Estimation of variance components and diagnostic analysis in unbalanced mixed linear models

Abstract

This dissertation presents a new estimation procedure for the variance components in the unbalanced mixed linear model. Without the non-negativity constraint, restricted maximum likelihood (REML) estimates are computed applying the Expectation-Maximization (EM) algorithm. The approach used is to consider the unbalanced data as "incomplete data" and the conceptual set of n replications of each factor combination as the "complete data". An updated vector of "inputed values" is used at each iteration. This produces the generalized average (GAVE) method, which is a natural extension of the AVE method used for balanced data. The GAVE procedure takes into account the problem of empty cells while keeping the diagnostic properties of the AVE method. Numerical examples are included, which show the close relationship between AVE and GAVE algorithms, clarify these methodologies, and illustrate graphical diagnostic analysis.