[R-sig-ME] Likelihood estimation by glm and glmer/lmer

[Ben Bolker]

anova(), AIC(), etc. work fine across glm / glmer models and have since
1.0-0 (Aug 2013).  More info on counting parameters (which are *numerator*
or *model* degrees of freedom, not *residual* df) is available at ...

http://bbolker.github.io/mixedmodels-misc/glmmFAQ.html#can-i-use-aic-for-mixed-models-how-do-i-count-the-number-of-degrees-of-freedom-for-a-random-effect


On Tue, Sep 5, 2017 at 4:55 AM, Phillip Alday <phillip.alday at mpi.nl> wrote:

> 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 Bürkner 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
>
>
> On 09/05/2017 10:24 AM, Toni Hernandez-Matias wrote:
> > 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
> >
>
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