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'.
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
gam.fit2, gam, mgcv, magic