Variational Bayesian EM Algorithm for Quantile Regression in Linear Mixed Effects Models

Weixian Wang and Maozai Tian ()
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Weixian Wang: School of statistics and Mathematics, Central University of Finance and Economics, Beijing 102206, China
Maozai Tian: Department of Medical Engineering and Technology, Xinjiang Medical University, Urumqi 830011, China

Mathematics, 2024, vol. 12, issue 21, 1-16

Abstract: This paper extends the normal-beta prime (NBP) prior to Bayesian quantile regression in linear mixed effects models and conducts Bayesian variable selection for the fixed effects of the model. The choice of hyperparameters in the NBP prior is crucial, and we employed the Variational Bayesian Expectation–Maximization (VBEM) for model estimation and variable selection. The Gibbs sampling algorithm is a commonly used Bayesian method, and it can also be combined with the EM algorithm, denoted as GBEM. The results from our simulation and real data analysis demonstrate that both the VBEM and GBEM algorithms provide robust estimates for the hyperparameters in the NBP prior, reflecting the sparsity level of the true model. The VBEM and GBEM algorithms exhibit comparable accuracy and can effectively select important explanatory variables. The VBEM algorithm stands out in terms of computational efficiency, significantly reducing the time and resource consumption in the Bayesian analysis of high-dimensional, longitudinal data.

Keywords: mixed effects models; normal-beta prime prior; variational Bayesian EM algorithm (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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