Monte Carlo Comparison of ANOVA, MIVQUE, REML, and ML Estimators of Variance Components

Abstract

For the one-way classification random model with unbalanced data, we compare five estimators of σ2 a and σ2 e , the among- and within-treatments variance components: analysis of variance (ANOVA), maximum likelihood (ML), restricted maximum likelihood (REML), and two minimum variance quadratic unbiased (MIVQUE) estimators. MIVQUE(0) is MIVQUE with a priori values = 0 and = 1; MIVQUE(A) is MIVQUE with the ANOVA estimates used as a priori's, We enforce nonnegativity for all estimators, setting any negative estimate to zero in accord with usual practice. The estimators are compared through their biases and MSE's, estimated by Monte Carlo simulation. Our results indicate that the ANOVA estimators perform well, except with seriously unbalanced data when σ2 a /σ2 e > 1; ML is excellent when σ2 a /σ2 e < 0.5, and MIVQUE(A) is adequate; further iteration to the REML estimates is unnecessary. When σ2 a /σ2 e ≥ 1, MIVQUE(0) (the default for SASS PROCEDURE VARCOMP) is poor for estimating σ2 a and very poor for σ2 e , even for just mildly unbalanced data.