https://rss.onlinelibrary.wiley.com/doi/pdf/10.1111/j.2517-6161.1977.tb01600.x

Maximum likelihood from incomplete data via the EM algorithm

SUMMARY Statistical and computational techniques for the analysis of data from a normal mixed model with two variances are discussed and illustrated. Two iterative algorithms for restricted maximum likelihood estimation (REML) of the variances are compared. It is shown that these algorithms are much simplified by the use of a preliminary eigenvalue-eigenvector analysis. Two numerical examples are used to illustrate the theory by showing how variance estimates are used in the estimation and testing of fixed effects in the model. Monte Carlo simulations indicate that actual alpha levels of the tests are close to the nominal levels despite the estimation of the variance components. Diagnostic techniques are employed to assess model assumptions.

Statistical and Computational Aspects of Mixed Model Analysis

Recent developments in the animal breeding literature facilitate estimation of the variance components in quantitative genetic models. However, computation remains intensive, and many of the procedures are restricted to specialized designs and models, unsuited to data arising from studies of natural populations. We develop algorithms that allow maximum likelihood estimation of variance components for data on arbitrary pedigree structures. The proposed methods can be implemented on microcomputers, since no intensive matrix computations or manipulations are involved. Although parts of our procedures have been previously presented, we unify these into an overall scheme whose intuitive justification clarifies the approach. Two examples are analyzed: one of data on a natural population of Salivia lyrata and the other of simulated data on an extended pedigree.

https://www.jstor.org/stable/pdfplus/2531445.pdf

Pedigree analysis for quantitative traits : variance components without matrix inversion

Statistical inference for fixed effects, random effects and components of variance in an unbalanced linear model with variance components will be discussed. Variance components will be estimated by Restricted Maximum Likelihood. Iterative procedures for computing the estimates, such as Fisher scoring and the EM-algorithm, are described.

The analysis of unbalanced linear models with variance components

Evolution of Statistical Design and Analysis of Experiments

The W transformation greatly reduces the computational bruden in obtaining maximum likelihood estimates for the mixed A.O.V. model. However, effective optimization methods for maximizing the likelihood must comptlte the matrix W at each iteration. This paper develops an efficient Cholesky type algorithm for forming W.

https://www.jstor.org/stable/info/1267524

J. A. Lorens

Papers

Improved Algorithm for the W-Transform in Variance Component Estimation