# R: Minimize GCV or UBRE score of a GAM using ‘outer’ iteration

gam.outer {mgcv} | R Documentation

## Minimize GCV or UBRE score of a GAM using ‘outer’ iteration

### Description

Estimation of GAM smoothing parameters is most stable if optimization of the UBRE or GCV score is outer to the penalized iteratively re-weighted least squares scheme used to estimate the model given smoothing parameters.

This routine optimizes a GCV or UBRE score in this way. Basically the GCV or UBRE score is evaluated for each trial set of smoothing parameters by estimating the GAM for those smoothing parameters. The score is minimized w.r.t. the parameters numerically, using `newton` (default), `optim` or `nlm`. Exact derivatives of the score can be used by fitting with `gam.fit2` or `link{gam.fit3}` (for exact first and second derivatives). This improves efficiency and reliability relative to relying on finite difference derivatives.

Not normally called directly, but rather a service routine for `gam`.

### Usage

    gam.outer(lsp,fscale,family,control,method,gamma,G,...)

### Arguments

`lsp` | The log smoothing parameters.
`fscale` | Typical scale of the GCV or UBRE score.
`family` | the model family.
`control` | control argument to pass to `gam.fit` if pure finite differencing is being used.
`method` | method list returned from `gam.method`. This defines the optimization method to use.
`gamma` | The degree of freedom inflation factor for the GCV/UBRE score.
`G` | List produced by `gam.setup`, containing most of what's needed to actually fit GAM.
`...` | other arguments, typically for passing on to `gam.fit2` (ultimately).

### Details

Estimation of smoothing parameters by optimizing GCV scores obtained at convergence of the P-IRLS iteration was proposed by O'Sullivan et al. (1986), and is here termed `outer' iteration.

### Author(s)

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

### References

O 'Sullivan, Yandall & Raynor (1986) Automatic smoothing of regression functions in generalized linear models. J. Amer. Statist. Assoc. 81:96-103.

http://www.maths.bath.ac.uk/~sw283/

### See Also

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

[Package mgcv version 1.3-27 Index]