Objective Bayesian Model Selection in Generalized Additive Models With Penalized Splines

<div><p>We propose an objective Bayesian approach to the selection of covariates and their penalized splines transformations in generalized additive models. The methodology is based on a combination of continuous mixtures of <i>g</i>-priors for model parameters and a multiplicity-correction prior for the models themselves. We introduce our approach in the normal model and extend it to nonnormal exponential families. A simulation study and an application with binary outcome is provided. An efficient implementation is available in the R package hypergsplines. Supplementary materials for this article are available online.</p>