Distribution Family and Canonical Link
For each distribution, more than one link can exist.
Different link functions may result in a slight difference in
estimates for parametric models. However, the difference
will be less pronounced for nonparametric models because of
the flexibility of nonparametric model forms.
To simplify the calculation, the GAM procedure uses the canonical
link.
The GAM procedure can fit the data from the Gaussian and binomial
distributions:
The Gaussian Model
With this model, the link function is the identity function,
and the generalized additive model is the additive model.
The Logistic Model
A binomial response model assumes that the proportion of
successes Y is such that Y has a Bin(n(x), p(x)) distribution.
The Bin(n(x), p(x)) refers to the binomial distribution with
parameters n(x) and p(x). Often the data are binary, in which
case n(x)=1. The canonical link is
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