Bayesian Piecewise Structural Equation Modeling for Interpretable Nonlinear Relations

• In Event: Statistical Frontiers: Bayesian Inference, Machine Learning, and Longitudinal Modeling

Abstract

Structural Equation Modeling (SEM) typically assumes linear relations among variables, which may oversimplify real-world nonlinear phenomena. While some SEM has incorporated methods like Bayesian P-splines and generalized additive models to accommodate nonlinear relations, their complex parameterizations can hinder interpretation. This study proposes Bayesian Piecewise SEM (BPSEM) to model nonlinear relations while maintaining interpretability. BPSEM approximates nonlinear relations using piecewise models with a finite number of knots, which signify locations where notable relational changes occur. By incorporating regularized horseshoe priors on slope differences between adjacent segments, BPSEM automatically shrinks negligible differences toward zero, identifying meaningful change points in structural paths while reducing complexity when fewer knots are needed. Monte Carlo simulations were conducted to evaluate the performance of this approach.

Authors

• Dayeon Lee, University of Maryland

• Gregory R. Hancock, University of Maryland