Abstract
Negative binomial regression has been widely applied in various research settings to account for counts with overdispersion. Yet, when the gamma scale parameter, \begin{document}$ \nu $\end{document} , is parameterized, there is no direct algorithmic solution to the Fisher Information matrix of the associated heterogeneous negative binomial regression, which seriously limits its applications to a wide range of complex problems. In this research, we propose a numerical method to calculate the Fisher information of heterogeneous negative binomial regression and accordingly develop a preliminary framework for analyzing incomplete counts with overdispersion. This method is implemented in R and illustrated using an empirical example of teenage drug use in America.
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