Although if log-likelihood is arbitrary up to an additive constant we
may add a sufficiently large constant onto any two AICs and push the
first non-equal digit of the two AICs as far down as we want!

Murray Jorgensen


Well, my two cents is (are?) that the AICs should definitely be
presented via round(AIC,0) or round(AIC,1) and not with signif()
as they are.  Deviance/AIC differences are really only important
on an absolute scale (agreeing with Murray Jorgensen).  Thus
I would consider the use of signif() rather than round() in
print.glm() a "misfeature" ...  (Does anyone know of a context
where *relative* differences in AIC or deviance are important?)

   Ben Bolker

I confess to agreeing with Drs. Jorgensen and Bolker. It can't be as 
simple as saying that

>  Third, in my limited statistical experience (I am a master's 
>  student) AIC is not a method where those extra digits ever really 
>  matter.  I did a project on AIC/BIC model selection.  IMO in order 
>  to use AIC properly you have to consider the models in a nearby 
>  neighborhood to the best AIC as just as good as the model with the 
>  best AIC and consider sensitivity in your estimates.    There is no 
>  real context where you can properly say "the fifth significant digit 
>  of AIC has decided that model A is better than model B, and so I 
>  discard model B.

In fact, the way I read Burnham and Anderson (2002, page 71) (as I 
quoted in my previous message) is that their claim contradicts this 
last claim. Within reason, one should interpret a difference of 2 
units the same way regardless of whether the two models have small or 
large AIC values. I am open to an understanding different from 
theirs, but I have yet to see a convincing argument.

   To this extent, as Dr. Bolker wrote, the current default output of 
glm can be misleading, depending on the absolute value of AIC. n.b., 
I love the glm function!

    Just think how many times the glm function has been used to 
analyze data sets that generate AIC values big enough to be truncated 
more than 2 AIC units. It is possible that there are published 
analyses containing incorrect claims as to equal model support (based 
on truncated AIC values generated by the default digits setting of 7).


S.
-- 
Steven Orzack

The Fresh Pond Research Institute
173 Harvey Street
Cambridge, MA. 02140
617 864-4307

www.freshpond.org
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