qgam: Bayesian Nonparametric Quantile Regression Modeling in R

Abstract

Generalized additive models (GAMs) are flexible non-linear regression models, which can be fitted efficiently using the approximate Bayesian methods provided by the mgcv R package. While the GAM methods provided by mgcv are based on the assumption that the response distribution is modeled parametrically, here we discuss more flexible methods that do not entail any parametric assumption. In particular, this article introduces the qgam package, which is an extension of mgcv providing fast calibrated Bayesian methods for fitting quantile GAMs (QGAMs) in R. QGAMs are based on a smooth version of the pinball loss of Koenker (2005), rather than on a likelihood function, hence jointly achieving satisfactory accuracy of the quantile point estimates and coverage of the corresponding credible intervals requires adopting the specialized Bayesian fitting framework of Fasiolo, Wood, Zaffran, Nedellec, and Goude (2021b). Here we detail how this framework is implemented in qgam and we provide examples illustrating how the package should be used in practice.

Keywords

• bayesian quantile regression
• generalized additive models
• regression splines
• calibrated bayes
• fast bayesian inference
• r