FINITE-MIXTURE STRUCTURAL EQUATION MODELS FOR RESPONSE-BASED SEGMENTATION AND UNOBSERVED HETEROGENEITY

Two endemic problems face researchers in the social sciences (e.g., Ma rketing, Economics, Psychology, and Finance): unobserved heterogeneity and measurement error in data. Structural equation modeling is a powe rful tool for dealing with these difficulties using a simultaneous equ ation framework with unobserved constructs and manifest indicators whi ch are error-prone. When estimating structural equation models, howeve r, researchers frequently treat the data as if they were collected fro m a single population (Muthen 1989). This assumption of homogeneity is often unrealistic. For example, in multidimensional expectancy value models, consumers from different market segments can have different be lief structures (Bagozzi 1982). Research in satisfaction suggests that consumer decision processes vary across segments (Day 1977). This pap er shows that aggregate analysis which ignores heterogeneity in struct ural equation models produces misleading results and that traditional fit statistics are not useful for detecting unobserved heterogeneity i n the data. Furthermore, sequential analyses that first form groups us ing cluster analysis and then apply multigroup structural equation mod eling are not satisfactory. We develop a general finite mixture struct ural equation model that simultaneously treats heterogeneity and forms market segments in the context of a specified model structure where a ll the observed variables are measured with error. The model is consid erably more general than cluster analysis, multigroup confirmatory fac tor analysis, and multigroup structural equation modeling. In particul ar, the model subsumes several specialized models including finite mix ture simultaneous equation models, finite mixture confirmatory factor analysis, and finite mixture second-order factor analysis. The finite mixture structural equation model should be of interest to academics i n a wide range of disciplines (e.g., Consumer Behavior, Marketing, Eco nomics, Finance, Psychology, and Sociology) where unobserved heterogen eity and measurement error are problematic. In addition, the model sho uld be of interest to market researcher; and product managers for two reasons. First, the model allows the manager to perform response-based segmentation using a consumer decision process model, while explicitl y allowing for both measurement and structural error. Second, the mode l allows managers to detect unobserved moderating factors which accoun t for heterogeneity. Once managers have identified the moderating fact ors, they can link segment membership to observable individual-level c haracteristics (e.g., socioeconomic and demographic variables) and imp rove marketing policy. We applied the finite mixture structural equati on model to a direct marketing study of customer satisfaction and esti mated a large model with unobserved constructs and 23 manifest indicat ors. The results show that there are three consumer segments that vary considerably in terms of the importance they attach to the various di mensions of satisfaction. In contrast, aggregate analysis is misleadin g because it incorrectly suggests that except for price all dimensions of satisfaction are significant for all consumers. Methodologically, the finite mixture model is robust; that is, the parameter estimates a re stable under double cross-validation and the method can be used to test large models. Furthermore, the double cross-validation results sh ow that the finite mixture model is superior to sequential data analys is strategies in terms of goodness-of-fit and interpretability. We per formed four simulation experiments to test the robustness of the algor ithm using both recursive and nonrecursive model specifications. Speci fically, we examined the robustness of different model selection crite ria (e.g, CAIC, BIG, and GFI) in choosing the correct number of cluste rs for exactly identified and overidentified models assuming that the distributional form is correctly specified. We also examined the effec t of distributional misspecification (i.e., departures from multivaria te normality) on model performance. The results show that when the dat a are heterogeneous, the standard goodness-of-fit statistics for the a ggregate model are not useful for detecting heterogeneity. Furthermore parameter recovery is poor. For the finite mixture model, however, th e BIC and CAIC criteria perform well in detecting heterogeneity and in identifying the true number of segments. In particular, parameter rec overy for both the measurement and structural models is highly satisfa ctory. The finite mixture method is robust to distributional misspecif ication; in addition, the method significantly outperforms aggregate a nd sequential data analysis methods when the form of heterogeneity is misspecified (i.e., the true model has random coefficients). Researche rs and practitioners should only use the mixture methodology when subs tantive theory supports the structural equation model, a priori segmen tation is infeasible, and theory suggests that the data are heterogene ous and belong to a finite number of unobserved groups. We expect thes e conditions to hold in many social science ay,plications and, in part icular, market segmentation studies. Future research should focus on l arge-scale simulation studies to test the structural equation mixture model using a wide range of models and statistical distributions. Theo retical research should extend the model by allowing the mixing propor tions to depend on prior information and/or subject-specific variables . Finally, in order to provide a huller treatment of heterogeneity, we need to develop a general random coefficient structural equation mode l. Such a model is presently unavailable in the statistical and psycho metric literatures.