Hi Bonnie,
Yes you should choose the one with the
smallest AIC or AICc. It is a great idea when you have
the chance to try other criteria and see what you get.
In Regression and Time Series Model Selection by
McQuarrie and Tsai (1999) - World Scientific the
authors compare many criteria many simulations and
examples comparing many different model selection
criteria (including the AICc, AICu, and AIC(alpha)).
Hjort and Claeskens (2003) present a model selection
criterion, called the Focused Information Criterion
(FIC). They take the view that the model selector
should focus on the parameter of interest. Their
method, unlike other model selection criterion, is
concerned with the actual use of the selected model.
Hjort, N. L., and Claeskens, G. (2003), Frequentist
Model Average Estimators, Journal of the American
Statistical Association, 98(464): 879-899.
The discussion and rejoinder section can be found in
the Journal of the American Statistical Association,
98(464): pages 917-945.
Best wishes, Paul
Paul Johnson
http://www.biostatsoftware.com
--- bonnie clark <[EMAIL PROTECTED]> wrote:
> Thank you very much for your many responses so far!
>
> >The reason for the confusion is that Bonnie
> presented the log likelihood
> >values with the wrong sign
>
> I presented the values that SAS gives for log
> likelihood of my GENMOD models
> with a negative binomial distribution. (I only
> presented the largest and
> smallest AIC of a list of many possible models).
>
> log likelihood k AIC
> 532.5052 16 -1033.0104
> 509.8392 58 -903.6784
>
> An (edited) response to explain why the positive
> values:
> [SAS reports only the 'pertinent part' of the
> likelihood; it leaves out
> constants that, if included, would result in the
> real likelihood and a
> negative log likelihood. Therefore, you can test
> which independent
> variables are significant, but you can't compare
> models fit with the
> negative binomial to models fit with the normal nor
> to models fit with the
> Poisson using the SAS output.]
>
> Is it OK to use this modified log likelihood in
> AIC?
>
> It sounds like, from most of the responses I
> received personally and on the
> list, that (if I decide to use AIC or AICc, which
> yielded the same order of
> models) I should choose the one with the smallest
> AIC, not the smallest
> absolute value of AIC.
>
> I am enjoying learning the different thoughts on
> if/how appropriate AIC is
> for ecological application.
> thank you!
> Bonnie
>
>
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