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.





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).


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


See Also

gam.fit3, gam, magic

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