significant terms in spline model using GAM

Hi.. I'm using gam() to fit a spline model for a data set that has two predictor
variables (say A and B). The results indicate that the higher order interaction
terms are significant. The R^2 jumps from .5 to .9 when I change the maximum
order for the interaction from 10 to 15 (i.e. (AB)^10 to (AB)^15). 

- This is perhaps not the best way of thinking about the interaction terms,
there are certainly no terms like (AB)^10 or (AB)^15 in the basis produced
by s(A,B,k=10 or 15).

Is there any
way of finding out which of the terms in the model are really "significant" so
that I could drop some of the terms from the model?

The default model selection used by gam() is GCV, a mean square error
criterion, and I'm not sure how useful it is to mix model selection by
hypothesis testing with GCV model selection. I think that your results
indicate that in GCV terms your original choice of k=10 was too
restrictive. 

If you want to do model selection by hypothesis testing you can -
s(A,B,k=10,fx=TRUE) is nested within s(A,B,k=15,fx=TRUE), for example -
however the process is not automated - you would have to construct
F-ratios (or deviance differences) yourself from the response data and the
fitted values. 

best,
Simon

_____________________________________________________________________

Simon Wood simon at stats.gla.ac.uk        www.stats.gla.ac.uk/~simon/

 Department of Statistics, University of Glasgow, Glasgow, G12 8QQ

  Direct telephone: (0)141 330 4530          Fax: (0)141 330 4814