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Re: st: RE: Exact Poisson Regression

From   David Airey <>
Subject   Re: st: RE: Exact Poisson Regression
Date   Sun, 17 Feb 2008 10:45:01 -0600


I read your review of Stata 9 and of exact statistics in various packages. Both were good reads. Thank you!


On Feb 16, 2008, at 9:14 AM, wrote:

Gary Anderson asks about whether anyone has developed an exact negative
command. No one has done that yet, but the folks at Cytel talked to me about
it back
in November 2005 when I gave an ASA LearnStat course in the Boston area.

The parameterization of the exact negative binomial would take the canonical
form; ie
it would not be the Poisson-gamma mixture model parameterization with which
statisticians are familiar. Therefore, it would not have the same
relationship to Poisson
overdispersion as does the NB-2 type of negative binomial, which is
estimated by using
the default form of -nbreg-. The canonical negative binomial can be used to
model count
data, and does a good job modeling data that is Poisson- overdispersed. I say
this because
negative binomial models can be overdispersed as well. But, because it does
not have
the log link as does Poisson (and NB-2), the canonical NB heterogeneity or
ancillary parameter
it cannot be used for direct comparisons with Poisson overdispersion as is
NB-2. Again, an exact NB
would be a canonical NB.

I submitted a maximum likelihood canonical NB Stata program to SSC last year
called -cnbreg-.
It has all of the bells and whistles as the usual Stata maximum likelihood
commands. I've been doing simulation studies on the NB-C model, as I call the
canonical NB in "Negative Binomial Regression", comparing it with Poisson,
NB-2, and NB-1 models. I intend to publish the results when completed.
NB-C is actually a nice model and can do a better job modeling some types of
data than NB-2 or NB-1.
I think it is worth the effort to construct an exact NB command, but I now
doubt that Cytel will get to it.
LogXact, Cytel's software application for modeling exact logistic and exact
Poisson models, is not alone any more in providing this capability to its
users. SAS and SPSS can model exact logistic models, and Stata both exact
logistic and exact Poisson. Because of the strong competition in this regard, it is
my understanding that Cytel is emphasizing development of packages such as
East, which is marketed to the clinical trials industry. I doubt that it will
develop an exact NB now. And since there are no published algorithms showing
how to do it, I very much doubt that SAS or SPSS will take it on. That leaves
Stata Corp. An exact NB, although of canonical parameterization, still would
be valuable for modeling counts with excessive correlation in the data. There
are great reasons why I think it worth the effort.

By the way, Bob Oster and I wrote an article for "The American Statistician"
(current issue) which compares the exact statistics capabilities of
StatXact/LogXact, SAS, SPSS, and Stata. Those of you who have an interest in exact
statistics may find the review to be helpful.

Joseph Hilbe

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