[R-sig-ME] [R-sig-eco] questio

[Ben Bolker]

  [taking the liberty of forwarding my answer to r-sig-mixed-models]

Mariela Sued wrote:
>  I am a mathematician  trying to interact
> with biologists.
> 
> I am working with a generalized mixed model, for  counting response
ors > corresponding to a number of visits that
> certain birds make to their nests, in a period of time (giving rise to an
> offset).
> One  random effect, since I have several observations coming from the same
> nests.
> 
> I am trying to present a multimodel approach (Burnham and Anderson). After
> reading the following phrase, I decide to ask for some help.
> 
> "First, AIC can be generalized to random-effects models, ultimately probably
> in way better than given here."
> 
> What would you suggest to use as AIC in this case?
> AIC? QAIC? QAIC_c?

  Well, QAIC is really for handling overdispersion in the residuals;
'corrected' (_c) versions of AIC are for handling finite-sample-size
corrections (AIC makes various asymptotic assumptions).  So the answers
depend on whether your data are (a) overdispersed, once you have
incorporated known grouping factors & covariates; (b) 'small' (while B&A
recommend always using corrected variants of AIC, they do also give a
rule of thumb of it being especially useful when (# obs)/(# parameters)
< 40.

  The biggest difficulty with using AIC for random-effects models is
parameter counting -- how many effective parameters/degrees of freedom
does a random effect represent?  Vaida and Blanchard (2005) offer a
useful perspective.  The bottom line: (A) *if* you are (1) not trying to
model-average over models with and without a particular random effect
and (2) not using a 'corrected' variant of AIC (where "# of residual
degrees of freedom" is incorporated in the penalty term), then the issue
doesn't come up.  (B) if you are interested in expected predictive
ability *at the level of the population* then random effects can be
counted as the number of variance parameters.  (C) if you are interested
in predictive ability at the level of random-effects units, see Vaida
and Blanchard 2005.  See also Bolker et al (2009) Trends in Ecology and
Evolution ...

> 
> On the other hand, using lmer or glmmMl I obtain different results  for the
> AIC.

  That is most likely because different additive constants are included
in each case.  If the log-likelihoods are different, that's more
interesting (but hard to diagnose without more details).

> Any suggestion?
> thanks for your attention
> Mariela
> 
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> 
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-- 
Ben Bolker
Associate professor, Biology Dep't, Univ. of Florida
bolker at ufl.edu / people.biology.ufl.edu/bolker
GPG key: people.biology.ufl.edu/bolker/benbolker-publickey.asc