A Bayesian variable selection approach to longitudinal quantile regression

The literature on variable selection for mean regression is quite rich, both in the classical as well as in the Bayesian setting. However, if the goal is to assess the effects of the predictors at different levels of the response variable then quantile regression is useful. In this paper, we develop a Bayesian variable selection method for longitudinal response at some prefixed quantile levels of the response. We consider an Asymmetric Laplace Distribution (ALD) for the longitudinal response, and develop a simple Gibbs sampler algorithm for variable selection at each quantile level. We analyze a dataset from the health and retirement study (HRS) conducted by the University of Michigan for understanding the relationship between the physical health and the financial health of the aged individuals. We consider the out-of-pocket medical expenses as our response variable since it summarizes the physical and the financial well-being of an aged individual. Our proposed approach efficiently selects the important predictors at different prefixed quantile levels. Simulation studies are performed to assess the practical usefulness of the proposed approach. We also compare the performance of the proposed approach to some other existing methods of variable selection in quantile regression.