Structural Equation Modeling and simultaneous clustering through the Partial Least Squares algorithm

The identification of different homogeneous groups of observations and their appropriate analysis in PLS-SEM has become a critical issue in many application fields. Usually, both SEM and PLS-SEM assume the homogeneity of all units on which the model is estimated, and approaches of segmentation present in literature, consist in estimating separate models for each segments of statistical units, which have been obtained either by assigning the units to segments a priori defined. However, these approaches are not fully acceptable because no causal structure among the variables is postulated. In other words, a modeling approach should be used, where the obtained clusters are homogeneous with respect to the structural causal relationships. In this paper, a new methodology for simultaneous non-hierarchical clustering and PLS-SEM is proposed. This methodology is motivated by the fact that the sequential approach of applying first SEM or PLS-SEM and second the clustering algorithm such as K-means on the latent scores of the SEM/PLS-SEM may fail to find the correct clustering structure existing in the data. A simulation study and an application on real data are included to evaluate the performance of the proposed methodology.