[R-sig-eco] nlme model specification

[David Hewitt]

>> On Thu, May 22, 2008 at 5:55 PM, Caroline Lehmann:
>> Models were compared and ranked using AICc. I would suggest modifying
>> this to BIC since there
>> are so many measurements.
> 
> Is there theory to support this suggestion?  I find choosing an *IC to
> be a confusing issue and would appreciate any pointers to theory,
> simulations, etc that may shed some light on the subject.
> 

Choosing a model selection method is indeed a confusing process. However, it
does not simply depend on the number of measurements. Oversimplifying
things, AIC/AICc are used for model selection following maximum likelihood
model fitting and BIC (and Bayes factors) are used in a Bayesian context
(likelihood + priors). The two approaches are different in a number of ways.

So NO, there is no theory specifically pointing to BIC and a Bayesian
strategy because there are "lots of measurements". However, there is more
theory than you (and I) care to know about regarding when to use a Bayesian
framework versus a "pure" likelihood framework. And, as in all academic
disputes, there is no clear consensus.

There's AIC/AICc, BIC, DIC, TIC, etc. and then simulation-based criteria as
well (about which I know zip). You can read Burnham and Anderson (2002) to
get their opinions about AIC and the information-theoretic strategy, and
among many other references I think EJ Wagenmakers sums up the Bayesian
perspective well in the 2007 paper listed here ("pratical solution to the
p-value problem"):

http://users.fmg.uva.nl/ewagenmakers/papers.html

It's a good read, even if you disagree with his conclusions about the
Bayesian strategy.

All that said, since you're dealing with random effects, Bayesian approaches
do appear to have the upper hand at present, and a shift in that direction
may be warranted.


-----
David Hewitt
Research Fishery Biologist
USGS Klamath Falls Field Station (USA)
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