Segmentation in Structural Equation Modeling Using a Combination of Partial Least Squares and Modified Fuzzy Clustering

Abstract

The application of a structural equation modeling (SEM) assumes that all data follow only one model. This assumption may be inaccurate in certain cases because individuals tend to differ in their responses, and failure to consider heterogeneity may threaten the validity of the SEM results. This study focuses on unobservable heterogeneity, where the difference between two or more data sets does not depend on observable characteristics. In this study, we propose a new method for estimating SEM parameters containing unobserved heterogeneity within the data and assume that the heterogeneity arises from the outer model and inner model. The method combines partial least squares (PLS) and modified fuzzy clustering. Initially, each observation was randomly assigned weights in each selected segment. These weights continued to be iteratively updated using a specific objective function. The sum of the weighted residual squares resulting from the outer and inner models of PLS-SEM is an objective function that must be minimized. We then conducted a simulation study to evaluate the performance of the method by considering various factors, including the number of segments, model specifications, residual variance of endogenous latent variables, residual variance of indicators, population size, and distribution of latent variables. From the simulation study and its application to the actual data, we conclude that the proposed method can classify observations into correct segments and precisely predict SEM parameters in each segment.