Christos, I would base choise of `m' on the AIC or GCV scores, (or on the REML or Marginal likelihood scores, if these have been used for smoothness selection). I don't think the m=2 basis will be strictly nested within the m=3 basis will it? So that rules out you option a. Option b is poor since the smoothing parameters really have a different meaning in the two cases.
Choosing `m' according to the same criterion you used for smoothness selection seems like the most self consistent approach. best, Simon On Wednesday 14 April 2010 19:19, Christos Argyropoulos wrote: > Hi, > > > > I am using GAMs (package mgcv) to smooth event rates in a penalized > regression setting and I was wondering if/how one can > > select the order of the derivative penalty. > > > > For my particular problem the order of the penalty (parameter "m" inside > the "s" terms of the formula argument) appears to > > have a larger effect on the AIC/deviance of the estimated model than the > number (or even the location!) of the knots for the covariate > > of interest. In particular, the estimated smooth changes shape from a > linear (default "m" (=2) value for a TP smooth or a P-spline > > smooth) with a edf of 2.06 to a non-linear one with a edf of 4.8-5.1 when > the "m" is raised to 3. There are no changes in the > > estimate shape of the smooth when I tried higher values of m and different > bases (thin plate, p-spline). > > > > The overall significance of the smooth term changes, but is <0.05 in both > cases, however the interpretation afforded by the > > shapes of the smooths are different. > > > > Smoothing the same dataset with a different approach to GAMs (BayesX) > results in shapes that are more like the ones I have been getting with m>=3 > rather than m=2 (I have not tried the conditional autoregressive > regressions of WinBUGS yet). > > Any suggestion on how to proceed to test the optimal order of the penalty > would be appreciated. The 2 approaches I am thinking of trying are: > > a) use un-penalized smoothing regressions and comparing the 2 models with > ANOVA > > b) First, fit the "m=2" model and extract the smoothing parameters of all > other smooth terms from that model. Second, fit a model in which the smooth > of the covariate of interest is set to "m=3" , fixing the parameters of all > other smooth terms appearing in the model statement to the values estimated > in the first step. Then I could compare the (m=2) v.s. (m=3) models with > ANOVA as the 2 models are properly nested within each other. > > > > Any other ideas? > > > > Sincerely, > > > > Christos Argyropoulos > > University of Pittsburgh > > > > > > _________________________________________________________________ > Hotmail: Trusted email with powerful SPAM protection. > > [[alternative HTML version deleted]] > > ______________________________________________ > R-help@r-project.org mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide > http://www.R-project.org/posting-guide.html and provide commented, minimal, > self-contained, reproducible code. -- > Simon Wood, Mathematical Sciences, University of Bath, Bath, BA2 7AY UK > +44 1225 386603 www.maths.bath.ac.uk/~sw283 ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.