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Title: A numerical method to compute Fisher information for a special case of heterogeneous negative binomial regression
Authors: Guo, X 
Fu, Q
Wang, Y 
Land, KC
Issue Date: Aug-2020
Source: Communications on pure and applied analysis, Aug. 2020, v. 19, no. 8, p. 4179-4189
Abstract: 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.
Keywords: Regression analysis
Incomplete counts
Heterogeneous negative binomial regression
Fisher information
Gamma scale parameter
Publisher: American Institute of Mathematical Sciences
Journal: Communications on pure and applied analysis 
ISSN: 1534-0392
DOI: 10.3934/cpaa.2020187
Rights: This article has been published in a revised form in Communications on Pure & Applied Analysis []. This version is free to download for private research and study only. Not for redistribution, re-sale or use in derivative works.
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