Linear Model Theory

Univariate, Multivariate, and Mixed Models

Keith E. Muller, Paul W. Stewart - Collection Wiley Series in Probability and Statistics

410 pages, parution le 22/08/2006

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Résumé

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.

L'auteur - Keith E. Muller

Ph.D., is Associate Professor of Biostatistics at the University of North Carolina at Chapel Hill. He teaches classes and seminars in the theory and practice of univariate and multivariate linear models with Gaussian errors. A SAS user since 1978, he is best known for his contributions to theory and practice of sample size and power calculations, including SAS/IML programs for power in repeated measures.

L'auteur - Paul W. Stewart

Paul W. Stewart, PhD, is Research Associate Professor of Biostatistics at The University of North Carolina at Chapel Hill.

Sommaire

Preface
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
Choosing the Form of a Linear Model for Analysis
General Theory of Multivariate Distributions
Scalar, Vector, and Matrix Gaussian Distributions
Univariate Quadratic Forms
Multivariate Quadratic Forms
Estimation for Univariate and Weighted Linear Models
Estimation for Multivariate Linear Models
Estimation for Generalizations of Multivariate Models
Estimation for Linear Mixed Models
Tests for Univariate Linear Moels
Tests for Multivariate Linear Models
Tests for Generalizations of Multivariate Linear Models
Tests for Linear Mixed Models
A Review of Multivariate and Univariate Linear Models
Sample Size for Univariate Linear Models
Sample Size for Multivariate Linear Models
Sample Size for Generalizations of Multivariate Models
Sample Size for Linear Mixed Models
Appendix: Computing Resources
References
Index

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Wiley
Auteur(s)	Keith E. Muller, Paul W. Stewart
Collection	Wiley Series in Probability and Statistics
Parution	22/08/2006
Nb. de pages	410
Format	16 x 24
Couverture	Relié
Poids	702g
Intérieur	Noir et Blanc
EAN13	9780471214885
ISBN13	978-0-471-21488-5