Bayesian semiparametric additive quantile regression

Abstract

Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in University of Innsbruck AbstractQuantile 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 modeling 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.

A spatiotemporal quantile regression model for emergency department expenditures

“…The ALD is a real‐valued continuous distribution characterized by location, precision, and skewness parameters μ , δ 2 , and τ ; by setting μ = 0 to ensure Q ϵ ( τ ) = 0, the density of ϵ is written explicitly as where denotes the indicator function. Recent empirical findings support the use of ALD even though it may fail to accurately represent the true error distribution. As such, the ALD should be regarded as a ‘working likelihood’ that yields valid estimates of conditional quantiles rather than a true depiction of the underlying data‐generating mechanism .…”

“…Like Waldmann et al . , we adopt a Bayesian modeling approach based on the asymmetric Laplace distribution (ALD), which we regard as a ‘working likelihood’ that yields consistent posterior estimates of conditional quantiles while providing efficient computation based solely on closed‐form full conditionals. Unlike Waldmann et al .…”

“…Unlike Waldmann et al . , however, our proposed model accommodates temporal heterogeneity. Moreover, unlike previous approaches, our model has a hierarchical structure incorporating both patient‐level and region‐level predictors as well as spatiotemporal random effects.…”

Quantile regression for mixed models with an application to examine blood pressure trends in China

“…Another avenue is to introduce dependence via random intercepts, as in Koenker (2004). Waldmann et al (2013) and Yue and Rue (2011) assumed asymmetric Laplace errors and included a random subject effect in the location parameter. Presenting separate methodology for marginal and conditional inference, Reich, Bondell and Wang (2010) accounted for within-cluster dependence via random intercepts and flexibly modeled the density using an infinite mixture of normals.…”

A sandwich likelihood correction for Bayesian quantile regression based on the misspecified asymmetric Laplace density

“…Therefore, the approach has been useful in many applications (e.g. Yu et al 2005;Yue and Rue 2011;Benoit and Van den Poel 2012;Alhamzawi and Yu 2013;Waldmann et al 2013). …”