[R-sig-ME] AIC in nlmer

[Ben Bolker]

On 11-04-12 05:41 PM, Helen Sofaer wrote:
> 
> Hi Ben,
> Thanks for taking a look at what I found. I’ll certainly use nlme for
> now, and I’ll look forward to seeing the issues in lme4 get resolved. I
> hadn’t realized that only the Laplace transformation was supposed to be
> functional in nlmer.
> 
> I was also wondering if there is any documentation about what constants
> are dropped in calculating the likelihoods in the different packages
> and/or using different approximation methods. 

  Nothing systematic that I know of. One often ends up having to do
things by trial and error, fitting identical models (where possible) in
different packages or digging through the code.

> As you mentioned, it’s
> often hard to tell if the likelihoods from different packages are
> comparable, and among other things, I’d like to compare the mixed models
> I’m building to a model with only fixed effects. The paper you
> suggested, which notes that the marginal AIC favors models without
> random effects, made me more curious to do this. My experience is that
> there’s no way to run a model without random effects in lme4, but I
> wasn’t sure about nlme. 

  In general gnls() (also in the nlme package) ought to let you fit
models equivalent to those fitted by nlme, but without random effects,
and since the functions are in the same package and (I believe) share
code, they should (??) have compatible likelihood/AIC calculations.

> More broadly, can a marginal AIC given by
> nlme/lme4, based on the likelihood after integrating over the random
> effect parameters, be compared to an AIC value based on a likelihood for
> a fixed-effect model (e.g. from nls), as long as the dropped constants
> don’t differ?

  It should be.  In the limit where the random effect has zero variance,
the marginal likelihood should be equivalent to evaluating the
likelihood at the same set of fixed parameters.

> 
> Thanks again,
> Helen
> 
> Helen Sofaer
> PhD Candidate in Ecology
> Colorado State University
> 
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