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 ![$\mb {x}_ i = [x_{i1},x_{i2},\cdots ,x_{ik}]$](images/statug_introreg0041.png){kind=small}
is a vector of k regressor for the ith observation, then an additive model represents the mean function as
![\[ \mr {E}[Y] = f_0 + f_1(x_{i1}) + f_2(x_{i2}) + \cdots + f_3(x_{i3}) \]](images/statug_introreg0042.png){kind=small}
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.