Bayesian regularized quantile structural equation models

Latent variables that should be examined using multiple observed variables are common in substantive research. The structural equation model (SEM) is widely recognized as the most important statistical tool for assessing interrelationships among latent variables. As a recent advancement, Bayesian quantile SEM provides a comprehensive assessment of the conditional quantile of the response latent variables given the explanatory covariates and latent variables. In this study, we develop Bayesian least absolute shrinkage and selection operator (Lasso) and Bayesian adaptive Lasso procedures to conduct simultaneous estimation and variable selection in the context of quantile SEM. We propose the use of the Markov chain Monte Carlo method to conduct Bayesian inference. Various features, including the finite sample performance of the proposed procedures, are validated through simulation studies. The proposed method is applied to investigate the determinants of the capital structure of Chinese-listed companies.