Estimation of intra-class correlation parameter for correlated binary data in common correlated models

Abstract

In common correlated models, the intra-class correlation parameter (ICC) provides a quantitative measure of the similarity between individuals within the same cluster and is of increasing interest and important use in biological and toxicological studies. The thesis mainly compares four estimators for the ICC parameter, including a new estimator that is based on the Cholesky decomposition. The new estimator is a specification of the UJ method proposed by Wang and Carey (2004) and has not been considered before. Analytic expressions of the asymptotic variances of the four estimators are obtained and extensive simulation studies are carried out. The bias, standard deviation, the mean square error and the relative efficiency of the estimators are compared. The results show that the new estimator performs well when the mean and intra-class correlation are small. Two real examples are used to investigate and compare the performance of these estimators in practice.