[R] Selecting derivative order penalty for thin plate spline regression (GAM - mgcv)

[Simon Wood]

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