The Bayesian Bridge of Quantile Structural Equation Model With Application

The structural equation model (SEM) is widely recognized as the most important statistical tool for evaluating the interrelationships between latent variables and is one of the latent variable models. As a recent advance, Bayesian quantile SEM provides a comprehensive quantitative assessment of the conditional response-latent variables given both explanatory and latent covariates. In this study, we propose a Bridge technique in Bayesian quantile regression, compare it with a Bayesian least absolute shrinkage and selection operator (Lasso) and perform simultaneous estimation and variable selection in the context of quantile SEM. We suggest using Gibbs samples to perform Bayesian inference. Simulations with different sample sizes show that the proposed method gives good results. The proposed method was applied to a group of patients with Kidney failure disease to study the factors affecting this disease.