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From |
Jhilbe@aol.com |

To |
statalist@hsphsun2.harvard.edu |

Subject |
st: Re: new command on SSC - hcnbreg |

Date |
Wed, 12 Sep 2007 19:01:46 EDT |

Kit has kindly posted my new Heterogeneous Canonical Negative Binomial regression program to the SSC site. One can download the files by typing at the Stata prompt: . ssc install hcnbreg Canonical Negative Binomial (NB-C) is a parameterization that derives the negative binomial directly from the exponential family form of the Negative Binomial PDF, and not as a Poisson-gamma mixture model. Thought of as a GLM model, the canonical form is the canonical link. nbreg allows you to model either the traditional NB-2 model, or NB-1, which has a constant dispersion. Both have been traditionally derived as Poisson-gamma mixtures. With respect to GLM, NB-2 is a log-linked negative binomial - which is not the canonical form. I posted a maximum likelihood NB-C regression program to SSC back in late 2005. Like nbreg, it estimates the heterogeniety parameter, called alpha. The heterogeneous NB-C model is analogous to Stata's gnbreg command, called "Generalized Negative Binomial". Actually the use of "generalized" here is unfortunate. There have been Generalized NB models discussed in the literature for years -- that are quite unlike Stata's version. LIMDEP (W Greene) and other sources refer to what Stata calls a generalized negative binomial as a heterogeneous negative binomial (NB-H). The NB-H command allows parameterization of the estimated heterogeniety parameter (alpha). This may provide the user with information about which predictors significantly impact unexplained correlation in the model, which in turn may help the user to determine how to further adjust the model for a more optimal fit. Anyhow, I have found that the canonical NB model can produce a better fitted model for certain count response models than can the more traditional negative binomial. Just remember that the NB-C model (as well as the heterogeneous NB-C which provides additional information) does not have the same relationship to Poisson as do NB-1 or NB-2. But it is a viable count model nonetheless. Joseph Hilbe ************************************** See what's new at http://www.aol.com * * 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/

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