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

[jhilbe@aol.com]

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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