Modeling the coverage probability of a confidence interval on the among-group variance component in the unbalanced random one-way model

The coverage probability of an approximate confidence interval on the among-group variance component, sigma(alpha)(2), in a one-way random model is modeled using generalized linear models techniques. The purpose of the proposed modeling is to derive an empirical relationship between the coverage probability on one hand, and k, n, phi and the model's variance components on the other hand, where k is the number of groups, n, is the total number of observations, and phi is a measure of imbalance for the design used. The latter quantities serve as control variables in the derived model, and the coverage probability is treated as the response variable. Contour plots generated from this model can be easily used to depict the effects of the control variables on the coverage probability. In particular, the plots are utilized to compare four methods for constructing approximate confidence intervals on sigma(alpha)(2). Additional advantages of the derived model include prediction of the coverage probability for a given method using only specified values of the control variables, and the determination of operating conditions that result in improved coverage probability within the region of interest.