Comparison of GEE, MINQUE, ML, and REML estimating equations for normally distributed data

Generalized estimating equations (GEE) provide a regression framework for analyzing correlated data that are not necessarily assumed to be normal. For linear mixed models assuming normality, maximum likelihood (ML) and restricted maximum likelihood (REML) are commonly used for estimating variance and covariance parameters. In the analysis of variance tradition, minimum norm quadratic unbiased estimation (MINQUE) has been developed to estimate variance and covariance components without relying on distributional assumptions. This article rewrites the ML, REML, and MINQUE estimating equations in a form similar to GEE. This form is not particularly useful for computations, but it provides a very clear picture of the similarities and differences of the four methods. The derivations are straightforward and suitable for a linear models course.