I have seen several queries about parameterizing the negative binomial scale
parameter. This is called 

the heterogeneous negative binomial. I have written a function called
"nbinomial" which is in the 

msme package on CRAN. Type ?nbinomial to see the help file.  The default
model is a negative binomial 

for which the dispersion parameter is directly related to mu, which is how
Stata, SAS, SPSS, Limdep, and

so forth parameterize the negative binomial. The direct parameterization
make sense in that the more 

variation or correlation there is in a Poisson model,  the greater is the
value of the dispersion parameter 

which is adjusting for the excessive variation. With this parameterization
the dispersion parameter is 

directly related to both mu, as well as the dispersion statistic, or Pearson
Chi2/(residual DOF).  

A dispersion parameter of 0 is Poisson, which is equidispersed. When the
dispersion parameter for 

other mixture models such as generalized Poisson and Poisson inverse
Gaussian is zero, the models 

reduce to Poisson. 

 

I also provide an option so that the output is similar to glm.nb, for which
the dispersion parameter 

is indirectly related to the mean.  

 

I have also provided the abililty of nbinomial to parameterize the
dispersion parameter, providing 

Coefficients, SEs, CIs etc for the predictors of the dispersion, as there
are coefficients etc for the mean 

parameter. 

  The output look nearly identical to glm.nb, except that I also display a
summary of Pearson residuals, 

As well as the null and residual Pearson Chi2, and dispersion statistic.
The dispersion parameter is listed 

At the bottom of the table of coefficients, with SE, Z, p-value and
confidence intervals. You may select 

any variable(s) in the data to be a predictor(s) of the dispersion.
Predictors of the dispersion parameter, 

if positive and significant, indicate that they influence the extra
variability of diswhich likely have a bearn 

 

  I also provide a number of saved post-estimation statistics when nbinomial
is run, which the analyst 

may use in additional analysis. 

The function is one of a number of functions that are included in Hilbe and
Robinson, "Methods of Statistical 

Model Estimation", Chapman  & Hall/CRC, which is due to be published in the
next two weeks. The msme 

Package should be thought of as an adjunct package to the COUNT package,
which is on CRAN and provides 

the data sets, functions and a host of scripts for Hilbe, "Negative Binomial
Regression", 2nd edition, Cambridge 

University Press (2011). 

 

Best, J. Hilbe

 

------------------------------------------------------------

Joseph M. Hilbe, PhD

Emer Prof, Univ of Hawaii & Adj Prof of Statistics,  Arizona St Univ;

SSA Program, NASA/Jet Propulsion Laboratory, Caltech

President, International Astrostatistics Association

Coordinating editor, Cambridge Univ Press Series on Predictive Analytics 

 

Email: hilbe@asu.edu  or jhilbe@aol.com

URL: http://works.bepress.com/joseph_hilbe/

 


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