gam.fit                 package:mgcv                 R Documentation

GAM P-IRLS estimation with GCV/UBRE smoothness estimation

Description:

     This is an internal function of package 'mgcv'. It is a
     modification of the function 'glm.fit', designed to be called from
     'gam'. The major modification is that rather than solving a
     weighted least squares problem at each IRLS step,  a weighted,
     penalized least squares problem is solved at each IRLS step with
     smoothing parameters associated with each penalty chosen by GCV or
     UBRE, using routine 'magic'.  For further information on usage see
     code for 'gam'. Some regularization of the  IRLS weights is also
     permitted as a way of addressing identifiability related problems
     (see  'gam.control'). Negative binomial parameter estimation is
     supported.

     The basic idea of estimating smoothing parameters at each step of
     the P-IRLS is due to Gu (1992), and is termed `performance
     iteration' or `performance oriented iteration'.

Author(s):

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

References:

     Gu (1992) Cross-validating non-Gaussian data. J. Comput. Graph.
     Statist. 1:169-179

     Gu and Wahba (1991) Minimizing GCV/GML scores with multiple
     smoothing parameters via the Newton method. SIAM J. Sci. Statist.
     Comput. 12:383-398

     Wood, S.N. (2000)  Modelling and Smoothing Parameter Estimation
     with Multiple  Quadratic Penalties. J.R.Statist.Soc.B
     62(2):413-428

     Wood, S.N. (2004) Stable and efficient multiple smoothing
     parameter estimation for generalized additive models. J. Amer.
     Statist. Ass. 99:637-686

See Also:

     'gam.fit3',  'gam', 'mgcv', 'magic'

