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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