Linear Model Theory
Univariate, Multivariate, and Mixed Models
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Linear Model Theory by Keith E. Muller
Book DescriptionA 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.
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Book DetailsISBN: 9780471214885
(241mm x 161mm x 24mm)
Imprint: John Wiley & Sons Inc
Publisher: John Wiley & Sons Inc
Publish Date: 22-Aug-2006
Country of Publication: United States
Books By Author Keith E. Muller
Regression and ANOVA, Paperback (February 2008)» View all books by Keith E. Muller
This set contains: 9780471469438 Regression and ANOVA: An Integrated Approach Using SAS(R) Software by Keith E. Muller, Bethel A. Fetterman and 9780471370383 Applied Statistics: Analysis of Variance and Regression, Third Edition by Ruth M. Mickey, Olive Jean Dunn, Virginia A. Clark.
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Author Biography - Keith E. Muller
KEITH E. MULLER, PhD, is Professor and Director of the Division of Biostatistics in the Department of Epidemiology and Health Policy Research in the College of Medicine at the University of Florida in Gainesville, as well as Professor Emeritus of Biostatistics at The University of North Carolina at Chapel Hill where the book was written. PAUL W. STEWART, PhD, is Research Associate Professor of Biostatistics at The University of North Carolina at Chapel Hill.
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