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Re: st: calculating AIC for log-logistic model
In our continuing discussion on this matter, Shige Song <firstname.lastname@example.org>
> 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.
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