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 1.3-23

Index]