Obtaining shape estimate from proc genmod instead of dispersion in negative binomial data

[JulieB]

Can someone explain the difference between the shape parameter and dispersion parameter in a negative binomial distribution?  When simulating a negative binomial distribution, I need to enter the mean and shape, but when I analyze my data in proc genmod, it does not output shape; it outputs dispersion.  I know that dispersion indicates whether or not the data fit a poisson distribution and values greater than 1 mean the data are over dispersed.  But that is not helping me - I need to take the dispersion estimate and convert it to a shape estimate, and I am uncertain as to how to do that.  Any help would be appreciated.

I'm on SAS v9.4

[StatDave]

There are various parameterizations (forms) of the negative binomial distribution. The parameterization that GENMOD uses can be seen in its documentation - see the Details:Response Probability Distributions. You need to compare that to whatever parameterization is involved in what you are doing. GENMOD's has a mean and dispersion parameter, and some might call the latter a "shape" parameter. Another parameterization is used by the probability functions in the DATA step like RAND and PDF. You can see that parameterization in the documentation of those functions. See also this note and possibly the Wikipedia page on the negative binomial distribution.