Studies of Multinomial

~~ Reader BYUNG sao KIM. Studies of Multinomial Mixture Models (Under the direction of Barry H. Margolin) We investigate certain inferential aspects of mixtures of multi-nomial distributions, both in nonparametric and parametric contexts. As a nonparametric mixture model we propose a k-population finite mixture of binomial distributions, which can be applied to the analysis of non-iid data generated from a series of toxicological experiments. A necessary and sufficient identifiability condition for the k-population finite mixture of binomials is obtained. The maximum likelihood estimates (MLE's) of the k-population finite mixture of binomials is computed via the EM algorithm (Dempster, Laird and Rubin, 1977), and the asymptotic properties of the MLE's are discussed. The identifiability condition is equivalent to the positive definiteness of the information matrix for the parameters. The MLE's and their sampling distributions, together with the data mentioned above, provide an empirical check of the statistical procedures proposed by Margolin, Kaplan and Zeiger (1981). The Dirichlet-multinomial distribution, a parametric mixture of multinomials, is discussed as a random group effects model for a one-way layout contingency table. Interest focuses on testing the hypothesis of no random effects. For this testing problem' Neyman's C(a) procedure yields a new test statistic, which is aymptotically superior to Pearson's chi-square test. This superiority is further evidenced by a Monte Carlo simulation study. A duality between the C(a) statistic and the Catanova statistic proposed by Light and Margolin (1971) is demonstrated. The random effects model for the one-way layout contingency table is extended within the framework of the Dirichlet-multinomial distribution to a balanced nested mixed effects model, and two hypothesis testing problems are investigated.