The estimation process in the Bayesian quantile structural equation modeling approach

Latent variable models define as a wide class of regression models with latent variables that cannot be directly measured, the most important latent variable models are structural equation models. Structural equation modeling (SEM) is a popular multivariate technique for analyzing the interrelationships between latent variables. Structural equation models have been extensively applied to behavioral, medical, and social sciences. In general, structural equation models includes a measurement equation to characterize latent variables through multiple observable variables and a mean regression type structural equation to investigate how the explanatory latent variables affect the outcomes of interest. Despite the importance of the structural equations model, it does not provide an accurate analysis of the relationships between the latent variables. Therefore, the quantile regression method will be presented within the structural equations model to obtain a comprehensive analysis of the latent variables. we apply the quantile regression method into structural equation models to assess the conditional quantile of the outcome latent variable given the explanatory latent variables and covariates. The posterior inference is performed using asymmetric Laplace distribution. The estimation is done using the Markov Chain Monte Carlo technique in Bayesian inference. The simulation was implemented assuming different distributions of the error term for the structural equations model and values for the parameters for a small sample size. The method used showed satisfactorily performs results.