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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