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Re: st: calculating AIC for log-logistic model


From   Shige Song <sgsong@ucla.edu>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: calculating AIC for log-logistic model
Date   Fri, 26 Jul 2002 20:30:26 -0700

Hi Bobby,

Thanks, that's very helpful for me, I appreciate that. 

Shige Song
Department of Sociology, UCLA

On Fri, 26 Jul 2002 09:21:34 -0500
rgutierrez@stata.com (Roberto G. Gutierrez, StataCorp.) wrote:

> In our continuing discussion on this matter, Shige Song <sgsong@ucla.edu>
> adds:
> 
> > Using the example from the book on page 224. Now the AIC should be
> > calculated as:
> 
> > AIC = -2lnL + 2(k+c) = -2*(-42.241) + 2*(2+2) = 92.482
> 
> > as reported in Table 13.2 on page231. Now I want to introduced the same set
> > of covariates ("protect" and "age") to the shape paremater (gamma), should
> > the AIC be like this:
> 
> > AIC = -2lnL + 2(k+c) = -2lnL + 2*(4+2)
> 
> > is that correct? Shoud I also include the constant term in the gamma
> > parameter equation (in you answer you said the constantt term in the main
> > equation should be excluded but you did not say what to do abont the
> > constant term in the gamma parameter equation). Thanks!
> 
> Your calculations are correct. k+c is incremenented by 2 to reflect the two
> new estimated parameters.  Whether you want to think of it as k increasing by
> 2 or c increasing by 2 is really a matter of personal taste.  I like to think
> of it as c since it represents things "ancillary" to the main equation, but it
> really does not matter.
> 
> Just follow this rule:  Set (k+c) to equal the _total_ number of all 
> estimated parameters for all equations, including _all_ constant terms.  
> 
> As to your other question, the constant term in the main equation is not
> counted in k because it is already counted in c:  c = 2 for the standard
> log-logistic model; 1 for shape parameter gamma + 1 for the scale parameter
> (the constant term in the main equation), but again we counted the constant
> term in c only as a convention.  It really doesn't matter as long as it 
> is counted somewhere.
> 
> --Bobby
> rgutierrez@stata.com
> *


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