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Re: st: BIC by deviance or liklihood

From   Maarten buis <>
Subject   Re: st: BIC by deviance or liklihood
Date   Tue, 17 Nov 2009 14:35:17 -0800 (PST)

--- On Tue, 17/11/09, Abdul Q Memon <> wrote:
> Could i get some one suggestions about either to use BIC
> estimated from deviance or likelihood after using negative 
> binomial with glm command in Stata.

Mechanically, there is no difference between the two; the 
deviance is just a linear transformation of the likelihood, so 
whatever conclusion you draw from the BIC based on the deviance 
should also follow from the BIC based on the likelihood. 

Conceptually, the deviance only makes sense if you can think of 
a saturated model. The typical example is a categorical 
dependent variable and only categorical explanatory varialbes. 
In that case we can represent the data, without loosing any 
information, as a (multidimensional) cross tabulation, and if we 
estimate a parameter for each cell, than the model is saturated. 
That saturated model will exactly reproduce that cross tabulation, 
and thus represents all the information that is present in the 
data. The deviance compares this full model with your model. It 
becomes harder to define a saturated model as soon as one or more 
of your variables are continuous variables or are a variable that, 
in principle, could have an infinite number of categories, like a 

Hope this helps,

Maarten L. Buis
Institut fuer Soziologie
Universitaet Tuebingen
Wilhelmstrasse 36
72074 Tuebingen


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