This is an internal function of package mgcv. It is a modification
of the function glm.fit, designed to be called from gam when perfomance iteration is selected (not the default). 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'.
gam.fit(G, start = NULL, etastart = NULL,
mustart = NULL, family = gaussian(),
control = gam.control(),gamma=1,
fixedSteps=(control$maxit+1),...)An object of the type returned by gam when fit=FALSE.
Initial values for the model coefficients.
Initial values for the linear predictor.
Initial values for the expected response.
The family object, specifying the distribution and link to use.
Control option list as returned by gam.control.
Parameter which can be increased to up the cost of each effective degree of freedom in the GCV or AIC/UBRE objective.
How many steps to take: useful when only using this routine to get rough starting values for other methods.
Other arguments: ignored.
A list of fit information.
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