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Generalized Additive Models: The GAM Procedure

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 k regressor for the ith observation, then an additive model represents the mean function as

The individual functions can have a parametric or nonparametric form. If all are parametric, PROC GAM fits a fully parametric model. If some are nonparametric, PROC GAM 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.