## Muller, Keith E.

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

**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.

- Author(s)
- Muller, Keith E.
- Stewart, Paul W.
- Publisher
- John Wiley and Sons, Inc.
- Publication year
- 2006
- Language
- en
- Edition
- 1
- Page amount
- 480 pages
- Category
- Natural Sciences
- Format
- Ebook
- eISBN (PDF)
- 9780470052136
- Printed ISBN
- 9780471214885