A Comparative Study of the Use of GAM and GLM in Air Pollution Research

Generalized additive models (GAMs) have been used as a standard analytic tool in time-series studies of air pollution and health during the last decade. A major statistical concern came into view recently about the appropriateness of the use of GAMs in the presence of concurvity, which is likely to be present in the data of all air pollution studies. It has been shown that the standard statistical software, such as S-plus with its gam function, can seriously overestimate the GAM model parameters and underestimate their variances in the presence of concurvity. A recently developed S-plus package, gam.exact, allows a robust assessment of parameter uncertainties for only symmetric smoothers. To date, the impact of concurvity on the parameter estimates has not been investigated fully and is limited to only high values. In this article, we have extended the scope of this investigation by encompassing a wide range of the degrees of concurvity and an alternative class of models. We have performed a simulation study where generalized linear models with natural cubic splines as the smoother function (GLM+NS) are compared systematically with GAMs with smoothing splines as the smoother function (GAM+S) in the presence of varying degrees of concurvity. We believe that, as GLM+NS provides a
straightforward parametric modeling approach, its comparison with the flexible non-parametric approach, GAMþS, is well warranted. Our results indicate that GLM+NS performs better than GAM+S in regard to bias and variance estimates when medium-to-high concurvity exists in the data. Results from our illustrative example with NMMAPS Pittsburgh data are consistent with our findings from the simulations. We conclude that non-parametric smoother based models should be used for exploratory analysis for their flexibility and easy use and for suggesting parametric smoother based models when concurvity exists in the time series data.

Keywords: concurvity; generalized additive model; generalized linear model; air pollution; time series

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