# Re: st: Positive log likelihoods in xtmixed models

 From "Michael Blasnik" <[email protected]> To <[email protected]> To <[email protected]> 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
*
* For searches and help try:
* http://www.stata.com/support/faqs/res/findit.html
* http://www.stata.com/support/statalist/faq
* http://www.ats.ucla.edu/stat/stata/