Likelihood estimation by glm and glmer/lmer

For "true likelihood" ... you should search the list archives for
discussions on REML vs ML estimation and D. Bates' comments on *the*
likelihood. But, yes, if you you use REML=FALSE in lmer, you are
estimating the likelihood.

However, there's another problem with using AIC/BIC to compare mixed vs.
non-mixed models, namely how to count parameters in mixed models.
There's also been some discussion here of late with issues in counting
parameters in mixed models. For Bayesian models using DIC and WAIC, this
seems to be somewhat less of a problem because the effective number of
parameters is estimated as part of the procedure (maybe Jarrod Hadfield
or Paul B?rkner can comment/correct here), but there doesn't seem to be
a clear answer for what the actual number of parameters in a model is.
This is related to the degrees of freedom issue (
https://cran.r-project.org/doc/FAQ/R-FAQ.html#Why-are-p_002dvalues-not-displayed-when-using-lmer_0028_0029_003f
).

All that said, there's an older post on this list that suggests that you
can use the deviance (which is -2 log likelihood) to compare lm and lmer
models:

https://stat.ethz.ch/pipermail/r-sig-mixed-models/2014q4/022723.html

I think newer versions of lme4 even support this explicitly without any
hacks.

tl;dr: compare the likelihoods with REML=FALSE, but be careful with
counting parameters and hence AIC, etc.

Best,
Phillip

Dear all,

I would like to compare AIC values of a null model estimated with glm
function and AIC values of models that only have random effects fitted with
glmer or lmer functions. I understand that they are comparable because both
estimate true likelihood. Could you confirm me this?

Thank you very much in advance,

Antonio