A Primer on Linear Models  book cover
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1st Edition

A Primer on Linear Models

Edited By

John F. Monahan





ISBN 9781420062014
Published March 31, 2008 by Chapman & Hall
304 Pages 6 B/W Illustrations

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Book Description

A Primer on Linear Models presents a unified, thorough, and rigorous development of the theory behind the statistical methodology of regression and analysis of variance (ANOVA). It seamlessly incorporates these concepts using non-full-rank design matrices and emphasizes the exact, finite sample theory supporting common statistical methods.

With coverage steadily progressing in complexity, the text first provides examples of the general linear model, including multiple regression models, one-way ANOVA, mixed-effects models, and time series models. It then introduces the basic algebra and geometry of the linear least squares problem, before delving into estimability and the Gauss–Markov model. After presenting the statistical tools of hypothesis tests and confidence intervals, the author analyzes mixed models, such as two-way mixed ANOVA, and the multivariate linear model. The appendices review linear algebra fundamentals and results as well as Lagrange multipliers.

This book enables complete comprehension of the material by taking a general, unifying approach to the theory, fundamentals, and exact results of linear models.

Table of Contents

Preface. Examples of the General Linear Model. The Linear Least Squares Problem. Estimability and Least Squares Estimators. Gauss–Markov Model. Distributional Theory. Statistical Inference. Further Topics in Testing. Variance Components and Mixed Models. The Multivariate Linear Model. Appendices. Bibliography.

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Reviews

"… I found the book very helpful. … the result is very nice, very readable, and in particular I like the idea of avoiding leaps in the development and proofs, or referring to other sources for the details of the proofs. This is a useful well-written instructive book."
International Statistical Review

"This work provides a brief, and also complete, foundation for the theory of basic linear models . . . can be used for graduate courses on linear models."
– Nicoleta Breaz, Zentralblatt Math

". . . well written . . . would serve well as the textbook for an introductory course in linear models, or as references for researchers who would like to review the theory of linear models."
Justine Shults, Department of Biostatistics, University of Pennsylvania School of Medicine, Journal of Biopharmaceutical Statistics