An empirical approach to determine a threshold for assessing overdispersion in Poisson and negative binomial models for count data

• Published in: Communications in statistics. Simulation and computation Vol. 47; no. 6; pp. 1722 - 1738
• Main Authors: Payne, Elizabeth H., Gebregziabher, Mulugeta, Hardin, James W., Ramakrishnan, Viswanathan, Egede, Leonard E.
• Format: Journal Article
• Language: English
• Published: United States Taylor & Francis 05.07.2018; Taylor & Francis Ltd
• Subjects: 62Fxx; Chi-square test; Computer simulation; Count data; Datasets; Economic models; Empirical analysis; outliers; Outliers (statistics); overdispersion; Pearson chi-square; Statistical analysis; Statistical tests; zero inflation; Count data; 62Fxx; outliers; Pearson chi-square; overdispersion; 62J12; zero inflation
• ISSN: 0361-0918; 1532-4141
• DOI: 10.1080/03610918.2017.1323223

Overdispersion is a problem encountered in the analysis of count data that can lead to invalid inference if unaddressed. Decision about whether data are overdispersed is often reached by checking whether the ratio of the Pearson chi-square statistic to its degrees of freedom is greater than one; however, there is currently no fixed threshold for declaring the need for statistical intervention. We consider simulated cross-sectional and longitudinal datasets containing varying magnitudes of overdispersion caused by outliers or zero inflation, as well as real datasets, to determine an appropriate threshold value of this statistic which indicates when overdispersion should be addressed.