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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/ ----------------------------------------- * * 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/

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