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Re: st: Positive log likelihoods in xtmixed models


From   "Michael Blasnik" <michael.blasnik@verizon.net>
To   <statalist@hsphsun2.harvard.edu>
To   <statalist@hsphsun2.harvard.edu>
Subject   Re: st: Positive log likelihoods in xtmixed models
Subject   RE: st: Positive log likelihoods in xtmixed models
Date   Thu, 18 Oct 2007 00:25:53 -0400


No, a likelihood is going to be between 0 and 1: it's a probability.
It's also going to be very small (usually).
That's why we maximise the log-likelihood.
Since the likelihood is between 0 and 1, the log-likelihood is going to
be negative.

That was my point: why am I getting large positive log-likelihoods in
the second model.
Actually, that isn't always true. As stated in the Stata faq http://www.stata.com/support/faqs/stat/pseudor2.html
***
For discrete distributions, the log likelihood is the log of a probability, so it is always negative (or zero). Thus 0 ? L1 ? L0, and so 0 ? L1/L0 ? 1, and so 0 ? pseudo-R2 ?1 for DISCRETE distributions.

For continuous distributions, the log likelihood is the log of a density. Since density functions can be greater than 1 (cf. the normal density at 0), the log likelihood can be positive or negative. Similarly, mixed continuous/discrete likelihoods like tobit can also have a positive log likelihood.
***

Michael Blasnik
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