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Analysis of Variance: Random and Mixed Effects Models

  • Mervyn G. Marasinghe
  • Kenneth J. Koehler
Chapter
Part of the Springer Texts in Statistics book series (STS)

Abstract

SAS procedures GLM and MIXED are used to illustrate the analysis of a variety of random and mixed effects models. These include one-way random models, two-way crossed and nested random effects models, and two-way mixed effects models. Applications include a variety of experiments with random effects including randomized blocks, nested factorials, and split-plot type experiments. Estimation and statistical inference associated with classical method of moments and maximum likelihood estimates are illustrated using SAS output from GLM and MIXED procedures. Particular attention is paid to how expected mean squares output by SAS are used to calculate estimates of variance components and how these may be different from those obtained from likelihood methods.

Keywords

Quadratic forms Normal equations Mixed-model equations Variance components REML MIVQUE Intraclass correlation Convergence criteria Type I sum of squares Type III sum of squares Expected mean squares Satterthwaite approximation Mixed model equations BLUPs Unconstrained parameters model Kenward-Roger Whole-plot design Subplot factor Least squares means 

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Mervyn G. Marasinghe
    • 1
  • Kenneth J. Koehler
    • 1
  1. 1.Department of StatisticsIowa State UniversityAmesUSA

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