ABSTRACT
There are several ways to estimate variance components for the general random effects model. Some of the procedures yield the same estimators when the design is balanced (equal sample sizes per cell and no missing cells) and different estimators when the design is not balanced. The four techniques discussed in this chapter are the method of moments, maximum likelihood, restricted, or residual maximum likelihood (REML), and MIVQUE. The method of moments produces unbiased estimates, maximum likelihood and REML estimators are consistent and have the usual large-sample-size properties of maximum likelihood estimates, and the MIVQUE method produces estimates having minimum variance within the class of quadratic unbiased estimates. When the design is balanced and the solutions for the variance components are all positive, the method of moments, REML, and MIVQUE estimators are identical. When the design is unbalanced, method-ofmoments estimates are easiest to compute, while the other three methods require iterative algorithms. On the other hand, the maximum likelihood, REML, and MIVQUE methods provide estimators with better properties than does the method of moments. REML is generally the preferred method of estimating the variance components.
