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E-raamat: Generalized Linear Models: with Applications in Engineering and the Sciences

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(Virginia Polytechnic and State University), (Georgia Institute of Technology), (University of Wyoming, USA), (Virginia Polytechnic Institute and State University)
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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.

Arvustused

"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)  

Preface xi
1 Introduction to Generalized Linear Models
1(8)
1.1 Linear Models
1(2)
1.2 Nonlinear Models
3(1)
1.3 The Generalized Linear Model
4(5)
2 Linear Regression Models
9(68)
2.1 The Linear Regression Model and Its Application
9(1)
2.2 Multiple Regression Models
10(24)
2.2.1 Parameter Estimation with Ordinary Least Squares
10(5)
2.2.2 Properties of the Least Squares Estimator and Estimation of σ2
15(4)
2.2.3 Hypothesis Testing in Multiple Regression
19(10)
2.2.4 Confidence Intervals in Multiple Regression
29(3)
2.2.5 Prediction of New Response Observations
32(2)
2.2.6 Linear Regression Computer Output
34(1)
2.3 Parameter Estimation Using Maximum Likelihood
34(5)
2.3.1 Parameter Estimation Under the Normal-Theory Assumptions
34(4)
2.3.2 Properties of the Maximum Likelihood Estimators
38(1)
2.4 Model Adequacy Checking
39(13)
2.4.1 Residual Analysis
39(4)
2.4.2 Transformation of the Response Variable Using the Box-Cox Method
43(2)
2.4.3 Scaling Residuals
45(5)
2.4.4 Influence Diagnostics
50(2)
2.5 Using R to Perform Linear Regression Analysis
52(2)
2.6 Parameter Estimation by Weighted Least Squares
54(4)
2.6.1 The Constant Variance Assumption
54(1)
2.6.2 Generalized and Weighted Least Squares
55(3)
2.6.3 Generalized Least Squares and Maximum Likelihood
58(1)
2.7 Designs for Regression Models
58(7)
Exercises
65(12)
3 Nonlinear Regression Models
77(42)
3.1 Linear and Nonlinear Regression Models
77(4)
3.1.1 Linear Regression Models
77(1)
3.1.2 Nonlinear Regression Models
78(1)
3.1.3 Origins of Nonlinear Models
79(2)
3.2 Transforming to a Linear Model
81(3)
3.3 Parameter Estimation in a Nonlinear System
84(18)
3.3.1 Nonlinear Least Squares
84(2)
3.3.2 The Geometry of Linear and Nonlinear Least Squares
86(1)
3.3.3 Maximum Likelihood Estimation
86(3)
3.3.4 Linearization and the Gauss-Newton Method
89(10)
3.3.5 Using R to Perform Nonlinear Regression Analysis
99(1)
3.3.6 Other Parameter Estimation Methods
100(1)
3.3.7 Starting Values
101(1)
3.4 Statistical Inference in Nonlinear Regression
102(4)
3.5 Weighted Nonlinear Regression
106(1)
3.6 Examples of Nonlinear Regression Models
107(1)
3.7 Designs for Nonlinear Regression Models
108(3)
Exercises
111(8)
4 Logistic and Poisson Regression Models
119(83)
4.1 Regression Models Where the Variance Is a Function of the Mean
119(1)
4.2 Logistic Regression Models
120(56)
4.2.1 Models with a Binary Response Variable
120(3)
4.2.2 Estimating the Parameters in a Logistic Regression Model
123(5)
4.2.3 Interpertation of the Parameters in a Logistic Regression Model
128(4)
4.2.4 Statistical Inference on Model Parameters
132(11)
4.2.5 Lack-of-Fit Tests in Logistic Regression
143(12)
4.2.6 Diagnostic Checking in Logistic Regression
155(7)
4.2.7 Classification and the Receiver Operating Characteristic Curve
162(2)
4.2.8 A Biological Example of Logistic Regression
164(4)
4.2.9 Other Models for Binary Response Data
168(1)
4.2.10 More than Two Categorical Outcomes
169(7)
4.3 Poisson Regression
176(8)
4.4 Overdispersion in Logistic and Poisson Regression
184(5)
Exercises
189(13)
5 The Generalized Linear Model
202(70)
5.1 The Exponential Family of Distributions
202(3)
5.2 Formal Structure for the Class of Generalized Linear Models
205(2)
5.3 Likelihood Equations for Generalized Linear models
207(4)
5.4 Quasi-Likelihood
211(2)
5.5 Other Important Distributions for Generalized Linear Models
213(3)
5.5.1 The Gamma Family
214(1)
5.5.2 Canonical Link Function for the Gamma Distribution
215(1)
5.5.3 Log Link for the Gamma Distribution
215(1)
