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st: RE: Negative vs positive log likelikood


From   "Maarten Buis" <M.Buis@fsw.vu.nl>
To   <statalist@hsphsun2.harvard.edu>
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

visiting address:
Buitenveldertselaan 3 (Metropolitan), room Z434 

+31 20 5986715

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



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