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: hi...@asu.edu or jhi...@aol.com URL: http://works.bepress.com/joseph_hilbe/ [[alternative HTML version deleted]] ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
