Variance components : estimates and diagnostics

Abstract

Numerical and graphical diagnostics are developed for investigating the usual analysis of variance estimators of variance components that arise in balanced, random effects models. Various linear combinations of variance components have a natural covariance interpretation. This leads to expressions for their estimators as sample covariances and to methods for detecting unusual observations and unstable estimators. General expressions are obtained pertaining to all balanced, complete factorial, random models and to a large class of partially nested designs. The covariance structure of the estimators is obtained. Computational formulae and convenient tabular and graphical displays are given for computing and examining the estimates. The diagnostics are analyzed both from a practical and from a theoretical point of view. Several illustrative examples are presented.