Partial regression method to fit a generalized additive model

Generalized additive models (GAMs) have been used as a standard analytic tool in studies of air pollution and health during the last decade. The air pollution measure is usually assumed to be linearly related to the health indicator and the effects of other covariates are modeled through smooth functions. A major statistical concern is
the appropriateness of fitting GAMs in the presence of concurvity. Generalized linear models (GLM) with natural cubic splines as smoothers (GLMþNS) have been shown to perform better than GAM with smoothing splines (GAMþS), in regard to the bias and variance estimates using standard model fitting methods. As nonparametric smoothers are attractive for their flexibility and easy implementation, search for alternative methods to fit GAMþS is warranted. In this article, we propose a method using partial residuals to fit GAMþS and call it the "partial regression" method. Simulation results indicate better performance of the proposed method compared to gam.exact function in S-plus, the standard tool in air pollution studies, in regard to bias and variance estimates. In addition, the proposed method is less sensitive to the degree of smoothing and accommodates asymmetric smoothers.

Keywords: GAM; partial residuals; air pollution; bias; concurvity

Department of Biostatistics, Graduate School of Public Health, University of Pittsburgh, Pennsylvania 15261, USA.