Bayesian quantile semiparametric mixed-effects double regression models

Semiparametric mixed-effects double regression models have been used for analysis of longitudinal data in a variety of applications, as they allow researchers to jointly model the mean and variance of the mixed-effects as a function of predictors. However, these models are commonly estimated based on the normality assumption for the errors and the results may thus be sensitive to outliers and/or heavy-tailed data. Quantile regression is an ideal alternative to deal with these problems, as it is insensitive to heteroscedasticity and outliers and can make statistical analysis more robust. In this paper, we consider Bayesian quantile regression analysis for semiparametric mixed-effects double regression models based on the asymmetric Laplace distribution for the errors. We construct a Bayesian hierarchical model and then develop an efficient Markov chain Monte Carlo sampling algorithm to generate posterior samples from the full posterior distributions to conduct the posterior inference. The performance of the proposed procedure is evaluated through simulation studies and a real data application.