PLS Typological Path Modeling: a model-based approach to classification

In many domains (marketing, social sciences, etc.) the variables of interest are often not directly observable. Complex causal relationships between such latent variables may be modeled by means of Structural Equation Models (SEM). Two different methodologies exist for the estimation of such models: SEM-ML (Maximum Likelihood Approach to Structural Equation Models), also known as LISREL (Linear Structural RELations) [Jöreskog, 1970], and SEM-PLS (Structural Equation Models by Partial Least Squares) [Tenenhaus et al., 2005], also known as PLS Path Modeling (PLS-PM). PLS-PM is often preferred in customer research for its “soft” modeling characteristics (namely no distributional assumptions). SEM assume homogeneity across the entire population. However, a unique model for all units may “hide” the differences in behaviors existing among the units. If in SEM-ML segmentation can be achieved by Finite Mixture Models [Day, 1969 and McLachlan et al., 2000], until now there is no unique solution for customer segmentation in a PLS-PM prospective. The traditional approach to segmentation in SEM, be it ML or PLS, consists in estimating separate models by assigning units to a priori classes obtained through external variables, or through a cluster analysis on the original variables. Yet, a priori information may not always be available and heterogeneity is rarely captured by well-known observable variables [Hahn et al., 2002]. Furthermore, traditional clustering procedures are not modelbased: they ignore the heterogeneity information contained in the models. In a PLS-PM framework the Finite Mixture Partial Least Squares approach (FIMIX-PLS) [Hahn et al, 2002; Ringle et al., 2005] has been developed. A generalization of STructural Equation finite Mixture Model (STEMM) [Jedidi et al., 1997] to a PLS framework, FIMIX-PLS, based on the EM algorithm, provides a fuzzy classification of the units. Nevertheless, the EM algorithm requires distributional assumptions at least on the latent endogenous variables. Additionally, the measurement model coefficients are assumed to remain the same across all classes. More recently a distribution-free approach to model-based segmentation has been developed: PLS Typological Path Modeling [Squillacciotti , 2005]. An extension of PLS Typological Regression [Esposito Vinzi et al., 2004], this approach to classification consists of an iterative procedure where the assignment of the units to the classes is based on their distance from the local model characterizing their class. In other words, the iterative algorithm starts with the estimation of the global PLS Path Model (over the entire sample). According to the results of the global model, classes are defined. Local models are then estimated (one for each group), and a measure of the distance of each unit from each local model is computed. Units are then re-assigned to the class corresponding to the closest local model: if this causes any changes in the composition of the classes, the local models are re-estimated and the distances are computed once again. When there is no change in the composition of the classes from one step to the following, the obtained local models are compared in terms of predictivity (R2) and of intensity of the structural links on the final endogenous latent variables. However, in both PLS Typological Path Modeling and FIMIX-PLS the number of classes is supposed to be known a priori, which is rarely the case in an exploratory approach. In FIMIX-PLS the choice of the optimal partition is based on the comparison among different model performance indicators (AIC, BIC, EN, etc.). Research concerning this issue is ongoing in PLS Typological Path Modeling. A second drawback, also common to both FIMIX-PLS and PLS Typological Path Modeling concerns the source of heterogeneity. Heterogeneity of path models is supposed to be concentrated in the estimated relationships between latent variables (structural coefficients). Groups however may also differ in the path diagram structure. An application of the proposed methodology to data from a customer satisfaction survey is presented.