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st: Dispersion parameter for a Negative Binomial model within GEE framework


From   jhilbe@aol.com
To   statalist@hsphsun2.harvard.edu
Subject   st: Dispersion parameter for a Negative Binomial model within GEE framework
Date   Thu, 23 Dec 2010 19:34:36 -0500 (EST)

Unfortunately the negative binomial heterogeneity or ancilalry parameter is not estimated using xtgee. It now is using the glm command, with the fam(nb ml) option. The best way to use xtgee for a negative binomial model is to do exactly what you suggested -- first determine the value of alpha from either nbreg or glm with the fam(nb ml) option. Use the resultant value as a constant (heterogeneity parameter) with the xtgee command. The GEE estimates will be better than if left with the default alpha=1 (a geometic GEE).

It would be preferable if alpha were estimated. SAS's Genmod procedure uses the methodf I outlined above for its NB GEE estimates. Genmod with the REPEATED option does estimate alpha except as a GLM. R has no NB GEE capability.

Prof Hardin and I are now in the process of writing a second edition of our GEE book (2002, Chapman & Hall/CRC) and a third edition of our Stata Press book, Generalized Linear Models and Extensions. Since xtgee is based on -glm-, it should be possible to amend the xtgee code to have it estimate alpha as well. There are some difficulties, but not severe enough that it cannot be done.

David is correct about zero inflation. However, excessive zero counts do give rise to excess correlation in the data, which is reflected in the value of alpha when estimated in a negative binomial model. The zero-inflated model is an attempt to adjust for the excess zeros.

My best to the Stata community for the holidays, as well as for 2011.

Joseph Hilbe




Date: Wed, 22 Dec 2010 18:02:38 -0500
From: David Greenberg <dg4@nyu.edu>
Subject: Re: st: Dispersion parameter for a Negative Binomial model within GEE framework The negative binomial regression model is not a fix for zero inflation, only for over-dispersion. David Greenberg, Sociology Department, New York University

- ----- Original Message -----
From: a b <andythezoologist@hotmail.com>

Date: Wednesday, December 22, 2010 4:21 am
Subject: st: Dispersion parameter for a Negative Binomial model within GEE framework
To: statalist@hsphsun2.harvard.edu

 Dear Statalisters,


 I have repeated measures data and I want to model at the population
average level, and hence I am using GEE. My data is also count data
and quite zero inflated - so I am modeling with a negative binomial
distribution.
 I was wondering how best to estimate the dispersion parameter (alpha
in Stata/k in Hardin and Hilbe) for the model?
 Do I just run a nbreg model, ignoring the repeated nature of the
data, and take the alpha estimate from there and subsitute it into
the GEE model?

 Many thanks for any help!



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