Bayesian double penalized quantile regression based on linear mixed effects model for longitudinal count data

This paper constructs a Bayesian double penalized quantile regression based on a linear mixed effects model for longitudinal count data, which can estimate parameters and select variables for fixed and random effects simultaneously. This model utilizes smoothed longitudinal count data as the response variable, incorporating conditional Laplace priors for both fixed and random effects. An efficient Gibbs sampling algorithm was derived for posterior statistical inference. Through simulations, we investigate the impact of parameter estimation and variable selection at different quantile levels under different model sparsities and random effects. In this study, it was found that the proposed method is superior to the Bayesian quantile regression in terms of error and stability of parameter estimation results. The effectiveness of double penalized quantile regression is demonstrated in two case studies involving the number of epileptic seizures and CD4 cell counts.