[R-sig-ME] AIC ranking and ML vs REML using glmer

[Ben Bolker]

Joanna Jack <joanna.jack at ...> writes:

> 
> >
> > Hello, I am quite new to mixed models and hoping to get some advice on the
> > following:
> >
> >
> > I want to rank mixed effects models with and without different predictors
> > using AIC.  The fixed effects are the predictors that will change, with one
> > random effect staying constant in all models. The models are not nested.  I
> > understand that  it's not possible to compare models with different fixed
> > effects using REML.  Consequently,  I should be selecting ML in order to
> > rank the models using AICs.  However, my response variable is poisson
> > distributed, so it has been suggested that I use a generalized linear model
> > where I can select family=poisson.  I found that glmer  in the lme4 package
> > allows me to have a Generalized Linear Mixed Effects Model.
> >
> > However, glmer does not provide the option to choose between REML and ML.
> >  I've been trying to figure out what it is using in this case.  When I run
> > the following model, it states that it has fit the model using the Laplace
> > approximation. In Bolker et al. (2008), it is mentioned that for this
> > approach, one must distinguish between ML and REML.  In this case, is the
> > package using ML?  More importantly, is it acceptable for me to be using
> > AIC to rank my various models when they have been fit with this
> > approximation?

  I have it on good authority that a few of the statements in Bolker (2008)
are out of date or slightly incorrect :-) . 

  glmer always uses ML: see http://glmm.wikidot.com/faq#reml-glmm

> >
> > model1<-glmer(ABUND~Type*DistfromRoad+(1|SiteID), family = poisson,
> > data=AB)
> >
> > I would also like to generate a null model with only my random effect, and
> > no fixed effects, in order to compare it with my other models.  The package
> > appears to run with the following code, but there appears to be conflicting
> > advice about whether or not this is a reasonable thing to ask of a mixed
> > model package.  Is there any reason to question the output that I get from
> > this:
> > nullmodel<-glmer(ABUND~(1|SiteID), family = poisson, data=AB)
> >

   I don't see why this is unreasonable.  Can you point to some of 
the conflicting advice?  (In part it's reasonable because it includes
an implicit intercept term, i.e. it's equivalent to ABUND~1+(1|SiteID) .
Some of the debate over appropriate models has to do with models
with the population-level effect set to zero, i.e. the appropriateness
of ABUND~0+(1|SiteID) ...)