Robust Bayesian variable selection for the quantile varying coefficient model

Quantile varying coefficient model was widely studied due to its ability in capturing dynamic covariate effects and robust estimation. From the Bayesian perspective, this paper proposes a novel estimation and variable selection method for quantile varying coefficient model by utilizing the generalized asymmetric Huberised-type distribution, which enhances robustness against outliers and heavy-tailed distributions while allowing flexible skewness and tail behavior. The multivariate spike-and-slab priors are introduced to conduct group-level variable selection to identify important/nonzero varying coefficients. An efficient adaptive random walk Metropolis-with-Gibbs sampling algorithm is designed for posterior inference through Markov chain Monte Carlo. The superior performance of our developed procedure is confirmed by comparing with several alternative competitors, in terms of estimation accuracy and variable selection, over different quantile levels as well as diverse error distributions in simulation studies. For practical application, we apply the proposed method to the plasma beta-carotene level data analysis to capture nonlinear patterns and select important variables.