R: Objective functions for GAM smoothing parameter estimation

gam2objective {mgcv} | R Documentation

## Objective functions for GAM smoothing parameter estimation

### Description

Estimation of GAM smoothing parameters is most stable if optimization of the UBRE/AIC or GCV score is outer to the penalized iteratively re-weighted least squares scheme used to estimate the model given smoothing parameters. These functions evaluate the GCV/UBRE/AIC score of a GAM model, given smoothing parameters, in a manner suitable for use by `optim` or `nlm`. Not normally called directly, but rather service routines for `gam.outer`.

### Usage

    gam2objective(lsp,args,...)
    gam2derivative(lsp,args,...)

### Arguments

`lsp` | The log smoothing parameters.
`args` | List of arguments required to call `gam.fit3`.
`...` | Other arguments for passing to `gam.fit3`.

### Details

`gam2objective` and `gam2derivative` are functions suitable for calling by `optim`, to evaluate the GCV/UBRE/AIC score and its derivatives w.r.t. log smoothing parameters.

`gam4objective` is an equivalent to `gam2objective`, suitable for optimization by `nlm` - derivatives of the GCV/UBRE/AIC function are calculated and returned as attributes.

The basic idea of optimizing smoothing parameters ‘outer’ to the P-IRLS loop was first proposed in O'Sullivan et al. (1986).

### Author(s)

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

### References

Wood, S.N. (2011) Fast stable restricted maximum likelihood and marginal likelihood estimation of semiparametric generalized linear models. Journal of the Royal Statistical Society (B) 73(1):3-36

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

Wood, S.N. (2008) Fast stable direct fitting and smoothness selection for generalized additive models. J.R.Statist.Soc.B 70(3):495-518

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

### See Also

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

[Package mgcv version 1.8-3 Index]