[R] ANOVA within a GAMM framework
s.wood at bath.ac.uk
Mon Oct 22 16:23:21 CEST 2007
This comparison is just as valid as it is for a regular linear mixed model,
which is all that the GAMM is in this case --- the smoothing parameters are
just variance components in your example.
In general you have to be a bit careful with generalized likelihood ratio
tests involving variance components, of course, since the null hypothesis
often involves restricting some variance parameters to the edge of their
possible range, which rather messes up the Taylor expansion about the null
parameter values that underpins the large sample distributional results used
in the glrt. Your example does involve such a problematic comparison, but the
result is so clear cut here that there is not really any doubt that inv_2 is
better in this case (I wonder if inv_1 even passes basic model checking?).
See Pinheiro and Bates (2000) for more info.
hope this is some use,
On Monday 22 October 2007 15:17, Maik Eisenbeiß wrote:
> Hi R user,
> I am using the gamm() function of the mgcv-package. Now I would like to
> decide on the random effects to include in the model. Within a GAMM
> framework, is it allowed to compare the following two models
> inv_1<-gamm(y~te(sat,inv),data=daten_final, random=list(proband=~1))
> inv_2<-gamm(y~te(sat,inv),data=daten_final, random=list(proband=~sat))
> with a likelihood ratio test for a traditional GLMM, like this:
> anova(inv_1$lme, inv_2$lme)
> The output is as follows:
> Model df AIC BIC logLik Test L.Ratio p-value
> inv_2$lme 1 10 21495.90 21557.59 -10737.95
> inv_1$lme 2 8 23211.12 23260.46 -11597.56 1 vs 2 1719.214 <.0001
> Or is this not in tune with the automatic smoothing parameter selection
> (i.e. it is not exactly the same for both model alternatives)?
> If not, how can I decide on the selection of random effects?
> Thanks in advance for your help.
> Best regards
> Dipl.-Kfm. Maik Eisenbeiß
> Marketing Centrum Münster
> Institut für Anlagen und Systemtechnologien
> Westfälische Wilhelms-Universität Münster
> Am Stadtgraben 1315
> 48143 Münster
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> E-Mail: maik.eisenbeiss at uni-muenster.de
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> Simon Wood, Mathematical Sciences, University of Bath, Bath, BA2 7AY UK
> +44 1225 386603 www.maths.bath.ac.uk/~sw283
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