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

Yu-Zhu Tian (), Man-Lai Tang, Wai-Sum Chan and Mao-Zai Tian
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Yu-Zhu Tian: Northwest Normal University
Man-Lai Tang: The Hang Seng University of Hong Kong
Wai-Sum Chan: The Chinese University of Hong Kong
Mao-Zai Tian: Renmin University of China

Computational Statistics, 2021, vol. 36, issue 2, No 22, 1289-1319

Abstract: Abstract 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.

Keywords: Quantile regression; Bridge penalty; Longitudinal ordinal data; Bond ratings; Posterior inference (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s00180-020-01037-4

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