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
p-value
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
0.0001
bloat.gamm3$lme 3 9 7910.987 7962.567 -3946.494 2 vs 3 4.269119
0.1183
Thanks
Dave
Hi R user,
I am using the gamm() function of the mgcv-package. Now I would like to
decide on the random effects to include in the model. Within a GAMM
framework, is it allowed to compare the following two models
inv_1<-gamm(y~te(sat,inv),data=daten_final, random=list(proband=~1))
inv_2<-gamm(y~te(sat,inv),data=daten_final, random=list(proband=~sat))
with a likelihood ratio test for a traditional GLMM, like this:
anova(inv_1$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,
Simon
David Warner
Research Fishery Biologist
USGS Great Lakes Science Center
1451 Green Road
Ann Arbor MI 48105
734.214.9392
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