|Introduction to Regression Procedures|
Generalized additive models are nonparametric models in which one or more regressor variables are present and can make different smooth contributions to the mean function. For example, if is a vector of regressor for the th observation, then an additive model represents the mean function as
The individual functions can have a parametric or nonparametric form. If all are parametric, the GAM procedure fits a fully parametric model. If some are nonparametric, the GAM procedure fits a semiparametric model. Otherwise, the models are fully nonparametric.
The generalization of additive models is akin to the generalization for linear models: nonnormal data are accommodated by explicitly modeling the distribution of the data as a member of the exponential family and by applying a monotonic link function that provides a mapping between the predictor and the mean of the data.