Bayesian inference for additive mixed quantile regression models

Yu Ryan Yue, Haavard Rue

Research output: Contribution to journalArticlepeer-review

68 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)84-96
Number of pages13
JournalComputational Statistics and Data Analysis
Volume55
Issue number1
DOIs
StatePublished - Jan 1 2011

Keywords

  • Additive mixed models
  • Asymmetric laplace distribution
  • Gaussian markov random fields
  • Gibbs sampling
  • Integrated nested laplace approximations
  • Quantile regression

ASJC Scopus subject areas

  • Statistics and Probability
  • Computational Mathematics
  • Computational Theory and Mathematics
  • Applied Mathematics

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