LARGE CLUSTER RESULTS FOR 2 PARAMETRIC MULTINOMIAL EXTRA VARIATION MODELS

Two parametric extra variation models are considered. Approximate clos ed-form expressions are given for the Fisher information matrices. The expressions are useful in computing maximum likelihood estimates and obtaining large cluster efficiencies. A simulation study shows that th e approximations perform very well even in clusters of moderate size. The models are applied in illustrative examples. A goodness-of-fit tes t is developed that is applicable even when the cluster sizes are uneq ual. The null distribution of the test statistic is shown to be well a pproximated by a chi-squared distribution. For the cluster size config urations in the examples. the test also has high power in distinguishi ng between the two models considered. The goodness-of-fit test shows t hat the new model provides adequate description of the data from the t hree experiments designed to study induced mutagenic effect.