Bayesian semiparametric additive quantile regression
Citable Link (URL):http://resolver.sub.uni-goettingen.de/purl?gs-1/10830
Quantile regression provides a convenient framework for analyzing the impact of covariates on the complete conditional distribution of a response variable instead of only the mean. While frequentist treatments of quantile regression are typically completely nonparametric, a Bayesian formulation relies on assuming the asymmetric Laplace distribution as auxiliary error distribution that yields posterior modes equivalent to frequentist estimates. In this paper, we utilize a location-scale mixture of normals representation of the asymmetric Laplace distribution to transfer different flexible modelling concepts from Gaussian mean regression to Bayesian semiparametric quantile regression. In particular, we will consider high-dimensional geoadditive models comprising LASSO regularization priors and mixed models with potentially non-normal random effects distribution modeled via a Dirichlet process mixture. These extensions are illustrated using two large-scale applications on net rents in Munich and longitudinal measurements on obesity among children. The impact of the likelihood misspecification that underlies the Bayesian formulation of quantile regression is studied in terms of simulations.
This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence (funded by the DFG, German Research Foundation) respectively.
Financial support from the German Research Foundation (DFG), grant KN 922/4-1 is gratefully acknowledged.