An interval estimate for the intraclass correlation in beta-binomial sampling

The beta-binomial distribution has been frequently applied to model intraclass correlation among dichotomous responses in cluster sampling. To avoid using sophisticated numerical procedures to calculate maximum likelihood estimates, many authors have proposed different moment estimators. Most of them focused their discussion, however, on point estimation only. In this paper, are have developed a closed-form interval estimate for the intraclass correlation, and have shown it has asymptotically correct coverage. We have further used a Monte Carlo simulation to evaluate the performance of the proposed interval estimation in a variety of situations. We have found that when the number of clusters is moderate (greater than or equal to 50), the proposed interval estimation performs reasonably well except for the situation where the intraclass correlation is large and the underlying mean response probability is small. Even when the number of clusters is as small as 20, the proposed interval estimation may still be useful in the situation where the intraclass correlation is small. Wie have also extended the proposed interval estimate to accommodate stratified sampling, in which each stratum has a different mean response probability but has a common intraclass correlation.