# RE: st: A +ve log-likelihood!!

 From siyama@who.int To statalist@hsphsun2.harvard.edu Subject RE: st: A +ve log-likelihood!! Date Thu, 27 May 2004 17:15:57 +0200

```That is simply BRILLIANT!!   Calculating the AIC (& BIC) is exactly why I
spotted the +ve-log-likelihood.

Thanks ever so much.

Amani

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of
rgutierrez@stata.com
Sent: 27 May 2004 16:58
To: statalist@hsphsun2.harvard.edu
Subject: Re: st: A +ve log-likelihood!!

> I am running an "streg" model with a Lognormal distribution and the
> log-likelihood of the fitted model turns positive.  I am not sure what
> happened here.

Two reasons this could happen (neither is an error):

1.  In general -ml- with continuous responses, recall that the likelihood is
a probability DENSITY, not a probability.  As such, when the scale is small
enough, the probability density can be greater than one, hence the
likelihood is greater than one, hence the log-likelihood is positive.

2.  In -streg, lognormal()- a constant term (does not depend on the
estimated
parameters) is added to the log-likelihood so as to make it directly
comparable to other log-likelihoods such as the Weibull and Exponential,
which themselves make the above constant-term adjustment so as to be
invariant to scale.

That is, we adjust Weibull and Exponential so that if you multiply the
survival times by a constant, you get the same log-likelihood.  However, in
doing so, you have to make the same adjustment to log-normal and the other
-streg- models so that you can compare log-likelihoods across all, calculate
things like AIC and BIC, etc.

In any case, if Amani wants the actual based-on-probability-density
log-likelihood, he can do the following after running -streg, dist(lnormal)-

. gen temp = sum(_st*_d*ln(_t))

. scalar real_ll = e(ll) - temp[_N]

. di scalar(real_ll)

--Bobby
rgutierrez@stata.com
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