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Re: st: calculating AIC for log-logistic model

From   [email protected] (Roberto G. Gutierrez, StataCorp.)
To   [email protected]
Subject   Re: st: calculating AIC for log-logistic model
Date   Thu, 25 Jul 2002 09:21:44 -0500

Shige Song <[email protected]> asks:

> In page 231 of the book by Cleves et al. (2002) the formula for calculating
> AIC for parametric hazard model is given by:

> AIC = -2lnL + 2(k+c)

> where k is the number of model covariates and c is the number of
> model-specific distributional parameters. My questions is: how to count the
> number of k if I want to include the same set of covariates in more than one
> distributional parameters? For example, I am estimating a log-logistic
> hazard model; instead of intrducing covariates to the scale parameter only,
> I want to introduce the same set of covariates to both the scale parameter
> and the shape parameter. In this case, should I count the number of
> covariates (k) twice, when caluclating the AIC?  Thanks a lot!

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.

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