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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