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

Research output: Journal article publicationJournal articleAcademic researchpeer-review

3 Citations (Scopus)


Negative binomial regression has been widely applied in various research settings to account for counts with overdispersion. Yet, when the gamma scale parameter, ν, 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.

Original languageEnglish
Pages (from-to)4179-4189
Number of pages11
JournalCommunications on Pure and Applied Analysis
Issue number8
Publication statusPublished - Aug 2020


  • Fisher information
  • Gamma scale parameter
  • Heterogeneous negative binomial regression
  • Incomplete counts
  • Overdispersion
  • Regression analysis

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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