Under-dispersion can be modeled using a generalized Poisson regression, and
has also been modeled using a 2-parameter log-gamma model. A double Poisson
model has also been used, but there is no software support for it that I know
of. Negative binomial only models overdispersion. Both the generalized
Poisson and 2-parameter log-gamma models are discussed in some detail in
Hilbe, Joseph M (2007), Negative Binomial Regression, Cambridge University
Press
and is also described in
Hardin, J.W and J.M. Hilbe (2007), Generalized Linear Models and Extensions,
2nd edition, Stata Press.
Again, you can get the commands to estimate under-dispersion by downloading
them from the book's web site.
Under-dispersion is quite rare in real data, but does occur. Actually, if
you don't have the above software, you can adjust the standard errors of the
under-dispersed Poisson model by scaling based on the Pearson dispersion sta
tistic. Simulation studies I have done have shown that it generally does a good
job in appropriately adjusting the under-dispersed model.
Joseph Hilbe
Date: Wed, 27 Feb 2008 12:57:52 -0500
From: "Austin Nichols" <[email protected]>
Subject: Re: st: Basic question to Count Data Models
> Another problem: Someone told me that "dispersion" or "under-dispersion"
> might be a problem with a Count Data Model. I did some research but
couldn�t
> find anyhting about that. Does anyone of you know whether this is true?
And if
> so, can you give me a hint or literature suggestion, what
"under-dispersion"
> is and how I could face it in my problem?
>
> Thanks a lot,
> Markus.
>
**************Ideas to please picky eaters. Watch video on AOL Living.
(http://living.aol.com/video/how-to-please-your-picky-eater/rachel-campos-duffy/
2050827?NCID=aolcmp00300000002598)
*
* 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/
