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Bayesian quantile regression for parametric nonlinear mixed effects models


  • Jing Wang



We propose quantile regression (QR) in the Bayesian framework for a class of nonlinear mixed effects models with a known, parametric model form for longitudinal data. Estimation of the regression quantiles is based on a likelihood-based approach using the asymmetric Laplace density. Posterior computations are carried out via Gibbs sampling and the adaptive rejection Metropolis algorithm. To assess the performance of the Bayesian QR estimator, we compare it with the mean regression estimator using real and simulated data. Results show that the Bayesian QR estimator provides a fuller examination of the shape of the conditional distribution of the response variable. Our approach is proposed for parametric nonlinear mixed effects models, and therefore may not be generalized to models without a given model form. Copyright Springer-Verlag 2012

Suggested Citation

  • Jing Wang, 2012. "Bayesian quantile regression for parametric nonlinear mixed effects models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 21(3), pages 279-295, August.
  • Handle: RePEc:spr:stmapp:v:21:y:2012:i:3:p:279-295 DOI: 10.1007/s10260-012-0190-7

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    References listed on IDEAS

    1. Koenker, Roger, 2004. "Quantile regression for longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 91(1), pages 74-89, October.
    2. Yu, Keming & Stander, Julian, 2007. "Bayesian analysis of a Tobit quantile regression model," Journal of Econometrics, Elsevier, vol. 137(1), pages 260-276, March.
    3. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
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    Cited by:

    1. Jang, Woosung & Wang, Huixia Judy, 2015. "A semiparametric Bayesian approach for joint-quantile regression with clustered data," Computational Statistics & Data Analysis, Elsevier, vol. 84(C), pages 99-115.
    2. repec:bla:istatr:v:84:y:2016:i:3:p:327-344 is not listed on IDEAS
    3. He, Yaoyao & Liu, Rui & Li, Haiyan & Wang, Shuo & Lu, Xiaofen, 2017. "Short-term power load probability density forecasting method using kernel-based support vector quantile regression and Copula theory," Applied Energy, Elsevier, vol. 185(P1), pages 254-266.
    4. Qifa Xu & Cuixia Jiang & Yaoyao He, 2016. "An exponentially weighted quantile regression via SVM with application to estimating multiperiod VaR," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 25(2), pages 285-320, June.


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