Regularized Variational Bayesian Approximations for Variable Selection in Extended Multiple-Indicators...

Variable selection in structural equation modeling has merged as a new concern in social and psychological studies. Researchers often aim to strike a balance between achieving predictive accuracy and fostering parsimonious explanations by identifying the most informative variables. While recent developments in Bayesian regularization methods offer promising solutions to promote model sparsity with much fewer "active" variables, their computational burden due to reliance on the Markov chain Monte Carlo technique limits practical utility. In response, this study proposes a variational Bayesian expectation-maximum algorithm (VBEM) for variable selection to extend the multiple-indicators multiple-causes (MIMIC) model. On the basis of traditional MIMIC models, a partially confirmatory framework that operates within the exploratory-confirmatory continuum is introduced, allowing for the flexible incorporation of substantive knowledge and regularization into both measurement and structural parts while accounting for factor correlation. The proposed method demonstrated its flexibility, reliability, and efficiency on both simulated and real data.