Fast stable direct fitting and smoothness selection for Generalized Additive Models

TL;DR

This paper introduces a new, efficient, and stable method for direct smoothness selection in Generalized Additive Models, overcoming convergence issues of previous iterative methods and enabling reliable fitting of GAMs and GAMMs.

Contribution

It develops the first computationally efficient and stable direct smoothness selection method for GAMs, improving over existing iterative schemes and handling GAMMs.

Findings

Lower mean computation times in simulations

Enhanced stability and convergence reliability

Effective fitting of generalized additive mixed models

Abstract

Existing computationally efficient methods for penalized likelihood GAM fitting employ iterative smoothness selection on working linear models (or working mixed models). Such schemes fail to converge for a non-negligible proportion of models, with failure being particularly frequent in the presence of concurvity. If smoothness selection is performed by optimizing `whole model' criteria these problems disappear, but until now attempts to do this have employed finite difference based optimization schemes which are computationally inefficient, and can suffer from false convergence. This paper develops the first computationally efficient method for direct GAM smoothness selection. It is highly stable, but by careful structuring achieves a computational efficiency that leads, in simulations, to lower mean computation times than the schemes based on working-model smoothness selection. The method also offers a reliable way of fitting generalized additive mixed models.