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st: RE: Exact Poisson Regression

Subject   st: RE: Exact Poisson Regression
Date   Sat, 16 Feb 2008 10:14:08 EST

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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