Dear r-sig-ecology group,

I have a general question about determining the significance of GAMM smooth
terms. I have fit a GAMM model with several smooth terms, some of which
contain an additional variance structures in the random part.

My summary of the model looks something like this:

Formula:
CHLASURF ~ s(KPPmld, bs = "cr", k = -1, fx = FALSE) + s(PARmld,
    bs = "cr", k = -1, fx = FALSE) + s(SST, bs = "cr", k = -1,
    fx = FALSE) + s(SSS, bs = "cr", k = -1, fx = FALSE) + s(DSISURF,
    bs = "cr", k = -1, fx = FALSE) + s(FESURF, bs = "cr", k = -1,
    fx = FALSE)

Parametric coefficients:
             Estimate Std. Error t value Pr(>|t|)
(Intercept) -0.001213   0.005727  -0.212    0.832

Approximate significance of smooth terms:
             edf Ref.df      F p-value
s(KPPmld)  8.272  8.272 294.19  <2e-16 ***
s(PARmld)  7.550  7.550 317.84  <2e-16 ***
s(SST)     8.584  8.584 128.16  <2e-16 ***
s(SSS)     7.909  7.909  51.73  <2e-16 ***
s(DSISURF) 7.356  7.356  13.94  <2e-16 ***
s(FESURF)  8.672  8.672  52.47  <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

R-sq.(adj) =  0.871  Scale est. = 0.084409  n = 5478



In this example KPPmld, PARmld, and DSISURF all have associated variance
structures.

Basically all terms are highly significant (due to the high n=5478), but I
would like to be able to rank the variables in terms of their importance.
Given that the above summary gives only "approximate significance", I
gathered that the best test would be to drop terms and refit the model, and
then to compare the "small" model with the full model using a Likelihood
ratio. Unfortunately, there are some cases where the fitting of the smaller
model doesn't converge (due to difficulties in fitting only 2 variance
structures instead of 3 - an annoyance that I alluded to in a previous
question but have been unable to remedy).

My question is, since a Likelihood ratio can not be calculated in all
cases, would it make sense to present the F-values above as a measure of
each terms importance in the model? Do I have any other options for such a
comparison? I have several geographic areas where I have fit similar models
and would like to be able to say something about overall trends in the
importance of the variables - something like in this graph (
http://dl.dropbox.com/u/52403158/F_value_plot.png). My number of samples is
always the same (n=5478), but the number of terms in each areas model can
be different, and of course the degrees of freedom in the smooth terms are
different for each area.

Many thanks for your help and advice.
Cheers,
Marc

	[[alternative HTML version deleted]]

