# st: RE: Negative vs positive log likelikood

 From "Maarten Buis" To Subject st: RE: Negative vs positive log likelikood Date Mon, 30 Jul 2007 14:56:36 +0200

```--- Dascha Orlova wrote:
> I have both positive and negative signs of the log
> likelihood and unfortunately I have no idea, which
> is better. I also wonder, whether small or large
> values indicate a better fit (f.e. whether LL of
> -365 is better (or worse) that -150).

The likelihood is proportional to the probability
of observing the data given the parameter estimates
and your model. To ensure that they are comparable
across models the models have to be nested, i.e.
you can get from the more complex model to the less
complex model by imposing a set of constraints on
the more complex model. If the models are nested
than a larger likelihood function means a larger
probability of observing the data, which is good.

A positive log likelihood means that the likelihood
is larger than 1. This is possible because the
likelihood is not itself the probability of
observing the data, but just proportional to it.

The likelihood is hardly ever interpreted in its
own right (though see (Edwards 1992[1972]) for an
exception), but rather as a test-statistic, or as
a means of estimating parameters. There are a number
of goodness of fit statistics based on the
likelihood: many of the pseudo-Rsquares, the AIC,
and the BIC.

A simple introduction to the likelihood is
(Eliason 1993)

Hope this helps,
Maarten

Edwards, A.W.F. (1992[1972]), "Likelihood", expanded
edition. Baltimore: The Johns Hopkins University
Press.

Eliason, Scott R. (1993), "Maximum Likelihood
Estimation, logic and practice". Thousand Oaks:
Sage.

-----------------------------------------
Maarten L. Buis
Department of Social Research Methodology
Vrije Universiteit Amsterdam
Boelelaan 1081
1081 HV Amsterdam
The Netherlands

Buitenveldertselaan 3 (Metropolitan), room Z434

+31 20 5986715

http://home.fsw.vu.nl/m.buis/
-----------------------------------------

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