Proposing a New Estimator of Overdispersion for Multinomial Data

Abstract

The classical approach of estimating overdispersion parameter, Φ, by Pearson's goodness of fit statistic is not appropriate when the data are sparse. We have considered several estimators of Φ, derived from the Pearson's statistic and the deviance statistic for multinomial data. The proposed estimator of Φ depending on the deviance statistic is shown to perform the best for increasing level of sparsity and overdispersion, regarding the root mean squared error. As a practical example dead recovery data collected on Herring gulls from Kent Island, Canada are considered. A parametric extra variation model finite mixture distribution is used in the simulation study.