Interval Estimation of the Intra-class Correlation in General Linear Mixed Effects Models

The computation of confidence intervals for the intra-class correlation coefficient is addressed under general linear mixed effects models. Higher order asymptotic procedures are applied to derive accurate confidence intervals and are compared with a confidence interval available in the literature based on an approximate beta distribution. One of the confidence intervals based on the higher order asymptotic procedure performs well in terms of coverage probability and expected width. Balanced and unbalanced data situations are separately considered. The results in the balanced case are illustrated with an example. It will be clear that higher order asymptotic procedures are generally applicable for the accurate interval estimation of functions of fixed effects and variance components in very general linear mixed and random effects models.