mgcv (version 1.3-21)

fix.family.link: Modify families for use in GAM fitting

Description

Generalized Additive Model fitting by `outer' iteration, requires extra derivatives of the variance and link functions to be added to family objects. The functions add what is needed.

Usage

fix.family.link(fam)
fix.family.var(fam)

Arguments

fam

A family.

Value

• A family object with extra component functions dvar and d2link.

Details

Outer iteration GAM estimation requires derivatives of the GCV/UBRE score, which are obtained by differentiating the P-IRLS GAM fitting iteration w.r.t. the model smoothing parameters. The expressions for the derivatives require the second derivative of the link w.r.t. the mean, and the first derivative of the variance function w.r.t. the mean. These functions add functions evaluating these quantities to a family.

If the family already has functions dvar and d2link then these functions simply return the family unmodified: this allows non-standard links to be used with gam when using outer iteration (performance iteration operates with unmodified families).

The dvar function is a function of a mean vector, mu, and returns a vector of corresponding first derivatives of the family variance function. The d2link function is also a function of a vector of mean values, mu: it returns a vector of second derivatives of the link, evaluated at mu.

If modifying your own family, note that you can often get away with supplying only a dvar function if your family only requires links that occur in one of the standard families.