Objective Bayesian Model Selection in Generalized Additive Models With Penalized Splines

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.