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`

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 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

*mgcv*version 1.9-1 Index]