Hello
I'm analyzing a dichotomous dependent variable (dv) with more than 100
measurements (within-subjects variable: hours24) per subject and more
than 100 subjects. The high number of measurements allows me to model
more complex temporal trends.
I would like to compare different models using GLM, GLMM, GAM and
GAMM, basically do demonstrate the added value of GAMs/GAMMs relative
to GLMs/GLMMs, by fitting splines. GLMMs/GAMMs are used to possibly
improve fits from GLMs/GAMs by accounting for serial dependence.
My idea is to use AIC to compare the different models. Ive noticed
that when setting up two seemingly identical models using the two
functions gam (of the package mgcv) and gamm4 (of the package with
same name), the AIC turns out to be different:
> gam.0<-gam(dv ~
s(hours24,fx=F,k=-1,bs=cc),method="ML",data=sdata, family=binomial)
> gamm.0<-gamm4(dv ~
s(hours24,fx=F,k=-1,bs=cc),method="ML",data=sdata, family=binomial)
Fit indices using the commands as shown are:
> logLik(gam.0)[1];deviance(gam.0);AIC(gam.0)
> logLik(gamm.0$mer);deviance(gamm.0$mer);attributes(summary(gamm.
0$mer))$AICtab[1]
gam.0: logLik=1149.6, deviance=2299.3, AIC=2316.0
gamm.0: logLik=1169.0, deviance=2338.0, AIC=2342.0
The differences between the two AIC values seem to be based on two
factors. First, gam uses the effective degrees of freedom
> sum(gam.0$edf)
[1] 8.372517
whereas gamm4 uses the value 2. Second the two log-likelihood values
already differ, probably because different estimation methods are used
but here is were my understanding ends. In any case from gamm4 I can
get the same value for the deviance as for gam by referring to the
deviance slot:
> gamm.0$...@deviance["disc"], which returns the value 2299.3, which
is the deviance without compensation for the null deviance.
My questions are:
- Is my suggested method of comparing fits among GLM, GLMM, GAM and
GAMM using AIC legitimate? Of course I will do additional model
plotting using residuals etc. as well but it seems important to me to
have a more direct method of comparing these models (Im aware of the
fact that AIC is a rough estimate when it comes to generalized mixed
models).
- If so, how can I compute the AICs using gam and gamm4 such that they
can be compared A) with each other and B) with AICs obtained from GLM/
GLMM?
Any suggestions are welcome
Andrea
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