fix.family.link             package:mgcv             R Documentation

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'.

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 and third
     derivatives of the link w.r.t. the mean, and the first and second
     derivatives 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', 'd2var', 'd2link' and
     'd3link' 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'. Higher derivatives are
     defined similarly.

     If modifying your own family, note that you can often get away
     with supplying only a 'dvar' and 'd2var', function if your family
     only requires links that occur in one of the standard families.

Value:

     A family object with extra component functions 'dvar', 'd2var',
     'd2link' and 'd3link'.

Author(s):

     Simon N. Wood simon.wood@r-project.org

See Also:

     'gam.fit3'

