gam.fit {mgcv} | R Documentation

## 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`. 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'.

### Author(s)

Simon N. Wood simon.wood@r-project.org

### 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

`gam.fit2`, `gam`, `mgcv`, `magic`

[Package mgcv version 1.3-22 Index]