gam.fit {mgcv} | R Documentation |
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 mgcv
or 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'.
Simon N. Wood simon.wood@r-project.org
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