Newton-Raphson and Related Algorithms for Maximum Likelihood Variance Component Estimation

Abstract

Three general purpose algorithms for maximum likelihood estimation of mean and variance components in mixed analysis of variance models are discussed. These are the Newton-Raphson algorithm, the Fisher scoring algorithm, and the Hemmerle and Hartley algorithm. Derivations for the first two are given and a unified presentation of all three makes some theoretical and practical comparisons possible. In addition the results of applying all three to a sequence of five problems are presented. The W transform of Hemmerle and Hartley is used throughout to reduce the computational burden associated with maximum likelihood variance component algorithms. The algorithms provide a unified approach to estimation and testing in the general mixed analysis of variance model.