A numerical method to compute Fisher information for a special case of heterogeneous negative binomial regression
Xin Guo, Qiang Fu, Yue Wang, Kenneth C. Land · Communications on Pure & Applied Analysis · 2020
Negative binomial regression has been widely applied in various research settings to account for counts with overdispersion. Yet, when the gamma scale parameter, $ u $, 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.