A Bayesian quantile regression approach to multivariate semi-continuous longitudinal data

Abstract

Quantile regression is a powerful tool for modeling non-Gaussian data, and also for modeling different quantiles of the probability distributions of the responses. We propose a Bayesian approach of estimating the quantiles of multivariate longitudinal data where the responses contain excess zeros. We consider a Tobit regression approach, where the latent responses are estimated using a linear mixed model. The longitudinal dependence and the correlations among different (latent) responses are modeled by the subject-specific vector of random effects. We consider a mixture representation of the Asymmetric Laplace Distribution (ALD), and develop an efficient MCMC algorithm for estimating the model parameters. The proposed approach is used for analyzing data from the health and retirement study (HRS) conducted by the University of Michigan, USA; where we jointly model (i) out-of-pocket medical expenditures, (ii) total financial assets, and (iii) total financial debt for the aged subjects, and estimate the effects of different covariates on these responses across different quantiles. Simulation studies are performed for assessing the operating characteristics of the proposed approach.