\HeaderA{gam.fit}{GAM P-IRLS estimation with GCV/UBRE smoothness estimation}{gam.fit}
\keyword{models}{gam.fit}
\keyword{smooth}{gam.fit}
\keyword{regression}{gam.fit}
\begin{Description}\relax
This is an internal function of package \code{mgcv}. It is a modification
of the function \code{glm.fit}, designed to be called from \code{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 \code{\LinkA{magic}{magic}}. 
For further information on usage see code for \code{gam}. Some regularization of the 
IRLS weights is also permitted as a way of addressing identifiability related problems (see 
\code{\LinkA{gam.control}{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'.
\end{Description}
\begin{Author}\relax
Simon N. Wood \email{simon.wood@r-project.org}
\end{Author}
\begin{References}\relax
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
\end{References}
\begin{SeeAlso}\relax
\code{\LinkA{gam.fit3}{gam.fit3}},  \code{\LinkA{gam}{gam}}, \code{\LinkA{mgcv}{mgcv}}, \code{\LinkA{magic}{magic}}
\end{SeeAlso}

