Large Cluster Results for Two Parametric Multinomial Extra Variation Models

Two parametric extra variation models are considered. Approximate closed-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 the approximations perform very well even in clusters of moderate size. The models are applied in illustrative examples. A goodness-of-fit test is developed that is applicable even when the cluster sizes are unequal. The null distribution of the test statistic is shown to be well approximated by a chi-squared distribution. For the cluster size configurations in the examples, the test also has high power in distinguishing between the two models considered. The goodness-of-fit test shows that the new model provides adequate description of the data from the three experiments designed to study induced mutagenic effect.