[R] GAMM and anove.lme question

From: David M Warner <dmwarner_at_usgs.gov>
Date: Wed, 19 Nov 2008 09:33:25 -0500

Greetings all
The help file for GAMM in mgcv indicates that the log likelihood for a GAMM reported using

summary(my.gamm$lme) (as an example) is not correct.

However, in a past R-help post (included below), there is some indication that the likelihood ratio test in anova.lme(mygamm$lme, mygamm1$lme) is valid.

How can I tell if anova.lme results are meaningful (are AIC, BIC, and logLik estimates accurate)?

The data include hydroacoustic estimates of fish biomass (lbloat) in 1,000 meter long intervals (elementary sampling units) from multiple transects (each 20-30 km long, tranf) in two different lakes and three different years.

bloat.gamm1 <- gamm(lbloat ~ s(depth), correlation=corSpher(c(30000, 0.01),form = ~ x+y|tranf, nugget=TRUE), data=fish3)

bloat.gamm2 <- gamm(lbloat ~ lakef + s(depth), correlation=corSpher(c(30000, 0.01),form = ~ x+y|tranf, nugget=TRUE), data=fish3)

bloat.gamm3 <- gamm(lbloat ~ lakef + s(depth, by=lakef), correlation=corSpher(c(30000, 0.01),form = ~ x+y|tranf, nugget=TRUE), data=fish3)

> anova.lme(bloat.gamm1$lme, bloat.gamm2$lme, bloat.gamm3$lme)

                Model df      AIC      BIC    logLik   Test   L.Ratio 
bloat.gamm1$lme     1  6 7916.315 7950.702 -3952.158  
bloat.gamm2$lme     2  7 7902.718 7942.835 -3944.359 1 vs 2 15.597489 
bloat.gamm3$lme     3  9 7910.987 7962.567 -3946.494 2 vs 3  4.269119 


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?

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,

David Warner
Research Fishery Biologist
USGS Great Lakes Science Center
1451 Green Road
Ann Arbor MI 48105

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