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
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),...)
G |
An object of the type returned by |
start |
Initial values for the model coefficients. |
etastart |
Initial values for the linear predictor. |
mustart |
Initial values for the expected response. |
family |
The family object, specifying the distribution and link to use. |
control |
Control option list as returned by |
gamma |
Parameter which can be increased to up the cost of each effective degree of freedom in the GCV or AIC/UBRE objective. |
fixedSteps |
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.
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