Finding groups in structural equation modeling 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 units on which the model is applied. The approaches of segmentation proposed in the literature, consist of estimating separate models for each segment of statistical units, assigning these units to segments defined a priori. These approaches are not fully acceptable because no causal structure is postulated among variables. In other words, a model approach should be used, where the clusters obtained are homogeneous, both with respect to the structural causal relationships, and the mean differences between clusters. Therefore, a new methodology is proposed, where simultaneously non-hierarchical clustering and PLS-SEM is applied. This methodology is motivated by the fact that the sequential approach (i.e., the application, first, of SEM or PLS-SEM and subsequently the use of a clustering algorithm on the latent scores obtained) may fail to find the correct clustering structure of data. A simulation study and an application on real data are included to evaluate the performance of the proposed methodology.