The GAMPL Procedure

PROC GAMPL Contrasted with PROC GAM

Both the GAMPL procedure and the GAM procedure in SAS/STAT software fit generalized additive models. However, the GAMPL procedure uses different approaches for constructing spline basis expansions, fitting generalized additive models, and testing smoothing components. The GAMPL procedure focuses on automatic smoothing parameter selection by using global model-evaluation criteria to find optimal models. The GAM procedure focuses on constructing models by fitting partial residuals against each smoothing term. In general, you should not expect similar results from the two procedures. The following subsections summarize the differences. For more information about the GAM procedure, see ChapterĀ 41: The GAM Procedure.

Constructing Spline Basis Expansions

The GAMPL procedure uses thin-plate regression splines to construct basis expansions for each spline term, and each term allows multiple variables. The GAM procedure uses univariate or bivariate smoothing splines to construct basis expansions, and each term allows only one or two variables. The thin-plate regression splines that PROC GAMPL uses are low-rank approximations to multivariate smoothing splines. The GAM procedure also allows loess smoothers.

Fitting Generalized Additive Models

The GAMPL procedure fits a generalized additive model that has fixed smoothing parameters by using a global design matrix and a roughness penalty matrix. The GAM procedure uses partial residuals to fit against single smoothing terms. For models that have unknown smoothing parameters, the GAMPL procedure estimates smoothing parameters simultaneously by optimizing global criteria such as generalized cross validation (GCV) and the unbiased risk estimator (UBRE). The GAM procedure estimates each smoothing parameter by optimizing the local criterion GCV one spline term at a time.

Distribution Families and Link Functions

The GAMPL procedure supports all the distribution families and all the link functions that the GAM procedure supports. In addition, PROC GAMPL fits models in the negative binomial family. PROC GAMPL supports any link function for each distribution, whereas PROC GAM supports only the canonical link for each distribution.

Testing Smoothing Components

The GAMPL procedure tests the total contribution for a spline term, including both linear and nonlinear trends. The GAM procedure tests the existence of nonlinearity for a spline term beyond the linear trend.

Model Inference

A global Bayesian posterior covariance matrix is available for models that are fitted by the GAMPL procedure. The confidence limits for prediction of each observation are available, in addition to componentwise confidence limits. For generalized additive models that are fitted by the GAM procedure, only the componentwise confidence limits are available, and they are based on the partial residuals for each smoothing term. The degrees of freedom for generalized additive models that are fitted by the GAMPL procedure is defined as the trace of the degrees-of-freedom matrix. The degrees of freedom for generalized additive models that are fitted by the GAM procedure is approximated by summing the trace of the smoothing matrix for each smoothing term.