A Comparison of Variance Component Estimators

Explicit solutions are given for the maxi111tm likelihood (ML) and restricted maximm likelihood (RDn.)equations under normality for four conn:non variance components mdels with balanced (equal subclass numbers) data.Solutions of the REML equations are identical to anazysis of variance (AOV) estimators.The ratio of mean squared errors of REML and ML solutions are also given.Unbalanced (unequal subclass numbers) data are used in a series of numerical trials to compare ML and REML procedures with 3 other estimation methods using a 2-way crossed classification mixed model with no interaction and 0 or 1 observation per cell.Results are similar to those reported by Hocking and Kutner [1975] for the BIB design.Collectively, these studies and those of Klotz, Milton, and Zacks [1969] point, with few exceptions, to the greater efficiency of ML estimators under a range of experimental settings.