IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v55y2011i1p84-96.html
   My bibliography  Save this article

Bayesian inference for additive mixed quantile regression models

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-9473(10)00193-3
    Download Restriction: Full text for ScienceDirect subscribers only.

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    2. Cai, Zongwu & Xu, Xiaoping, 2009. "Nonparametric Quantile Estimations for Dynamic Smooth Coefficient Models," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 371-383.
    3. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    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. 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.
    7. 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.
    8. 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.
    9. 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.
    10. Yu, Keming & Moyeed, Rana A., 2001. "Bayesian quantile regression," Statistics & Probability Letters, Elsevier, vol. 54(4), pages 437-447, October.
    11. 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.
    12. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. Philip Kostov & Julie Le Gallo, 2015. "Convergence: A Story of Quantiles and Spillovers," Kyklos, Wiley Blackwell, vol. 68(4), pages 552-576, November.
    3. 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.
    4. 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.
    5. 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.
    6. repec:bla:jorssa:v:180:y:2017:i:1:p:315-340 is not listed on IDEAS
    7. 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.
    8. repec:bpj:sndecm:v:22:y:2018:i:2:p:0:n:4 is not listed on IDEAS
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. Sobotka, Fabian & Kneib, Thomas, 2012. "Geoadditive expectile regression," Computational Statistics & Data Analysis, Elsevier, vol. 56(4), pages 755-767.
    14. repec:eee:csdana:v:126:y:2018:i:c:p:92-111 is not listed on IDEAS
    15. repec:bla:istatr:v:84:y:2016:i:3:p:327-344 is not listed on IDEAS
    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.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:55:y:2011:i:1:p:84-96. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: http://www.elsevier.com/locate/csda .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.