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Re: st: AKAIKE formula


From   Maarten buis <maartenbuis@yahoo.co.uk>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: AKAIKE formula
Date   Tue, 13 Apr 2010 01:06:28 -0700 (PDT)

--- On Tue, 13/4/10, Paulo Regis wrote:
> I have a question about Akaike Info Criterion. Stata
> calculates aic (using "estac ic" after the regression
> command) with the formula:
> 
> AIC = -2 * log (likelihood) + 2 * (k+1)  ;  k=
> number of parameters
> 
> 
> In the linear regression model, this is similar to use the
> formula:
> 
> AIC = n*ln(RSS/n) +2*(k+1),   RSS = residuals SS
> 
> This was addressed before in this list by the following
> post:
> 
> http://www.stata.com/statalist/archive/2003-09/msg00365.html
> 
> However, my problem is that I want to compare OLS with IV
> models using AKAIKE. The command "estac ic" is not available
> for -ivreg. Can I compute the AIC by myself using the second
> formula? 

The logic behind this is that in a linear regression the 
log likelihood is a function of the RSS. So, you would need
to argue that in -ivreg- the likelihood would need to derive
the likelihood of your model and show that it is a similar 
function of the RSS. I haven't done so, but I am doubtful 
that that is the case.

Moreover, differences in fit statistic are not a good way of
choosing between an IV model and an non-IV model like -regress-.
The whole point of IV models, as I understand them, is that
you believe some of the association between a variable of 
interest x and the dependent variable y is spurious, and you
use instrumental variables to throw away the spurious 
association and (hopefully) keep the "real" association. A
fit statistic cannot distinguish between "real" and "spurious"
association, so a non-IV model should "fit" better because it
doesn't throw the spurious part of the association away. So,
differences in fit statistic cannot help you in choosing 
between these models, at best they tell you how much 
information is being thrown away by the IV method, but since
throwing away information is the whole point of IV methods
(because you have a theory that this information is "bad"),
that does not help much.

-- Maarten

--------------------------
Maarten L. Buis
Institut fuer Soziologie
Universitaet Tuebingen
Wilhelmstrasse 36
72074 Tuebingen
Germany

http://www.maartenbuis.nl
--------------------------


      

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