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Bayesian inference for additive mixed quantile regression models

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  • Yue, Yu Ryan
  • Rue, Håvard

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.

Suggested Citation

  • Yue, Yu Ryan & Rue, Håvard, 2011. "Bayesian inference for additive mixed quantile regression models," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 84-96, January.
    • Handle: RePEc:eee:csdana:v:55:y:2011:i:1:p:84-96
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    References listed on IDEAS

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    Cited by:

    1. repec:bpj:sndecm:v:22:y:2018:i:2:p:0:n:4 is not listed on IDEAS
    2. 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.
    3. Ando, Tomohiro & Bai, Jushan, 2018. "Quantile co-movement in financial markets: A panel quantile model with unobserved heterogeneity," MPRA Paper 88765, University Library of Munich, Germany.
    4. repec:eee:csdana:v:126:y:2018:i:c:p:92-111 is not listed on IDEAS
    5. Philip Kostov & Julie Le Gallo, 2015. "Convergence: A Story of Quantiles and Spillovers," Kyklos, Wiley Blackwell, vol. 68(4), pages 552-576, November.
    6. Seongil Jo & Taeyoung Roh & Taeryon Choi, 2016. "Bayesian spectral analysis models for quantile regression with Dirichlet process mixtures," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(1), pages 177-206, March.
    7. 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.
    8. repec:bla:istatr:v:84:y:2016:i:3:p:327-344 is not listed on IDEAS
    9. 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.
    10. 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.
    11. repec:bla:jorssa:v:180:y:2017:i:1:p:315-340 is not listed on IDEAS
    12. 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.
    13. 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.
    14. 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.
    15. Sobotka, Fabian & Kneib, Thomas, 2012. "Geoadditive expectile regression," Computational Statistics & Data Analysis, Elsevier, vol. 56(4), pages 755-767.
    16. 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.
    17. 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.
    18. 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.

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