Thank you Dr Hilbe for a useful discussion on the exact negative
binomial, and the citation to the review of software packages for exact
methods.
Best wishes, Garry
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Subject: st: RE: Exact Poisson Regression
Gary Anderson asks about whether anyone has developed an exact negative
binomial 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 most 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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