Linear Model Theory

<b>A precise and accessible presentation of linear model theory, illustrated with data examples</b> <p>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 <i>Linear Model Theory: Univariate, Multivariate, and Mixed Models</i> presents a unified treatment in order to make clear the distinctions among the three classes of models.</p> <p><i>Linear Model Theory: Univariate, Multivariate, and Mixed Models</i> 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.</p> <p>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:</p> <ul> <li>A review of matrix algebra for linear models</li> <li>The general linear univariate model</li> <li>The general linear multivariate model</li> <li>Generalizations of the multivariate linear model</li> <li>The linear mixed model</li> <li>Multivariate distribution theory</li> <li>Estimation in linear models</li> <li>Tests in Gaussian linear models</li> <li>Choosing a sample size in Gaussian linear models</li> </ul> <p>Filling the need for a text that provides the necessary theoretical foundations for applying a wide range of methods in real situations, <i>Linear Model Theory: Univariate, Multivariate, and Mixed Models</i> centers on linear models of interval scale responses with finite second moments. Models with complex predictors, complex responses, or both, motivate the presentation.</p>