5.6 A Class of Link Functions---The Power Function
216(1)
5.7 Inference and Residual Analysis for Generalized Linear Models
217(3)
5.8 Examples with the Gamma Distribution
220(9)
5.9 Using R to Perform GLM Analysis
229(4)
5.9.1 Logistic Regression, Each Response is a Success or Failure
231(1)
5.9.2 Logistic Regression, Response is the Number of Successes Out of n Trials
232(1)
5.9.3 Poisson Regression
232(1)
5.9.4 Using the Gamma Distribution with a Log Link
233(1)
5.10 GLM and Data Transformation
233(7)
5.11 Modeling Both a Process Mean and Process Variance Using GLM
240(10)
5.11.1 The Replicated Case
240(4)
5.11.2 The Unreplicated Case
244(6)
5.12 Quality of Asymptotic Results and Related Issues
250(17)
5.12.1 Development of an Alternative Wald Confidence Interval
250(9)
5.12.2 Estimation of Exponential Family Scale Parameter
259(1)
5.12.3 Impact of Link Misspecification on Confidence Interval Coverage and Precision
260(1)
5.12.4 Illustration of Binomial Distribution with a True Identity Link but with Logit Link Assumed
260(2)
5.12.5 Poisson Distribution with a True Identity Link but with Log Link Assumed
262(1)
5.12.6 Gamma Distribution with a True Inverse Link but with Log Link Assumed
263(1)
5.12.7 Summary of Link Misspecification on Confidence Interval Coverage and Precision
264(1)
5.12.8 Impact of Model Misspecification on Confidence Interval Coverage and Precision
264(3)
Exercises
267(5)
6 Generalized Estimating Equations
272(47)
6.1 Data Layout for Longitudinal Studies
272(2)
6.2 Impact of the Correlation Matrix R
274(1)
6.3 Iterative Procedure in the Normal Case, Identity Link
275(2)
6.4 Generalized Estimating Equations for More Generalized Linear Models
277(6)
6.4.1 Structure of Vj
278(5)
6.4.2 Iterative Computation of Elements in R
283(1)
6.5 Examples
283(25)
6.6 Summary
308(3)
Exercises
311(8)
7 Random Effects in Generalized Linear Models
319(89)
7.1 Linear Mixed Effects Models
320(34)
7.1.1 Linear Regression Models
320(2)
7.1.2 General Linear Mixed Effects Models
322(4)
7.1.3 Covariance Matrix, V
326(6)
7.1.4 Parameter Estimation in the General Linear Mixed Model
332(2)
7.1.5 Statistical Inference on Regression Coefficients and Variance Components
334(3)
7.1.6 Conditional and Marginal Means
337(1)
7.1.7 Estimation of the Random Coefficients
338(2)
7.1.8 Examples Revisited
340(6)
7.1.9 Diagnostics
346(8)
7.2 Generalized Linear Mixed Models
354(34)
7.2.1 The Generalized Linear Mixed Model
357(3)
7.2.2 Parameter Estimation in the GLMM
360(6)
7.2.3 Statistical Inference on Regression Coefficients and Variance Components
366(2)
7.2.4 Subject-Specific Versus Population-Averaged Prediction Models
368(1)
7.2.5 Examples Revisited
369(13)
7.2.6 Diagnostics
382(6)
7.3 Generalized Linear Mixed Models Using Bayesian Methods
388(9)
7.3.1 Model Formulation
388(2)
7.3.2 Bayesian Inference
390(5)
7.3.3 Inference on Response Distribution Characteristics
395(2)
Exercises
397(11)
8 Designed Experiments and the Generalized Linear Model
408(56)
8.1 Introduction
408(1)
8.2 Experimental Designs for Generalized Linear Models
409(28)
8.2.1 Review of Two-Level Factorial and Fractional Factorial Designs
409(2)
8.2.2 Finding Optimal Designs in GLMs
411(10)
8.2.3 The Use of Standard Designs in Generalized Linear Models
421(3)
8.2.4 Orthogonal Designs in GLM: The Variance-Stabilizing Link
424(3)
8.2.5 Use of Other Links
427(9)
8.2.6 Further Comments Concerning the Nature of the Design
436(1)
8.3 GLM Analysis of Screening Experiments
437(21)
Exercises
458(6)
Appendix A.1 Background on Basic Test Statistics 464(3)
Appendix A.2 Background from the Theory of Linear Models 467(5)
Appendix A.3 The Gauss-Markov Theorem, Var(ε) = σ2I 472(2)
Appendix A.4 The Relationship Between Maximum Likelihood Estimation of the Logistic Regression Model and Weighted Least Squares 474(4)
Appendix A.5 Computational Details for GLMs for a Canonical Link 478(3)
Appendix A.6 Computational Details for GLMs for a Noncanonical Link 481(3)
References 484(9)
Index 493
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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