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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Weixian Wang & Maozai Tian, 2024. "Variational Bayesian EM Algorithm for Quantile Regression in Linear Mixed Effects Models," Mathematics, MDPI, vol. 12(21), pages 1-16, October.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:21:p:3311-:d:1504071
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    References listed on IDEAS

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    3. Koenker, Roger, 2004. "Quantile regression for longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 91(1), pages 74-89, October.
    4. Xiaoning Li & Mulati Tuerde & Xijian Hu, 2023. "Variational Bayesian Inference for Quantile Regression Models with Nonignorable Missing Data," Mathematics, MDPI, vol. 11(18), pages 1-31, September.
    5. Yonggang Ji & Haifang Shi, 2020. "Bayesian variable selection in linear quantile mixed models for longitudinal data with application to macular degeneration," PLOS ONE, Public Library of Science, vol. 15(10), pages 1-34, October.
    6. Yu, Keming & Moyeed, Rana A., 2001. "Bayesian quantile regression," Statistics & Probability Letters, Elsevier, vol. 54(4), pages 437-447, October.
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