Abstract
SUMMARY The Dirichlet-multinomial distribution is formulated as a model for contingency tables generated by cluster sampling schemes. This model provides an alternative justification for some results of Altham (1976) and enables an extension of her results to the case of unequal cluster sizes. The model also provides a convenient framework for the fitting and testing of general log linear models in contingency tables. The asymptotic distributions of the Pearson and likelihood ratio chi-squared statistics are shown to be multiples of chi-squared random variables and this result permits a simple modification of the usual procedures when faced with a cluster sample.
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