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Re: st: what does mean by log likelihood value


From   Richard Williams <richardwilliams.ndu@gmail.com>
To   statalist@hsphsun2.harvard.edu, statalist@hsphsun2.harvard.edu
Subject   Re: st: what does mean by log likelihood value
Date   Fri, 12 Aug 2011 09:40:59 -0500

At 08:09 AM 8/12/2011, Maarten Buis wrote:
On Fri, Aug 12, 2011 at 2:45 PM, dk wrote:
> Thanks for the reply. Am I right that the log likelihood value depends
> on the data it ... it can be very high or low depending on the data.

It also depends on the model and on how the programmer chose to
implement the likelihood. Often there is a constant in the likelihood
function that one can either leave in or out without affecting the
maximum. This won't change the estimates, the variance-covariance
matrix, or comparisons of log-likelihoods between models, but it does
influence the log-likelihoods themselves.

> can we use the log likelihood value for making some comments about the
> model. eg low log likelihood value 10.00 or high 222.33. how this
> should be interpreted or used to make comment about the model.

Under certain circumstances you can compare log likelihoods between
models, but absolute statements on individual likelihoods are
impossible.

The safest thing to do is to just not even try to interpret them.

Yes, I have never seen anybody go on at great length interpreting an LL value. It would be like discussing the residual sums of squares in an OLS regression. The LL's are more like a necessary evil that help you get to things like LR Chi-square contrasts between models. See the -lrtest- command. The LR chi2 statistic often reported by models has been calculated using LL statistics.


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Richard Williams, Notre Dame Dept of Sociology
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