Objective functions for GAM smoothing parameter estimation
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.
gam2objective(lsp,args,...) gam2derivative(lsp,args,...)
lsp |
The log smoothing parameters. |
args |
List of arguments required to call |
... |
Other arguments for passing to |
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).
Simon N. Wood simon.wood@r-project.org
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
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