Linear Model Theory (PDF)

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.