A Finite Mixture Distribution for Modelling Multinomial Extra Variation
Jorge G. Morel, Neerchal K. Nagaraj · Biometrika · 1993
We propose a new distribution to model categorical data exhibiting overdispersion when the overdispersion is believed to be caused by clumped sampling. The proposed distribution is a finite mixture of multinomial random variables. The finite mixture representation facilitates computation of the maximum likelihood estimator. For large cluster sizes, we derive an approximation for the Fisher information matrix of the model, and an explicit expression for the joint asymptotic efficiency of the maximum likelihood estimator relative to a quasi-likelihood estimator. Some key words: Clumped data; Clusters; Dirichlet-multinomial distribution; Fisher information matrix; Quasi-likelihood estimator.