[R-sig-ME] glmm AIC/LogLik reliability

Ben Bolker bolker at ufl.edu
Wed Jan 28 20:11:36 CET 2009

  I would argue that there's very little we *can* trust
in the realm of GLMM inference, with the exception
of randomization/parametric bootstrapping (and possibly
Bayesian) approaches.

   I think AIC is no worse than anything else in this regard,
except that it hasn't been explored as carefully
as some of the alternatives: thus we suspect by analogy
that there are problems similar to those of the LRT,
but we don't know for sure.
Vaida and Blanchard (2005), Greven (2008), and Burnham
and White (2002) are good references.  There are
two basic issues:
  (1) if you choose to include models that differ
in their random effects components, how do you count
"effective" degrees of freedom?
  (2) how big a sample does it take to reach the
"asymptopia" of AIC?  If you're not there, what is
the best strategy for finite-size correction?  If
you use AICc, what should you put in for effective
residual degrees of freedom?

   Ben Bolker

D O S Gillespie wrote:
> Dear R-Sig-ME -
> Lets assume that I am going to use a model averaging AIC based  
> approach to evaluate nested glmm's.
> I would like to assume that the estimation of AIC and LogLik in the  
> glmm's of lmer are consistent enough (precise, if not accurate) to use  
> in this framework. I realize that we don't trust anova(m1, m2), mainly  
> due to df and tests statistics issues.
> I realise that some of you may suggest that this is not the correct  
> framework.  If so, can you distinguish arguments about the philosophy  
> of AIC model averaging from the practical implementation - i.e. is the  
> output consistent enough to use if, even if you don't believe the  
> answer.  Perhaps they are too intertwined.
> Thanks,
> Duncan Gillespie
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Ben Bolker
Associate professor, Biology Dep't, Univ. of Florida
bolker at ufl.edu / www.zoology.ufl.edu/bolker
GPG key: www.zoology.ufl.edu/bolker/benbolker-publickey.asc

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