A Comparison of Designs and Estimators For the Two-Stage Nested Random Model

Abstract

The problem of selecting a design and estimating procedure for estimating with minimum mean squared error (MSE) the variance components in a two-stage nested random model is considered. For balanced designs a modified maximum likelihood (ML) estimator is superior, and for this estimator the optimal design is less sensitive to the intra-class correlation τ for τ ≤ .5 than those designs based on minimizing the variance of the usual analysis of variance (AOV) estimator. For τ > .5, where an unbalanced design is preferable, asymptotic results were derived to indicate optimal designs for ML and AOV estimators; ML estimators have smaller MSE's than truncated AOV estimators or iterated least squares estimators. The optimal number of classes is somewhat less than the number needed for minimizing the variance of the usual AOV estimator. Large sample results for unbalanced designs were compared with small sample results obtained by simulation for a wide range of intra-class correlation and several selected designs.

KEY WORDS:

• Maximum likelihood
• Random effects model
• Experimental design
• Analysis of variance
• Iterated least squares