A multinomial model for cross classified data with a measure of dependency

This paper presents a modified multinomial model for analyzing behaviour among wildlife populations. It assumes that the covariance matrix of the observed proportions is a multiple of the covariance matrix under simple random sampling. The model also allows a measure of dependency among the clusters within subpopulations, a type of dependency that assumes the relationships among units are the same for any two units. In addition, this paper illustrates the fact that the incorrect application of the Pearson chi-square statistic based on simple random sampling can produce misleading results when frequencies are obtained from a non-multinomial sampling scheme. Data obtained from a study of wild turkeys are analyzed using the proposed multinomial model.