A First Course in Linear Model Theory / Edition 2

by Nalini Ravishanker, Zhiyi Chi, Dipak K. Dey

Overview

Thoroughly updated throughout, A First Course in Linear Model Theory, Second Edition is an intermediate-level statistics text that fills an important gap by presenting the theory of linear statistical models at a level appropriate for senior undergraduate or first-year graduate students. With an innovative approach, the authors introduce to students the mathematical and statistical concepts and tools that form a foundation for studying the theory and applications of both univariate and multivariate linear models. In addition to adding R functionality, this second edition features three new chapters and several sections on new topics that are extremely relevant to the current research in statistical methodology. Revised or expanded topics include linear fixed, random and mixed effects models, generalized linear models, Bayesian and hierarchical linear models, model selection, multiple comparisons, and regularized and robust regression.

New to the Second Edition:

• Coverage of inference for linear models has been expanded into two chapters.
• Expanded coverage of multiple comparisons, random and mixed effects models, model selection, and missing data.
• A new chapter on generalized linear models (Chapter 12).
• A new section on multivariate linear models in Chapter 13, and expanded coverage of the Bayesian linear models and longitudinal models.
• A new section on regularized regression in Chapter 14.
• Detailed data illustrations using R.

The authors' fresh approach, methodical presentation, wealth of examples, use of R, and introduction to topics beyond the classical theory set this book apart from other texts on linear models. It forms a refreshing and invaluable first step in students'study of advanced linear models, generalized linear models, nonlinear models, and dynamic models.

Product Details

ISBN-13:	9781439858059
Publisher:	Taylor & Francis
Publication date:	10/19/2021
Series:	Chapman & Hall/CRC Texts in Statistical Science
Edition description:	2nd ed.
Pages:	530
Product dimensions:	7.00(w) x 10.00(h) x (d)

About the Author

Nalini Ravishanker, Zhiyi Chi and Dipak K. Dey are Professors in the Department of Statistics at the University of Connecticut, Storrs, USA.

Table of Contents

1. A Review of Vector and Matrix Algebra. 2. Properties of Special Matrices. 3. Generalized Inverses and Solutions to Linear Systems. 4. The General Linear Model. 5. Multivariate Normal and Related Distributions. 6. Sampling from the Multivariate Normal Distribution. 7. Inference for the General Linear Model-I. 8. Inference for the General Linear Model-II. 9. Multiple Linear Regression Models. 10. Fixed-Effects Linear Models. 11. Random-Effects and Mixed-Effects Models. 12. Generalized Linear Models. 13. Special Topics. 14. Miscellaneous Topics. Appendices.

Editorial Reviews

"A First Course in Linear Model Theory is an excellent graduate-level textbook that comprehensively covers the now classical linear regression model. Its well-structured organization, thorough mathematical review, and clear presentation of core concepts make it an excellent, self-contained resource for a first course in linear models, both for instructors and students. Moreover, the book offers numerous examples, several exercises (some with solutions), R code, and detailed proofs for key results, making it also a good resource for self-study."

Carlos Cinelli, University of Washington USA, The American Statistician, October 2023.

From the Publisher

Ravishanker and Dey (both statistics, U. of Connecticut) present this intermediate-level statistics textbook designed for senior undergraduate and first-year graduate students. The text covers the standard theory of linear models, with numerous applications in simple and multiple regression, and fixed, random, and mixed-effects models; introduces generalized linear models with examples; and presents some current topics, including Bayesian linear, general additive, dynamic linear and longitudinal models. The text is written for a two-semester course, but includes suggested adaptions to a one-semester course. Requires some knowledge of statistics, including elementary sampling distributions, basic estimation theory and hypothesis testing at an undergraduate level. Annotation c. Book News, Inc., Portland, OR (booknews.com)