PCA-PI-PLS-ABS: A new approach for uncovering directional heterogeneity in PLS-SEM

Standard Partial Least Squares Structural Equation Modeling (PLS-SEM) methods often fail to detect significant structural relationships when Simpson's Paradox is present in the data (e.g., when one subgroup has a positive effect while another subgroup has a negative effect). In such cases the subgroup effects may be cancelled in the aggregate (global) model, so that the pooled coefficient describes neither subgroup. This article introduces PCA-PI-PLS-ABS, a new approach designed to efficiently reveal such directional heterogeneity. Monte Carlo simulation validation shows that this method successfully separates data groups with opposite directions (β_A = 1.0 and β_B = -1.0) with a segmentation accuracy of 94%, where the standard global model fails to capture this relationship. This method offers a solution with the following key characteristics: Integrating Power Iteration-based Principal Component Analysis (PCA) for faster computational estimation of outer weights. Applies Angle-Based Segmentation (ABS) using geometric transformations to group observations based on the similarity of their structural relationships. Capable of separating sub-populations with mutually opposing path coefficients. The method is deliberately targeted: it separates subgroups whose structural relationships differ in direction and is not intended to separate subgroups that share a direction and differ only in effect size. We characterise this boundary explicitly through a calibrated minimum detectable angular separation, so that researchers can judge in advance whether the procedure is feasible for their own data.