ABSTRACT

This chapter reviews the linear models estimation. It recasts the one-factor and two-factor models into the general linear model framework. In addition, regression and analysis of covariance are briefly developed. The general linear hypothesis approach is compact and mathematically elegant. Ordinary least squares estimators are inefficient if the variances are not all equal. The chapter develops connections between least squares, weighted least squares and maximum likelihood (ML) without proof. The assumption of normality allows consideration of ML and restricted ML methods. ML, or minimum deviance, estimates agree with generalized least squares estimates, up to the choice of variances. While reference is made to likelihoods, there is no attempt to develop formal theory of inference. Analysis of covariance combines the flavor of factorial models and regression. The restricted ML estimates of variance components have a natural interpretation in random and mixed effects models.