gam.fit
GAM P-IRLS estimation with GCV/UBRE smoothness estimation
Description
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'.
Usage
gam.fit(G, start = NULL, etastart = NULL, mustart = NULL, family = gaussian(), control = gam.control(),gamma=1, fixedSteps=(control$maxit+1),...)
Arguments
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. |
Value
A list of fit information.
Author(s)
Simon N. Wood [email protected]
References
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
See Also
Copyright (©) 1999–2012 R Foundation for Statistical Computing.
Licensed under the GNU General Public License.