R: GAM P-IRLS estimation with GCV/UBRE smoothness estimation

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 `gam` when `fit=FALSE`.
`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 `gam.control`.
`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

`gam.fit3`, `gam`, `magic`

[Package mgcv version 1.8-17 Index]