Non-Negative Estimates of Variance Components

Abstract

In many analyses of variance it is appropriate to consider the effects as randomly chosen from a population; thus providing a model II analysis in the terminology of Eisenhart. Interest then centers on the variances of the effects and on the components of variance. The usefulness of this technique is limited by the frequent occurrence of negative estimates of the variance components which are by definition non-negative quantities. This paper presents a method of data analysis, applicable to many of the more popular models, which always yields non-negative estimates. Recently a simple algorithm, the pool-the-minimum-violator algorithm, has been developed [11] as a result of maximizing the likelihood function of the mean squares subject to a set of constraints. This paper has been prepared as a less mathematical companion article to [11] in order to treat the more applied aspects of the problem. 2. AN EXAMPLE