Bayesian Quantile Regression with Lasso and Adaptive Lasso Penalty for Binary Longitudinal Data

In many medical studies، in order to describe the course of illness and treatment effects، longitudinal studies are used. In longitudinal studies، responses are measured frequently over time، but sometimes these responses are discrete and with two-state. Recently Binary quantile regression methods to analyze this kind of data have been taken into consideration. In this paper، quantile regression model with Lasso and adaptive Lasso penalty for longitudinal data with dichotomous responses is provided. Since in both methods posteriori distributions of the parameters are not in explicit form، thus the full conditional posteriori distributions of parameters are calculated and the Gibbs sampling algorithm is used to deduction. To compare the performance of the proposed methods with the conventional methods، a simulation study was conducted and at the end، applications to a real data set are illustrated.