One method a colleague and I used recently to deal with the random  
effects/number of parameters issue is the Conditional AIC as proposed  
by Vaida and Blanchard in conjunction with lme4.

Vaida, F., and S. Blanchard. 2005. Conditional Akaike information for  
mixed-effects models. Biometrika 92:351-370.

The basic idea is to use the effective degrees of freedom as well as  
the likelihood conditioned on the random effects.  However, they point  
out that this is only needed if you are testing models with versus  
without the random effects, rather than if the random effects you are  
using are the same across all models.

-Jarrett


----------------------------------------
Jarrett Byrnes
Population Biology Graduate Group, UC Davis
Bodega Marine Lab
707-875-1969
http://www-eve.ucdavis.edu/stachowicz/byrnes.shtml

>>>



>>>
>>
>> Others on the list are far better positioned than I to expound, but  
>> as a
>> lurker in stats journals I see a lot more work on model selection  
>> methods
>> for models with random effects in a Bayesian context. For instance,  
>> type
>> "random effects model selection" into Google and almost all the  
>> first 20
>> results are Bayesian. David Anderson told me personally that he  
>> thinks I-T
>> methods (AICc) are really struggling with random effects. I don't  
>> honestly
>> know how the various packages in R calculate the AIC values for  
>> models with
>> random effects (of course, you can look and see), but I'd guess it's
>> something you have to be rather careful about. I still need to read  
>> Pinheiro
>> and Bates, obviously.
>>
>
> I think you're right that there is some shaky ground here, and Doug
> Bates has pointed out some issues on the R-sig-mixed-models list (I
> can't seem to find the thread right now).  One of the issues is that
> mixed models are generally fit with REML, which is not ML and
> therefore does not technically conform to the derivations of the *IC.
> If you fit a mixed model with ML instead, bias is introduced. Another
> issue that is a bit murky is the question of how many parameters are
> being estimated in a model with random effects. In this thread we have
> discussed models with  huge numbers of random effects (i.e. >300
> intercept adjustments, >300 slope adjustments for diameter, >300 slope
> adjustments for vineload, etc), yet we only increase k in the AIC/BIC
> equations by 1 per variance component because technically the random
> effects are predicted while the variance components are estimated.
>
> best,
> Kingsford Jones
>
>


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