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st: Re: new command on SSC - hcnbreg


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  




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