Semiparametric penalized generalized additive models for environmental research and epidemiology

Abstract

AbstractFor more than a decade generalized additive models (GAMs) have been successfully applied in various environmental studies, for instance to evaluate the impact of air pollution on health. The air pollution measure is usually connected with the health indicator in a parametric fashion whilst the effects of other covariates are modelled through nonparametric smooth functions. This is the motivation for the widely used semiparametric GAMs. The backfitting‐GAM methodology, and its popular implementation in S‐Plus, constitutes the standard approach. Here we consider its limitations and offer an alternative penalized likelihood concept. The primary limitations are the lack of tools for multiple data‐driven smoothing parameter choice, slow convergence of the iterative backfitting algorithm when concurvity is present, and unstable biased estimates of the regression coefficients and their standard errors in the semiparametric case, even more pronounced under concurvity. The penalized likelihood methodology when combined with cubic spline smoothers allows for a computationally efficient and complete parametric representation of a GAM, either nonparametric or semiparametric. It helps circumvent most of the mentioned GAM flaws in environmental research and epidemiology (e.g. in studies of human exposure to particulate matter). Finally, we discuss various evidence from simulation experiments in the literature, concerning the proper use of the GAM methodology. Copyright © 2009 John Wiley & Sons, Ltd.