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.