Assessing the performance of normal-based and REML-based confidence intervals for the intraclass correlation coefficient

Using normal distribution assumptions, one can obtain confidence intervals for variance components in a variety of applications. A normal-based interval, which has exact coverage probability under normality, is usually constructed from a pivot so that the endpoints of the interval depend on the data as well as the distribution of the pivotal quantity. Alternatively, one can employ a point estimation technique to form a large-sample (or approximate) confidence interval. A commonly used approach to estimate variance components is the restricted maximum likelihood (REML) method. The endpoints of a REML-based confidence interval depend on the data and the asymptotic distribution of the REML estimator. In this paper, simulation studies are conducted to evaluate the performance of the normal-based and the REML-based intervals for the intraclass correlation coefficient under non-normal distribution assumptions. Simulated coverage probabilities and expected lengths provide guidance as to which interval procedure is favored for a particular scenario. Estimating the kurtosis of the underlying distribution plays a central role in implementing the REML-based procedure. An empirical example is given to illustrate the usefulness of the REML-based confidence intervals under non-normality.