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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   Thu, 25 Jul 2002 13:45:03 -0700

On Thu, 25 Jul 2002 09:21:44 -0500
rgutierrez@stata.com (Roberto G. Gutierrez, StataCorp.) wrote:

> In short, you count them twice.  Think in terms of how many parameters you are
> estimating, rather than how many distinct covariates you are using.
> 
> In a standard log-logistic model, you have one shape parameter, gamma, and so
> you set c=1 when calculating AIC.  If you choose to model gamma (or ln(gamma)
> as is the case) on a set of covariates, c changes from 1 (for the constant
> term that is always there) to 1 + how many covariates you are modelling
> ln(gamma) on.  So, it is really c that increases while k stays the same.
> 
> Note however that k is just the number of covariates in the main equation, and
> not 1 + this number.  This is merely by convention, and we chose not to count
> the constant term in the main equation.
> 
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!

Shige
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