[R-sig-eco] nlme model specification

[Kingsford Jones]

On Fri, May 23, 2008 at 12:05 PM, David Hewitt <dhewitt37 at gmail.com> wrote:
>
>
>
>>> 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.
>

I don't think it is useful to put this in a Bayesian vs. frequentist
framework. Burnham and Anderson write:

"AIC can be justified as Bayesian using a
'savvy' prior on models that is a function of sample size and the number of
model parameters Furthermore, BIC can be derived as a non-Bayesian result.
Therefore, arguments about using AIC versus BIC for model selection cannot be
from a Bayes versus frequentist perspective."

see: http://www2.fmg.uva.nl/modelselection/presentations/AWMS2004-Burnham-paper.pdf


> 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.

Can you expound on the last paragraph?

thank you,

Kingsford Jones

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