gam.outer: Minimize GCV or UBRE score of a GAM using 'outer' iteration

In mgcv: Mixed GAM Computation Vehicle with Automatic Smoothness Estimation

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

Description

Estimation of GAM smoothing parameters is most stable if optimization of the smoothness selection score (GCV, GACV, UBRE/AIC, REML, ML etc) is outer to the penalized iteratively re-weighted least squares scheme used to estimate the model given smoothing parameters.

This routine optimizes a smoothness selection score in this way. Basically the 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), bfgs, optim or nlm. Exact (first and second) derivatives of the score can be used by fitting with gam.fit3. 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,optimizer,
          criterion,scale,gamma,G,start=NULL,nei=NULL,...)

Arguments

lsp	The log smoothing parameters.
fscale	Typical scale of the GCV or UBRE/AIC score.
family	the model family.
control	control argument to pass to gam.fit if pure finite differencing is being used.
method	method argument to gam defining the smoothness criterion to use (but depending on whether or not scale known).
optimizer	The argument to gam defining the numerical optimization method to use.
criterion	Which smoothness selction criterion to use. One of "UBRE", "GCV", "GACV", "REML" or "P-REML".
scale	Supplied scale parameter. Positive indicates known.
gamma	The degree of freedom inflation factor for the GCV/UBRE/AIC score.
G	List produced by mgcv:::gam.setup, containing most of what's needed to actually fit a GAM.
start	starting parameter values.
nei	List specifying neighbourhood structure if NCV used. See gam.
...	other arguments, typically for passing on to gam.fit3 (ultimately).

Details

See Wood (2008) for full details on ‘outer iteration’.

Author(s)

Simon N. Wood [e-mail]

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

https://www.maths.ed.ac.uk/~swood34/

See Also

gam.fit3, gam, magic

mgcv documentation built on May 29, 2024, 4:34 a.m.