Bayesian variable selection in high-dimensional ordinal quantile regression models

Abstract Quantile regression (QR) provides a flexible statistical framework for modeling the entire conditional distribution of the response variable, making it useful for analysis in various fields. Despite its advantages, existing methods for QR often encounter numerical challenges in high-dimensional settings, especially for those with ordinal responses. In this paper, we use a latent-response framework to construct a Bayesian hierarchical model to conduct parameter estimation and variable selection for ordinal QR. Using the asymmetric Laplace working likelihood and the horseshoe prior for the regression coefficients, we obtain the posterior samples to be screened by the sequential two-means clustering to identify significant predictors. Extensive numerical results via simulation studies and two real-data applications demonstrate the competitive performance of our approach over some other existing Bayesian methods for ordinal data analysis. The illustrative datasets on educational attainment and liver cancer methylation analyses highlight the practical utility of our proposed approach in both low- and high-dimensional scenarios.