Quantifying overdispersion effects in count regression data

Czado, Claudia und Sikora, I. (2002): Quantifying overdispersion effects in count regression data. Sonderforschungsbereich 386, Discussion Paper 289

Abstract

The Poisson regression model is often used as a first model for count data with covariates. Since this model is a GLM with canonical link, regression parameters can be easily fitted using standard software. However the model requires equidispersion, which might not be valid for the data set under consideration. There have been many models proposed in the literature to allow for overdispersion. One such model is the negative binomial regression model. In addition, score tests have been commonly used to detect overdispersion in the data. However these tests do not allow to quantify the effects of overdispersion. In this paper we propose easily interpretable discrepancy measures which allow to quantify the overdispersion effects when comparing a negative binomial regression to Poisson regression. We propose asymptotic $\alpha$-level tests for testing the size of overdispersion effects in terms of the developed discrepancy measures. A graphical display of p-values curves can then be used to allow for an exact quantification of the overdispersion effects. This can lead to a validation of the Poisson regression or a discrimination of the Poisson regression with respect to the negative binomial regression. The proposed asymptotic tests are investigated in small samples using simulation and applied to two examples.

• Dokumententyp: Paper
• Keywords: Poisson regression, negative binomial regression, quantification of overdispersion
• Fakultät: Mathematik, Informatik und Statistik > Statistik > Sonderforschungsbereich 386 ; Sonderforschungsbereiche > Sonderforschungsbereich 386
• Themengebiete: 500 Naturwissenschaften und Mathematik > 510 Mathematik
• Sprache: Englisch