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Generalized Linear Models: with Applications in Engineering and the Sciences, 2nd Edition

ISBN: 978-0-470-45463-3
496 pages
March 2010
Generalized Linear Models: with Applications in Engineering and the Sciences, 2nd Edition (0470454636) cover image
Praise for the First Edition

"The obvious enthusiasm of Myers, Montgomery, and Vining and their reliance on their many examples as a major focus of their pedagogy make Generalized Linear Models a joy to read. Every statistician working in any area of applied science should buy it and experience the excitement of these new approaches to familiar activities."
—Technometrics

Generalized Linear Models: With Applications in Engineering and the Sciences, Second Edition continues to provide a clear introduction to the theoretical foundations and key applications of generalized linear models (GLMs). Maintaining the same nontechnical approach as its predecessor, this update has been thoroughly extended to include the latest developments, relevant computational approaches, and modern examples from the fields of engineering and physical sciences.

This new edition maintains its accessible approach to the topic by reviewing the various types of problems that support the use of GLMs and providing an overview of the basic, related concepts such as multiple linear regression, nonlinear regression, least squares, and the maximum likelihood estimation procedure. Incorporating the latest developments, new features of this Second Edition include:

  • A new chapter on random effects and designs for GLMs

  • A thoroughly revised chapter on logistic and Poisson regression, now with additional results on goodness of fit testing, nominal and ordinal responses, and overdispersion

  • A new emphasis on GLM design, with added sections on designs for regression models and optimal designs for nonlinear regression models

  • Expanded discussion of weighted least squares, including examples that illustrate how to estimate the weights

  • Illustrations of R code to perform GLM analysis

The authors demonstrate the diverse applications of GLMs through numerous examples, from classical applications in the fields of biology and biopharmaceuticals to more modern examples related to engineering and quality assurance. The Second Edition has been designed to demonstrate the growing computational nature of GLMs, as SAS®, Minitab®, JMP®, and R software packages are used throughout the book to demonstrate fitting and analysis of generalized linear models, perform inference, and conduct diagnostic checking. Numerous figures and screen shots illustrating computer output are provided, and a related FTP site houses supplementary material, including computer commands and additional data sets.

Generalized Linear Models, Second Edition is an excellent book for courses on regression analysis and regression modeling at the upper-undergraduate and graduate level. It also serves as a valuable reference for engineers, scientists, and statisticians who must understand and apply GLMs in their work.

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Preface.

