Linear Models: The Theory and Application of Analysis of Variance / Edition 1

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Overview

Linear Models explores the theory of linear models and the dynamic relationships that these models have with Analysis of Variance (ANOVA), experimental design, and random and mixed-model effects. This one-of-a-kind book emphasizes an approach that clearly explains the distribution theory of linear models and experimental design starting from basic mathematical concepts in linear algebra. This book is a valuable book for courses on linear models at the upper-undergraduate and graduate levels. It is also an excellent reference for practitioners who use linear models to conduct research in the fields of econometrics, psychology, sociology, biology, and agriculture.
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Editorial Reviews

From the Publisher
"Solved examples throughout bring clarity to otherwise difficult, complex concepts. Highly recommended." (CHOICE, March 2009)
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Product Details

  • ISBN-13: 9780470025666
  • Publisher: Wiley, John & Sons, Incorporated
  • Publication date: 8/4/2008
  • Series: Wiley Series in Probability and Statistics Series , #634
  • Edition description: New Edition
  • Edition number: 1
  • Pages: 272
  • Product dimensions: 6.20 (w) x 9.30 (h) x 0.80 (d)

Meet the Author

Brenton R. Clarke, PhD, is Senior Lecturer in Mathematics and Statistics at Murdoch University, Australia. A former president of the Western Australian Branch of the Statistical Society of Australia, Dr. Clarke has published numerous journal articles in his areas of research interest, which include linear models, robust statistics, and time series analysis.
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Table of Contents

1 Introduction 1

2 Projection Matrices and Vector Space Theory 17

3 Least Squares Theory 33

4 Distribution Theory 53

5 Helmert Matrices and Orthogonal Relationships 77

6 Further Discussions of ANOVA 113

7 Residual Analysis: Diagnostics and Robustness 159

8 Models That Include Variance Components 179

9 Likelihood Approaches 195

10 Uncorrelated Residuals Formed from the Linear Model 209

11 Further inferential questions relating to ANOVA 225

References 229

Index 237

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