# Linear Model Theory: Univariate, Multivariate, and Mixed Models

Copyright © 2006 John Wiley & Sons, Inc. All rights reserved.

Author(s): Keith E. Muller, Paul W. Stewart

Published Online: 30 JAN 2012 09:55AM EST

Print ISBN: 9780471214885

Online ISBN: 9780470052143

DOI: 10.1002/0470052147

## About this Book

**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.