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st: Re: Akaike information criterion


From   "Scott Merryman" <smerryman@kc.rr.com>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: Re: Akaike information criterion
Date   Wed, 17 Sep 2003 22:05:11 -0500

----- Original Message ----- 
From: "Jennifer Ng" <ycng@telus.net>
To: <statalist@hsphsun2.harvard.edu>
Sent: Tuesday, September 16, 2003 9:17 PM
Subject: st: Akaike information criterion


> Hi all,
>
> I would like to get the Akaike information criterion (AIC) to figure out how
> many lags in my model.  I checked the reference guide and figured out that
> estimate can help.
> So, my program is as followed:
>
> Regress Y X Z
> est store AIC
> estimates stats *
>
> Then I saw that in the reference page 353, it shows the equation of AIC = -2
> log (likelihood) + 2df.
>
> I remembered that AIC = log (sum(e-sq)/n) + 2k/n  and I checked a few
> textbooks and the AIC is the latter one.  Are they equivalent?  Did I use
> the wrong command/equation?
>

Yes they are equivalent.  On page [R] 353 the "df" term refers to the number of
parameters estimated, including the constant.

The most commonly used definition and the one given by Akaike is AIC = -2
ln(likelihood) + 2#parameters.

For the case of linear regression models it can be written as AIC =
n*ln(sigma^2) +2*parameters, where sigma^2 = RSS/n.

In addition to -est stats *- , you might find J. Scott Long and Jeremy
Freese's -fitstat- helpful.

Hope this helps,
Scott




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