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,
>
>
>
> 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 <bol...@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:
>>
>> Sent from the R help mailing list archive at Nabble.com.
>>
>> ______________________________________________
>> R-help@r-project.org mailing list
>>
>> PLEASE do read the posting guide
>>
>> and provide commented, minimal, self-contained, reproducible code.
>>
>
>
>
--
Frank E Harrell Jr Professor and Chair School of Medicine
Department of Biostatistics Vanderbilt University
______________________________________________
R-help@r-project.org mailing list
PLEASE do read the posting guide
and provide commented, minimal, self-contained, reproducible code.
