Linear Model Theory: Univariate, Multivariate, and Mixed Models (Google eBook)

Keith E. Muller, Paul W. Stewart

John Wiley & Sons, Oct 6, 2006 - Mathematics - 480 pages

A precise and accessible presentation of linear model theory, illustrated with data examples

Statisticians often use linear models for data analysis and for developing new statistical methods. Most books on the subject have historically discussed univariate, multivariate, and mixed linear models separately, whereas Linear Model Theory: Univariate, Multivariate, and Mixed Models presents a unified treatment in order to make clear the distinctions among the three classes of models.

Linear Model Theory: Univariate, Multivariate, and Mixed Models begins with six chapters devoted to providing brief and clear mathematical statements of models, procedures, and notation. Data examples motivate and illustrate the models. Chapters 7-10 address distribution theory of multivariate Gaussian variables and quadratic forms. Chapters 11-19 detail methods for estimation, hypothesis testing, and confidence intervals. The final chapters, 20-23, concentrate on choosing a sample size. Substantial sets of excercises of varying difficulty serve instructors for their classes, as well as help students to test their own knowledge.

The reader needs a basic knowledge of statistics, probability, and inference, as well as a solid background in matrix theory and applied univariate linear models from a matrix perspective. Topics covered include:

• A review of matrix algebra for linear models
• The general linear univariate model
• The general linear multivariate model
• Generalizations of the multivariate linear model
• The linear mixed model
• Multivariate distribution theory
• Estimation in linear models
• Tests in Gaussian linear models
• Choosing a sample size in Gaussian linear models

Filling the need for a text that provides the necessary theoretical foundations for applying a wide range of methods in real situations, Linear Model Theory: Univariate, Multivariate, and Mixed Models centers on linear models of interval scale responses with finite second moments. Models with complex predictors, complex responses, or both, motivate the presentation.

Contents

• 1 Matrix Algebra for Linear Models: 1
• 2 The General Linear Univariate Model: 39
• 3 The General Linear Multivariate Model: 55
• 4 Generalizations of the Multivariate Linear Model: 79
• 5 The Linear Mixed Model: 91
• 6 Choosing the Form of a Linear Model for Analysis: 101
• 7 General Theory of Multivariate Distributions: 115
• 8 Scalar Vector and Matrix Gaussian Distributions: 139
• 9 Univariate Quadratic Forms: 169
• 10 Multivariate Quadratic Forms: 193
• 11 Estimation for Univariate and Weighted Linear Models: 209
• 12 Estimation for Multivariate Linear Models: 243
• 13 Estimation for Generalizations of Multivariate Models: 263
• 14 Estimation for Linear Mixed Models: 279
• 15 Tests for Univariate Linear Models: 289
• 16 Tests for Multivariate Linear Models: 311
• 17 Tests for Generalizations of Multivariate Linear Models: 337
• 18 Tests for Linear Mixed Models: 341
• 19 A Review of Multivariate and Univariate Linear Models: 349
• 20 Sample Size for Univariate Linear Models: 361
• 21 Sample Size for Multivariate Linear Models: 371
• 22 Sample Size for Generalizations of Multivariate Models: 383
• 23 Sample Size for Linear Mixed Models: 385
• Appendix Computing Resources: 387
• References: 393
• Index: 405

Popular passages

Page xiii - Professor in the Department of Biostatistics at the University of North Carolina at Chapel Hill, working as co-director of the Biostatistics team for the Lipid Research Clinic.‎

About the author

KEITH E. MULLER, PhD, is Professor and Director of the Division of Biostatistics in the Department of Epidemiology and Health Policy Research in the College of Medicine at the University of Florida in Gainesville, as well as Professor Emeritus of Biostatistics at The University of North Carolina at Chapel Hill where the book was written.

PAUL W. STEWART, PhD, is Research Associate Professor of Biostatistics at The University of North Carolina at Chapel Hill.

Bibliographic information

• Title: Linear Model Theory: Univariate, Multivariate, and Mixed Models; Wiley series in probability and statistics
• Authors: Keith E. Muller, Paul W. Stewart
• Publisher: John Wiley & Sons, 2006
• ISBN: 0470052139, 9780470052136
• Length: 480 pages
• Subjects: Mathematics / Probability & Statistics / General