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Jhilbe@aol.com |

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statalist@hsphsun2.harvard.edu |

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 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 **************The year's hottest artists on the red carpet at the Grammy Awards. Go to AOL Music. (http://music.aol.com/grammys?NCID=aolcmp00300000002565) * * 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/

**Follow-Ups**:**st: RE: RE: Exact Poisson Regression***From:*"Lachenbruch, Peter" <Peter.Lachenbruch@oregonstate.edu>

**st: RE: RE: Exact Poisson Regression***From:*Garry Anderson <g.anderson@unimelb.edu.au>

**Re: st: RE: Exact Poisson Regression***From:*David Airey <david.airey@vanderbilt.edu>

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