Bayesian bridge-randomized penalized quantile regression for ordinal longitudinal data, with application to firm’s bond ratings

Empirical studies in various fields, such as clinical trials, environmental sciences, psychology, as well as finance and economics, often encounter the task of conducting statistical inference for longitudinal data with ordinal responses. In such situation, it may not be valid of using the orthodox modeling methods of continuous responses. In addition, most traditional methods of modeling longitudinal data tend to depict the average variation of the outcome variable conditionally on covariates, which may lead to non-robust estimation results. Quantile regression is a natural alternative for describing the impact of covariates on the conditional distributions of an outcome variable instead of the mean. Furthermore, in regression modeling, excessive number of covariates may be brought into the models which plausibly result in reduction of model prediction accuracy. It is desirable to obtain a parsimonious model that only retains significant and meaningful covariates. Regularized penalty methods have been shown to be efficient for conducting simultaneous variable selection and coefficient estimation. In this paper, Bayesian bridge-randomized penalty is incorporated into the quantile mixed effects models of ordinal longitudinal data to conduct parameter estimation and variable selection simultaneously. The Bayesian joint hierarchical model is established and an efficient Gibbs sampler algorithm is employed to perform posterior statistical inference. Finally, the proposed approach is illustrated using simulation studies and applied to an ordinal longitudinal real dataset of firm bond ratings.