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Bayesian quantile regression for parametric nonlinear mixed effects models

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  • Jing Wang

Abstract

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

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  • 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

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    1. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    2. Ying Yuan & Guosheng Yin, 2010. "Bayesian Quantile Regression for Longitudinal Studies with Nonignorable Missing Data," Biometrics, The International Biometric Society, vol. 66(1), pages 105-114, March.
    3. Koenker, Roger, 2004. "Quantile regression for longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 91(1), pages 74-89, October.
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    5. Yu, Keming & Stander, Julian, 2007. "Bayesian analysis of a Tobit quantile regression model," Journal of Econometrics, Elsevier, vol. 137(1), pages 260-276, March.
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    Cited by:

    1. Christian E. Galarza & Luis M. Castro & Francisco Louzada & Victor H. Lachos, 2020. "Quantile regression for nonlinear mixed effects models: a likelihood based perspective," Statistical Papers, Springer, vol. 61(3), pages 1281-1307, June.
    2. 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.
    3. Geraci, Marco, 2014. "Linear Quantile Mixed Models: The lqmm Package for Laplace Quantile Regression," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 57(i13).
    4. Georges Bresson & Guy Lacroix & Mohammad Arshad Rahman, 2021. "Bayesian panel quantile regression for binary outcomes with correlated random effects: an application on crime recidivism in Canada," Empirical Economics, Springer, vol. 60(1), pages 227-259, January.
    5. Geraci, Marco, 2019. "Modelling and estimation of nonlinear quantile regression with clustered data," Computational Statistics & Data Analysis, Elsevier, vol. 136(C), pages 30-46.
    6. 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.
    7. 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.
    8. Ali Aghamohammadi, 2018. "Bayesian analysis of dynamic panel data by penalized quantile regression," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(1), pages 91-108, March.
    9. Yunwen Yang & Huixia Judy Wang & Xuming He, 2016. "Posterior Inference in Bayesian Quantile Regression with Asymmetric Laplace Likelihood," International Statistical Review, International Statistical Institute, vol. 84(3), pages 327-344, December.

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