[R] is AIC always 100% in evaluating a model?

[Frank E Harrell Jr]

Tal Galili wrote:
> Hi Ben,
> I just wished to give a small remark about your claim:
> "it's best not to consider hypothesis testing (statistical significance) and
> AIC in the same analysis."
> 
> Since in the case of forward selection for orthogonal matrix's, it can be
> shown that AIC is like using a P to enter rule of 0.16.  For further
> reference see:page 3 of: "A SIMPLE FORWARD SELECTION PROCEDURE BASED
> ONFALSE DISCOVERY RATE CONTROL" BY YOAV BENJAMINI AND YULIA GAVRILOV,
> http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.aoas/1239888367
> 
> 
> Cheers,
> Tal Galili

Tal,

That is not limited to orthogonal designs.  When used for one variable 
at a time variable selection. AIC is just a restatement of the P-value, 
and as such, doesn't solve the severe problems with stepwise variable 
selection other than forcing us to use slightly more sensible alpha 
values.  As an aside, some statisticians try to deal with multiplicity 
problems caused by stepwise variable selection by making alpha smaller 
than 0.05.  This increases bias by giving variables whose effects are 
estimated with error a greater relative chance of being selected.  alpha 
typically needs to be 0.5 or greater to avoid problems with stepwise 
variable selection.

AIC was designed to compare two pre-specified models.

Variable selection does not compete well with shrinkage methods that 
simultaneously model all potential predictors.

Frank

> 
> 
> 
> 
> 
> On Sat, Jul 4, 2009 at 1:46 AM, Ben Bolker <bolker at ufl.edu> wrote:
> 
>>
>>
>> alexander russell-2 wrote:
>>> Hello,
>>> I'd like to say that it's clear when an independent variable can be ruled
>>> out generally speaking; on the other hand in R's AIC with bbmle, if one
>>> finds a better AIC value for a model without the given independent
>>> variable,
>>> versus the same model with, can we say that the independent variable is
>>> not
>>> likely to be significant(in the ordinary sense!)?
>>>
>>> That is, having made a lot of models from a data set, then the best two
>>> are
>>> say 78.2 and 79.3 without and with (a second independent variable
>>> respectively) should we say it's better to judge the influence of the 2nd
>>> IV
>>> as insignificant?
>>> regards,
>>> -shfets
>>> _____________________________________
>>>
>>>
>> Without meaning to sound snarky, it's best not to consider hypothesis
>> testing (statistical significance) and AIC in the same analysis.
>> If you want to decide whether predictor variables have a significant
>> effect on a response, you should consider their effect in the full model,
>> via Wald test, likelihood ratio test, etc..  If you want to find the model
>> with the best expected predictive capability (i.e. lowest expected
>> Kullback-Leibler distance), you should use AIC.
>>
>>  Burnham and Anderson, among others, say this repeatedly.
>>
>>  In general, for a one-parameter difference, hypothesis testing
>> is "more conservative" than AIC (e.g., critical log-likelihood difference
>> for a p-value of 0.05 under the LRT test is 1.92, while the log-likelihood
>> difference required to say that a model is expected to have better
>> predictive capability/lower AIC is 1) -- but since they are designed to
>> answer
>> such different questions, it's not even a fair comparison.
>>
>>  Ben Bolker
>>
>> --
>> View this message in context:
>> http://www.nabble.com/is-AIC-always-100--in-evaluating-a-model--tp24323538p24329622.html
>> Sent from the R help mailing list archive at Nabble.com.
>>
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>>
> 
> 
> 


-- 
Frank E Harrell Jr   Professor and Chair           School of Medicine
                      Department of Biostatistics   Vanderbilt University