Bayesian estimators of the intraclass correlation coefficient in the one-way random effects model

In this paper Bayesian methods are used to estimate the intraclass correlation coefficient in the balanced one-way random effects model. An estimator associated with the likelihood function derived from a pivotal quantity along with estimators using reference priors are considered. In addition, an estimator based on a posterior median is examined. These estimators are compared to one another and to the REML (restricted maximum likelihood) estimator in terms of MSE (mean-squared error). A beta-type approximation to the pivotal likelihood is considered. This can be combined with a beta prior to produce closed-form expressions that approximate the posterior mean and mode. These approximations generally perform well as judged by Bayes risk. Of the estimators considered the authors recommend the one obtained from the pivotal approach. The authors indicate how the estimation procedures may be extended to the unbalanced one-way random effects model.