Variance components estimation with missing cells

Abstract

The problem of estimating variance components in the random and mixed linear models has no satisfactory solution for the unbalanced data case. The techniques for estimating variance components for unbalanced data are either iterative (maximum likelihood type) or the solution to a system of linear equations (ANOVA type). None of the traditional procedures yield closed form expressions for the estimators. In the unbalanced case there are competing ANOVA tables which could be used, but there is no clear evidence that any one of them yields optimal estimates. Even in the balanced case, there has been confusion regarding the use and interpretation of negative estimates. There has been little work done on assessing the model and the associated data from a diagnostic standpoint. This dissertation will examine computational and diagnostic forms of estimators based on ANOVA-like techniques for the balanced and unbalanced random and mixed linear models with extensions to factorial models in the missing cell case. The calculation of the estimators shows natural diagnostics for examining the data and the model assumptions. Why negative estimates of variance components can arise is shown.