1. Introduction to Generalized Linear Models.

1.1 Linear Models.

1.2 Nonlinear Models.

1.3 The Generalized Linear Model.

2. Linear Regression Models.

2.1 The Linear Regression Model and Its Application.

2.2 Multiple Regression Models.

2.3 Parameter Estimation Using Maximum Likelihood.

2.4 Model Adequacy Checking.

2.5 Using R to Perform Linear Regression Analysis.

2.6 Parameter Estimation by Weighted Least Squares.

2.7 Designs for Regression Models.

3. Nonlinear Regression Models.

3.1 Linear and Nonlinear Regression Models.

3.2 Transforming to a Linear Model.

3.3 Parameter Estimation in a Nonlinear System.

3.4 Statistical Inference in Nonlinear Regression.

3.5 Weighted Nonlinear Regression.

3.6 Examples of Nonlinear Regression Models.

3.7 Designs for Nonlinear Regression Models.

4. Logistic and Poisson Regression Models.

4.1 Regression Models Where the Variance Is a Function of the Mean.

4.2 Logistic Regression Models.

4.3 Poisson Regression.

4.4 Overdispersion in Logistic and Poisson Regression.

5. The Generalized Linear Model.

5.1 The Exponential Family of Distributions.

5.2 Formal Structure for the Class of Generalized Linear Models.

5.3 Likelihood Equations for Generalized Linear models.

5.4 Quasi-Likelihood.

5.5 Other Important Distributions for Generalized Linear Models.

5.6 A Class of Link Functions—The Power Function.

5.7 Inference and Residual Analysis for Generalized Linear Models.

5.8 Examples with the Gamma Distribution.

5.9 Using R to Perform GLM Analysis.

5.10 GLM and Data Transformation.

5.11 Modeling Both a Process Mean and Process Variance Using GLM.

5.12 Quality of Asymptotic Results and Related Issues.

6. Generalized Estimating Equations.

6.1 Data Layout for Longitudinal Studies.

6.2 Impact of the Correlation Matrix R.

6.3 Iterative Procedure in the Normal Case, Identity Link.

6.4 Generalized Estimating Equations for More Generalized Linear Models.

6.5 Examples.

6.6 Summary.

7. Random Effects in Generalized Linear Models.

7.1 Linear Mixed Effects Models.

7.2 Generalized Linear Mixed Models.

7.3 Generalized Linear Mixed Models Using Bayesian.

8. Designed Experiments and the Generalized Linear Model.

8.1 Introduction.

8.2 Experimental Designs for Generalized Linear Models.

8.3 GLM Analysis of Screening Experiments.

Appendix A.1 Background on Basic Test Statistics.

Appendix A.2 Background from the Theory of Linear Models.

Appendix A.3 The Gauss—Markov Theorem, Var(ε) = σ2I.

Appendix A.4 The Relationship Between Maximum Likelihood Estimation of the Logistic Regression Model and Weighted Least Squares.

Appendix A.5 Computational Details for GLMs for a Canonical Link.

Appendix A.6 Computations Details for GLMs for a Noncanonical Link.

References.

Index. 

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Raymond H. Myers, PhD, is Professor Emeritus in the Department of Statistics at Virginia Polytechnic Institute and State University. He has more than forty years of academic experience in the areas of experimental design and analysis, response surface analysis, and designs for nonlinear models. A Fellow of the American Statistical Society, Dr. Myers is the coauthor of numerous books including Response Surface Methodology: Process and Product Optimization Using Designed Experiments, Third Edition (Wiley).

Douglas C. Montgomery, PhD, is Regents' Professor of Industrial Engineering and Statistics at Arizona State University. Dr. Montgomery has more than thirty years of academic and consulting experience and has devoted his research to engineering statistics, specifically the design and analysis of experiments. He has authored or coauthored numerous journal articles and twelve books, including Response Surface Methodology: Process and Product Optimization Using Designed Experiments, Third Edition; Introduction to Linear Regression Analysis, Fourth Edition; and Introduction to Time Series Analysis and Forecasting, all published by Wiley.

G. Geoffrey Vining, PhD, is Professor in the Department of Statistics at Virginia Polytechnic Institute and State University. A Fellow of both the American Statistical Association and the American Society for Quality, Dr. Vining is also the coauthor of Introduction to Linear Regression Analysis, Fourth Edition (Wiley).

Timothy J. Robinson, PhD, is Associate Professor in the Department of Statistics at the University of Wyoming. He has written numerous journal articles in the areas of design of experiments, response surface methodology, and applications of categorical data analysis in engineering, medicine, and the environmental sciences.

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  • This new edition has been thoroughly extended to include the latest developments in the field, the most relevant computational approaches, and the most relevant examples from the fields of engineering and the physical sciences.
  • The authors now provide a new emphasis on GLM design, with new sections on designs for regression models, optimal designs for nonlinear regression models, and a new chapter on experimental designs of GLMs.
  • A new chapter on random effects in generalized linear models provides a thorough discussion of the Bayesian approach.
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  • Additional and new examples from various fields of study are provided throughout, and can be easily worked with using the SAS, Minitab, JMP, and R software packages, making it accessible to a wide audience.
  • A related Web site houses supplementary material, including computer commands and additional data sets.
  • Extensive illustrations and screen shots promote the computational nature of the text as well as the many modeling and design capabilities of the applied JMP software.

 

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"Generalized linear models, second edition, is an excellent book for courses on regression analysis and regression modeling at the upper-undergraduate and graduate levels. It also serves as a valuable reference for engineers, scientists, and statisticians who must understand and apply GLMs in their work." (Mathematical Reviews, 2011)

 

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