Parameter Estimation and Variable Selection in Bayesian Quantile Regression Models

• Activity Number: 318 - Robust Regression Methods: From Independent Observations to Spatial Dependence
• Type: Topic Contributed
• Date/Time: Tuesday, August 9, 2022 : 2:00 PM to 3:50 PM
• Sponsor: International Indian Statistical Association
• Author(s): Mai Dao* and Min Wang and Souparno Ghosh
• Companies: Wichita State University and The University of Texas at San Antonio and U. Nebraska-Lincoln
• Keywords: Bayesian quantile regression; variable selection; Gibbs sampler; importance sampling; binary response

Abstract

In this talk, we construct a Bayesian hierarchical modeling framework for simultaneously conducting parameter estimation and variable selection for quantile regression models. We first impose the asymmetric Laplace distribution on the model errors and then specify a quantile-dependent prior for the regression coefficients, which allows researchers to set different priors for different orders of quantiles. This specification yields great flexibility in Bayesian quantile modeling, especially in scenarios with binary response variables. By utilizing the normal-exponential mixture representation of the asymmetric Laplace distribution, we propose a novel three-stage computational scheme starting with an expectation-maximization algorithm and then a Gibbs sampler followed by an importance re-weighting step to draw independent Markov chain Monte Carlo samples from the full conditional posterior distributions of the unknown parameters. The performance of the proposed Bayesian method is illustrated through a series of simulation studies and real-data applications.