "causal" model. (See, for example, Churchill and Suprenant 1982; Mackenzie and Lutz 1989). There is some danger, however, that readers whose interest is in the substantive aspects of these consumer behavior studies may unsuspectingly assume that because LISREL was employed, the causality has been established in the correlational data. The use of LISREL should not distract one's attention from rigorously applying a priori logic as the only acid test of causality in correlational data.

When the data are experimental (with truly independent variables), the acid test of causality is still a priori logic (since some other unmeasured variable could intervene between the manipulated variable and the measured effect); but here additionally we would have empirical basis to support the causal hypothesis if the "effect" estimate is significant. This "effect" may be estimated either via the more conventional Analysis of Variance (ANOVA) procedure or via LISREL. If LISREL is chosen to be employed, it is simply because it is more efficient and/or because it can handle latent constructs (and multiple indicators of these latent constructs are available). The LISREL procedure in and of itself does nothing, even in the experimental data, to reinforce or dispute the hypothesized causality. LISREL is simply a technique to estimate the value of the theory-driven causal path, and not to further any claims about the causal nature of the estimated effect.

Conclusion

LISREL cannot establish causality. It is perfectly legitimate to use LISREL to test causal models which are theoretically grounded. And when LISREL supports them, it is legitimate to assert empirical validity for those causal models. It is to be understood, however, that the grounds for claims of causality continue to reside in a priori reasoning, and not in the empirical estimation technique; it does not matter that the moniker on that technique is LISREL.

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