Bayesian weighted composite quantile regression for multivariate semi-continuous longitudinal data

This study proposes a Bayesian framework for multivariate semi-continuous longitudinal data analysis based on the composite asymmetric Laplace distribution (CALD). We propose a Tobit weighted composite quantile regression (TWCQR) model that incorporates latent variables through the Tobit framework to address semi-continuity. The latent responses are modeled via a linear mixed-effects structure, incorporating individual-specific random effects to capture correlations across multiple response variables. A joint hierarchical likelihood is derived using the mixture representation of CALD, and the Markov Chain Monte Carlo (MCMC) algorithm is developed for posterior inference of unknown parameters and latent variables. The proposed method is illustrated through comprehensive simulations and applied to the Health and Retirement Study (HRS) dataset and the Primary Biliary Cirrhosis (PBC) dataset.