Automatic structure recovery for generalized additive models

In this article, we propose an automatic structure recovery method for generalized additive models (GAMs) by extending Wu and Stefanski's approach. In a similar vein, the proposed method is based on a local scoring algorithm coupled with local polynomial smoothing, along with a kernel-based variable selection approach. Given a specific degree $M$, the goal is to identify predictors contributing polynomially at different degrees up to $M$ and predictors that contribute beyond degree $M$. By focusing on two GAMs, logistic regression and Poisson regression, we illustrate the performance of the proposed method using Monte Carlo simulation studies and two real data examples.