Bayesian inference for additive mixed quantile regression models
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.
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Sokbae Lee & Joel L. Horowitz, 2004.
"Nonparametric Estimation of an Additive Quantile Regression Model,"
Econometric Society 2004 Far Eastern Meetings
721, Econometric Society.
- 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.
- Joel Horowitz & Sokbae 'Simon' Lee, 2004. "Nonparametric estimation of an additive quantile regression model," CeMMAP working papers CWP07/04, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
- 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.
- Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
- 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.
- 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.
- H�vard 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.
- 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.
- Yu, Keming & Moyeed, Rana A., 2001. "Bayesian quantile regression," Statistics & Probability Letters, Elsevier, vol. 54(4), pages 437-447, October.
- Cai, Zongwu & Xu, Xiaoping, 2008. "Nonparametric Quantile Estimations for Dynamic Smooth Coefficient Models," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1595-1608.
- 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.
- 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.
- 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.
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: (Zhang, Lei)
If references are entirely missing, you can add them using this form.