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Bayesian inference for additive mixed quantile regression models

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Listed author(s):
  • Yue, Yu Ryan
  • Rue, Håvard
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    Abstract

    Quantile regression problems in practice may require flexible semiparametric forms of the predictor for modeling the dependence of responses on covariates. Furthermore, it is often necessary to add random effects accounting for overdispersion caused by unobserved heterogeneity or for correlation in longitudinal data. We present a unified approach for Bayesian quantile inference on continuous response via Markov chain Monte Carlo (MCMC) simulation and approximate inference using integrated nested Laplace approximations (INLA) in additive mixed models. Different types of covariate are all treated within the same general framework by assigning appropriate Gaussian Markov random field (GMRF) priors with different forms and degrees of smoothness. We applied the approach to extensive simulation studies and a Munich rental dataset, showing that the methods are also computationally efficient in problems with many covariates and large datasets.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0167-9473(10)00193-3
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    Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

    Volume (Year): 55 (2011)
    Issue (Month): 1 (January)
    Pages: 84-96

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    Handle: RePEc:eee:csdana:v:55:y:2011:i:1:p:84-96
    Contact details of provider: Web page: http://www.elsevier.com/locate/csda

    Keywords: Additive mixed models Asymmetric Laplace distribution Gaussian Markov random fields Gibbs sampling Integrated nested Laplace approximations Quantile regression;

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    1. Horowitz, Joel L. & Lee, Sokbae, 2005. "Nonparametric Estimation of an Additive Quantile Regression Model," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1238-1249, December.
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    4. Ludwig Fahrmeir & Stefan Lang, 2001. "Bayesian inference for generalized additive mixed models based on Markov random field priors," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 50(2), pages 201-220.
    5. De Gooijer J.G. & Zerom D., 2003. "On Additive Conditional Quantiles With High Dimensional Covariates," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 135-146, January.
    6. Li, Youjuan & Liu, Yufeng & Zhu, Ji, 2007. "Quantile Regression in Reproducing Kernel Hilbert Spaces," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 255-268, March.
    7. Håvard Rue, 2001. "Fast sampling of Gaussian Markov random fields," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 325-338.
    8. R. L. Eubank & Chunfeng Huang & Y. Muñoz Maldonado & Naisyin Wang & Suojin Wang & R. J. Buchanan, 2004. "Smoothing spline estimation in varying-coefficient models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(3), pages 653-667.
    9. Brezger, Andreas & Lang, Stefan, 2006. "Generalized structured additive regression based on Bayesian P-splines," Computational Statistics & Data Analysis, Elsevier, vol. 50(4), pages 967-991, February.
    10. Roger Koenker & Ivan Mizera, 2004. "Penalized triograms: total variation regularization for bivariate smoothing," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(1), pages 145-163.
    11. Yu, Keming & Moyeed, Rana A., 2001. "Bayesian quantile regression," Statistics & Probability Letters, Elsevier, vol. 54(4), pages 437-447, October.
    12. Keming Yu & Zudi Lu, 2004. "Local Linear Additive Quantile Regression," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 31(3), pages 333-346.
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    Cited by:

    1. Genya Kobayashi & Hideo Kozumi, 2012. "Bayesian analysis of quantile regression for censored dynamic panel data," Computational Statistics, Springer, vol. 27(2), pages 359-380, June.
    2. Xianhua Dai & Wolfgang Karl Härdle & Keming Yu, 2014. "Do Maternal Health Problems Influence Child's Worrying Status? Evidence from British Cohort Study," SFB 649 Discussion Papers SFB649DP2014-021, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    3. Sriram, Karthik, 2015. "A sandwich likelihood correction for Bayesian quantile regression based on the misspecified asymmetric Laplace density," Statistics & Probability Letters, Elsevier, vol. 107(C), pages 18-26.
    4. Elisabeth Waldmann & Thomas Kneib & Yu Ryan Yu & Stefan Lang, 2012. "Bayesian semiparametric additive quantile regression," Working Papers 2012-06, Faculty of Economics and Statistics, University of Innsbruck.
    5. Bouoiyour, Jamal & Selmi, Refk & Miftah, Amal, 2015. "“Every cloud has a silver lining”; to what extent does the Arab Spring accelerate the integration among Arab monarchies?," MPRA Paper 70942, University Library of Munich, Germany.
    6. Yuta Kurose & Yasuhiro Omori, 2012. "Bayesian Analysis of Time-Varying Quantiles Using a Smoothing Spline," CIRJE F-Series CIRJE-F-845, CIRJE, Faculty of Economics, University of Tokyo.
    7. Martins, Thiago G. & Simpson, Daniel & Lindgren, Finn & Rue, Håvard, 2013. "Bayesian computing with INLA: New features," Computational Statistics & Data Analysis, Elsevier, vol. 67(C), pages 68-83.
    8. Alexander Razen & Wolfgang Brunauer & Nadja Klein & Thomas Kneib & Stefan Lang & Nikolaus Umlauf, 2014. "Statistical Risk Analysis for Real Estate Collateral Valuation using Bayesian Distributional and Quantile Regression," Working Papers 2014-12, Faculty of Economics and Statistics, University of Innsbruck.
    9. Karthik Sriram & R. V. Ramamoorthi & Pulak Ghosh, 2016. "On Bayesian Quantile Regression Using a Pseudo-joint Asymmetric Laplace Likelihood," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 78(1), pages 87-104, February.
    10. Maria Marino & Alessio Farcomeni, 2015. "Linear quantile regression models for longitudinal experiments: an overview," METRON, Springer;Sapienza Università di Roma, vol. 73(2), pages 229-247, August.
    11. Sobotka, Fabian & Kneib, Thomas, 2012. "Geoadditive expectile regression," Computational Statistics & Data Analysis, Elsevier, vol. 56(4), pages 755-767.

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