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Re: st: calculating AIC for log-logistic model


From   rgutierrez@stata.com (Roberto G. Gutierrez, StataCorp.)
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: calculating AIC for log-logistic model
Date   Fri, 26 Jul 2002 09:21:34 -0500

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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