Myers / Montgomery / Vining Generalized Linear Models

with Applications in Engineering and the Sciences
2. Auflage 2012
ISBN: 978-0-470-55697-9
Verlag: John Wiley & Sons
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 520 Seiten, E-Book

Reihe: Wiley Series in Probability and Statistics

Praise for the First Edition
"The obvious enthusiasm of Myers, Montgomery, and Vining andtheir reliance on their many examples as a major focus of theirpedagogy make Generalized Linear Models a joy to read. Everystatistician working in any area of applied science should buy itand experience the excitement of these new approaches to familiaractivities."
--Technometrics
Generalized Linear Models: With Applications in Engineeringand the Sciences, Second Edition continues to provide a clearintroduction to the theoretical foundations and key applications ofgeneralized linear models (GLMs). Maintaining the same nontechnicalapproach as its predecessor, this update has been thoroughlyextended to include the latest developments, relevant computationalapproaches, and modern examples from the fields of engineering andphysical sciences.
This new edition maintains its accessible approach to the topicby reviewing the various types of problems that support the use ofGLMs and providing an overview of the basic, related concepts suchas multiple linear regression, nonlinear regression, least squares,and the maximum likelihood estimation procedure. Incorporating thelatest developments, new features of this Second Editioninclude:
* 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 andordinal responses, and overdispersion
* A new emphasis on GLM design, with added sections on designs forregression models and optimal designs for nonlinear regressionmodels
* Expanded discussion of weighted least squares, includingexamples that illustrate how to estimate the weights
* Illustrations of R code to perform GLM analysis
The authors demonstrate the diverse applications of GLMs throughnumerous examples, from classical applications in the fields ofbiology and biopharmaceuticals to more modern examples related toengineering and quality assurance. The Second Edition hasbeen designed to demonstrate the growing computational nature ofGLMs, as SAS®, Minitab®, JMP®, and R softwarepackages are used throughout the book to demonstrate fitting andanalysis of generalized linear models, perform inference, andconduct diagnostic checking. Numerous figures and screen shotsillustrating computer output are provided, and a related FTP sitehouses supplementary material, including computer commands andadditional data sets.
Generalized Linear Models, Second Edition is an excellentbook for courses on regression analysis and regression modeling atthe upper-undergraduate and graduate level. It also serves as avaluable reference for engineers, scientists, and statisticians whomust understand and apply GLMs in their work.

Autoren/Hrsg.

Myers, Raymond H.

Montgomery, Douglas C.

Vining, G. Geoffrey

Robinson, Timothy J.

Inhaltsverzeichnis

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 theMean.
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 LinearModels.
5.3 Likelihood Equations for Generalized Linear models.
5.4 Quasi-Likelihood.
5.5 Other Important Distributions for Generalized LinearModels.
5.6 A Class of Link Functions--The Power Function.
5.7 Inference and Residual Analysis for Generalized LinearModels.
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 UsingGLM.
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 LinearModels.
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 LinearModel.
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 LinearModels.
Appendix A.3 The Gauss--Markov Theorem, Var(epsilon) =sigma²I.
Appendix A.4 The Relationship Between Maximum LikelihoodEstimation of the Logistic Regression Model and Weighted LeastSquares.
Appendix A.5 Computational Details for GLMs for a CanonicalLink.
Appendix A.6 Computations Details for GLMs for a NoncanonicalLink.
References.
Index.

Über Autor(innen)

Raymond H. Myers, PhD, is Professor Emeritus in theDepartment of Statistics at Virginia Polytechnic Institute andState University. He has more than forty years of academicexperience in the areas of experimental design and analysis,response surface analysis, and designs for nonlinear models. AFellow of the American Statistical Society, Dr. Myers is thecoauthor of numerous books including Response SurfaceMethodology: Process and Product Optimization Using DesignedExperiments, Third Edition (Wiley).
Douglas C. Montgomery, PhD, is Regents' Professor ofIndustrial Engineering and Statistics at Arizona State University.Dr. Montgomery has more than thirty years of academic andconsulting experience and has devoted his research to engineeringstatistics, specifically the design and analysis of experiments. Hehas authored or coauthored numerous journal articles and twelvebooks, including Response Surface Methodology: Process andProduct Optimization Using Designed Experiments, Third Edition;Introduction to Linear Regression Analysis, Fourth Edition; andIntroduction to Time Series Analysis and Forecasting, allpublished by Wiley.
G. Geoffrey Vining, PhD, is Professor in the Departmentof Statistics at Virginia Polytechnic Institute and StateUniversity. A Fellow of both the American Statistical Associationand the American Society for Quality, Dr. Vining is also thecoauthor of Introduction to Linear Regression Analysis, FourthEdition (Wiley).
Timothy J. Robinson, PhD, is Associate Professor in theDepartment of Statistics at the University of Wyoming. He haswritten numerous journal articles in the areas of design ofexperiments, response surface methodology, and applications ofcategorical data analysis in engineering, medicine, and theenvironmental sciences.