# Linear Model Theory:

Univariate, Multivariate, and Mixed Models (Google eBook)
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.

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### 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
 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

 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
 23 Sample Size for Linear Mixed Models 385 Appendix Computing Resources 387 References 393 Index 405 Copyright

### 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.

### References to this book

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### References from web pages

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