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Bayesian composite quantile regression for linear mixed-effects models

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  • Yuzhu Tian
  • Heng Lian
  • Maozai Tian

Abstract

Longitudinal data are commonly modeled with the normal mixed-effects models. Most modeling methods are based on traditional mean regression, which results in non robust estimation when suffering extreme values or outliers. Median regression is also not a best choice to estimation especially for non normal errors. Compared to conventional modeling methods, composite quantile regression can provide robust estimation results even for non normal errors. In this paper, based on a so-called pseudo composite asymmetric Laplace distribution (PCALD), we develop a Bayesian treatment to composite quantile regression for mixed-effects models. Furthermore, with the location-scale mixture representation of the PCALD, we establish a Bayesian hierarchical model and achieve the posterior inference of all unknown parameters and latent variables using Markov Chain Monte Carlo (MCMC) method. Finally, this newly developed procedure is illustrated by some Monte Carlo simulations and a case analysis of HIV/AIDS clinical data set.

Suggested Citation

  • Yuzhu Tian & Heng Lian & Maozai Tian, 2017. "Bayesian composite quantile regression for linear mixed-effects models," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(15), pages 7717-7731, August.
    • Handle: RePEc:taf:lstaxx:v:46:y:2017:i:15:p:7717-7731
    DOI: 10.1080/03610926.2016.1161798
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    Cited by:

    1. Zhen Yu & Keming Yu & Wolfgang K. Härdle & Xueliang Zhang & Kai Wang & Maozai Tian, 2022. "Bayesian spatio‐temporal modeling for the inpatient hospital costs of alcohol‐related disorders," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(S2), pages 644-667, December.
    2. Jennifer Betz & Maximilian Nagl & Daniel Rösch, 2022. "Credit line exposure at default modelling using Bayesian mixed effect quantile regression," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(4), pages 2035-2072, October.
    3. Xiaowen Dai & Libin Jin & Lei Shi, 2023. "Quantile regression in random effects meta-analysis model," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 32(2), pages 469-492, June.
    4. Yingying Hu & Huixia Judy Wang & Xuming He & Jianhua Guo, 2021. "Bayesian joint-quantile regression," Computational Statistics, Springer, vol. 36(3), pages 2033-2053, September.

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