Bayesian Quantile Structural Equation Models

Abstract

Structural equation modeling is a common multivariate technique for the assessment of the interrelationships among latent variables. Structural equation models have been extensively applied to behavioral, medical, and social sciences. Basic structural equation models consist of a measurement equation for characterizing latent variables through multiple observed variables and a mean regression-type structural equation for investigating how explanatory latent variables influence outcomes of interest. However, the conventional structural equation does not provide a comprehensive analysis of the relationship between latent variables. In this article, we introduce 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 estimation is conducted in a Bayesian framework with Markov Chain Monte Carlo algorithm. The posterior inference is performed with the help of asymmetric Laplace distribution. A simulation shows that the proposed method performs satisfactorily. An application to a study of chronic kidney disease is presented.

Keywords:

• asymmetric Laplace distribution
• latent variable models
• quantile regression
• MCMC methods

ACKNOWLEDGMENTS

We would like to express our sincere thanks to the editor and two anonymous reviewers for their valuable suggestions that helped improve this article greatly. We thank Professor J. C. N. Chan from the Department of Medicine and Therapeutics of the Chinese University of Hong Kong for providing the data in the real example.