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,...)The log smoothing parameters.
List of arguments required to call gam.fit3.
Other arguments for passing to gam.fit3.
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).
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