Bayesian effect selection in structured additive quantile regression

Abstract

Bayesian structured additive quantile regression is an established tool for regressing outcomes with unknown distributions on a set of explanatory variables and/or when interest lies with effects on the more extreme values of the outcome. Even though variable selection for quantile regression exists, its scope is limited. We propose the use of the Normal Beta Prime Spike and Slab (NBPSS) prior in Bayesian quantile regression to aid the researcher in not only variable but also effect selection. We compare the Bayesian NBPSS approach to statistical boosting for quantile regression, a current standard in automated variable selection in quantile regression, in a simulation study with varying degrees of model complexity and illustrate both methods on an example of childhood malnutrition in Nigeria. The NBPSS prior shows good performance in variable and effect selection as well as prediction compared to boosting and can thus be recommended as an additional tool for quantile regression model building.