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Sensitivity of Test for Overdispersion in Poisson Regression
Author(s) -
Xiang Liming,
Lee Andy H.
Publication year - 2005
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.200310096
Subject(s) - overdispersion , count data , poisson regression , poisson distribution , quasi likelihood , statistics , mathematics , regression analysis , regression , zero inflated model , sensitivity (control systems) , econometrics , medicine , population , engineering , environmental health , electronic engineering
Overdispersion or extra‐Poisson variation is very common for count data. This phenomenon arises when the variability of the counts greatly exceeds the mean under the Poisson assumption, resulting in substantial bias for the parameter estimates. To detect whether count data are overdispersed in the Poisson regression setting, various tests have been proposed and among them, the score tests derived by Dean (1992) are popular and easy to implement. However, such tests can be sensitive to anomalous or extreme observations. In this paper, diagnostic measures are proposed for assessing the sensitivity of Dean's score test for overdispersion in Poisson regression. Applications to the well‐known fabric faults and Ames salmonella assay data sets illustrate the usefulness of the diagnostics in analyzing overdispersed count data. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)