R help - Jun 2007 - mgcv: lowest estimated degrees of freedom

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")
b) Bivariate tensor products of TPRS with shrinkage?

Thanks for any help,

Julian Burgos

-- 
Julian M. Burgos

Fisheries Acoustics Research Lab
School of Aquatic and Fishery Science
University of Washington

1122 NE Boat Street
Seattle, WA  98105 

Phone: 206-221-6864

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