Research Design and Model Estimation Under the Partially Confirmatory Latent Variable Modeling Framework with Multi-Univariate Bayesian Lassos

Abstract

This research builds upon existing developments of the partially confirmatory approach by introducing predictors and regularizations to two additional parameter matrices: structural and differential coefficients. The outcome is a comprehensive framework called partially confirmatory latent variable modeling (PCLVM), where researchers can apply different regularizations to four parameter matrices individually or collectively, and in full or in part. With PCLVM, applied researchers can design a variety of research studies for different purposes, depending on the combinations of different regularizations. It employs a mixed estimation algorithm combining univariate and multivariate Bayesian Lassos for measurement- and structural-level regularizations with or without correlated residuals. The attractiveness of the proposed framework was demonstrated through a variety of typical cases that can be readily estimated and widely encountered in practice. Simulation studies and real-life data analysis were adopted to showcase the performance and versatility of PCLVM and its comparisons with exploratory structural equation modeling.