Fitting Generalized Additive Models with the GAM Procedure in SAS 9 . 2

Generalized additive models are useful in finding predictor-response relationships in many kinds of data without using a specific model. They combine the ability to explore many nonparametric relationships simultaneously with the distributional flexibility of generalized linear models. The approach often brings to light nonlinear dependency structures in your data. This paper discusses an example of fitting generalized additive models with the GAM procedure, which provides multiple types of smoothers with automatic selection of smoothing parameters. This paper uses the ODS Statistical Graphics to produce plots of integrated additive and smoothing components. INTRODUCTION PROC GAM is a powerful tool for nonparametric regression modeling. PROC GAM provides great flexibility in modeling predictor-response relationships, as do other nonparametric SAS/STAT procedures such as the TPSPLINE and the LOESS procedures. However, unlike PROC TPSPLINE and PROC LOESS, PROC GAM scales well with the increasing dimensionality and it yields interpretable models. You often benefit from this exploratory modeling with PROC GAM because it can inspire parsimonious parametric models. Hastie and Tibshirani (1986, 1990) proposed the underlying methodology for the generalized additive models. Their models combine the ability to model data from distributions in the exponential family as generalized linear models (Nelder andWedderburn 1972) with the ability to approximate multivariate regression functions by using additive models (Stone 1985). Additive models assume nonparametric smoothing splines for predictors in regression models. Generalized linear models assume the dependency of the dependent variable on additive predictors through a monotonic nonlinear link function specified by a distribution member in the exponential family. By combining these two assumptions, generalized additive models can be used in a wide range of modeling scenarios. Features of PROC GAM include: support of univariate smoothing splines, local regression smoothers, and bivariate thin-plate smoothing splines the ability to fit both nonparametric and semiparametric models support of multiple SCORE statements support of user-specified smoothing parameters or automatic smoothing parameter selection by optimizing the GCV (generalized cross validation) criterion In addition to these features, PROC GAM in SAS 9.2 adds the following new functionalities: fast approximate analysis of deviance graphical display support via the ODS Statistical Graphics system character response support and sort order options for binary models sort order options for categorical variables The next section describes the methodology and the fitting procedure that underlie generalized additive models. 1 Statistics and Data Analysis SAS Global Forum 2008