A FINITE MIXTURE DISTRIBUTION FOR MODELING MULTINOMIAL EXTRA VARIATION

We propose a new distribution to model categorical data exhibiting ove rdispersion when the overdispersion is believed to be caused by clumpe d sampling. The proposed distribution is a finite mixture of multinomi al random variables. The finite mixture representation facilitates com putation of the maximum likelihood estimator. For large cluster sizes, we derive an approximation for the Fisher information matrix of the m odel, and an explicit expression for the joint asymptotic efficiency o f the maximum likelihood estimator relative to a quasi-likelihood esti mator.