[R] mgcv: lowest estimated degrees of freedom

[Simon Wood]

On Thursday 21 June 2007 19:51, Julian Burgos wrote:
> Dear list,
>
> I do apologize if these are basic questions.  I am fitting some GAM
> models using the mgcv package and following the model selection criteria
> proposed by Wood and Augustin (2002, Ecol. Model. 157, p. 157-177).  One
> criterion to decide if a term should be dropped from a model is if the
> estimated degrees of freedom (EDF) for the term are close to their lower
> limit.
>
> What would be the minimum number of EDF's for
> a) Univariate thin plate regression splines(TPRS) with shrinkage, i.e.
> s(...,bs="ts")
zero (that's sort of the point of the shrinkage smooths: the smoothing penalty 
can actually zero a term completely with high enough smoothing parameter).

> b) Bivariate tensor products of TPRS with shrinkage?
Also zero. The penalties for the marginal smooths can shrink terms to zero, 
and this gets inherited by the tensor product penalties. So, with high enough 
smoothing parameters, the term will be shrunk to zero (and hence have zero 
EDF).

Simon

> Simon Wood, Mathematical Sciences, University of Bath, Bath, BA2 7AY UK
> +44 1225 386603  www.maths.bath.ac.uk/~sw283