Bayesian Quantile Semiparametric Mixed‐Effects Double Regression Models for Analyzing Longitudinal Data With Non‐Ignorable Missing Responses

ABSTRACT Semiparametric mixed‐effects double regression models have demonstrated satisfactory efficacy across diverse applications of longitudinal studies. However, the estimation of these models often relies on the assumptions of normally distributed errors and complete data with no missing values. Therefore, such restrictions may limit the practical usage of these models when analyzing longitudinal data that exhibit heavy‐tailed behaviors and/or contain missing values. This paper introduces a Bayesian quantile regression‐based semiparametric mixed‐effects double regression model for examining longitudinal data with non‐ignorable missing responses. Here, the quantile regression is used to address non‐normality issues, and the missing mechanism is defined through a logistic regression model. Our proposed algorithm can concurrently model both the mean and variance of the mixed effects as functions of predictors while investigating the predictor effects at different quantiles of interest. Additionally, we utilize the Bayesian adaptive LASSO hierarchical model to devise an effective Metropolis‐Hastings‐within‐Gibbs computation algorithm for both estimation and variable selection purposes. Finally, we conduct different simulation studies and a real‐data example to demonstrate the successful implementation of our proposed Bayesian methodology.