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."—TechnometricsGeneralized 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 GLMsA thoroughly revised chapter on logistic and Poisson regression, now with additional results on goodness of fit testing, nominal and ordinal responses, and overdispersionA new emphasis on GLM design, with added sections on designs for regression models and optimal designs for nonlinear regression modelsExpanded discussion of weighted least squares, including examples that illustrate how to estimate the weightsIllustrations of R code to perform GLM analysisThe 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.
Author(s): Raymond H. Myers, Douglas C. Montgomery, G. Geoffrey Vining, Timothy J. Robinson
Edition: 2
Publisher: Wiley
Year: 2010
Language: English
Pages: 521
Tags: Библиотека;Компьютерная литература;R;
Generalized Linear Models: With Applications in Engineering and the Sciences......Page 5
Contents......Page 7
Preface......Page 13
1.1 Linear Models......Page 17
1.2 Nonlinear Models......Page 19
1.3 The Generalized Linear Model......Page 20
2.1 The Linear Regression Model and Its Application......Page 25
2.2.1 Parameter Estimation with Ordinary Least Squares......Page 26
2.2.2 Properties of the Least Squares Estimator and Estimation of σ2......Page 31
2.2.3 Hypothesis Testing in Multiple Regression......Page 35
2.2.4 Confidence Intervals in Multiple Regression......Page 45
2.2.5 Prediction of New Response Observations......Page 48
2.3.1 Parameter Estimation Under the Normal-Theory Assumptions......Page 50
2.3.2 Properties of the Maximum Likelihood Estimators......Page 54
2.4.1 Residual Analysis......Page 55
2.4.2 Transformation of the Response Variable Using the Box–Cox Method......Page 59
2.4.3 Scaling Residuals......Page 61
2.4.4 Influence Diagnostics......Page 66
2.5 Using R to Perform Linear Regression Analysis......Page 68
2.6.1 The Constant Variance Assumption......Page 70
2.6.2 Generalized and Weighted Least Squares......Page 71
2.7 Designs for Regression Models......Page 74
Exercises......Page 81
3.1.1 Linear Regression Models......Page 93
3.1.2 Nonlinear Regression Models......Page 94
3.1.3 Origins of Nonlinear Models......Page 95
3.2 Transforming to a Linear Model......Page 97
3.3.1 Nonlinear Least Squares......Page 100
3.3.3 Maximum Likelihood Estimation......Page 102
3.3.4 Linearization and the Gauss–Newton Method......Page 105
3.3.5 Using R to Perform Nonlinear Regression Analysis......Page 115
3.3.6 Other Parameter Estimation Methods......Page 116
3.3.7 Starting Values......Page 117
3.4 Statistical Inference in Nonlinear Regression......Page 118
3.5 Weighted Nonlinear Regression......Page 122
3.6 Examples of Nonlinear Regression Models......Page 123
3.7 Designs for Nonlinear Regression Models......Page 124
Exercises......Page 127
4.1 Regression Models Where the Variance Is a Function of the Mean......Page 135
4.2.1 Models with a Binary Response Variable......Page 136
4.2.2 Estimating the Parameters in a Logistic Regression Model......Page 139
4.2.3 Interpellation of the Parameters in a Logistic Regression Model......Page 144
4.2.4 Statistical Inference on Model Parameters......Page 148
4.2.5 Lack-of-Fit Tests in Logistic Regression......Page 159
4.2.6 Diagnostic Checking in Logistic Regression......Page 171
4.2.7 Classification and the Receiver Operating Characteristic Curve......Page 178
4.2.8 A Biological Example of Logistic Regression......Page 180
4.2.9 Other Models for Binary Response Data......Page 184
4.2.10 More than Two Categorical Outcomes......Page 185
4.3 Poisson Regression......Page 192
4.4 Overdispersion in Logistic and Poisson Regression......Page 200
Exercises......Page 205
5.1 The Exponential Family of Distributions......Page 218
5.2 Formal Structure for the Class of Generalized Linear Models......Page 221
5.3 Likelihood Equations for Generalized Linear models......Page 223
5.4 Quasi-Likelihood......Page 227
5.5 Other Important Distributions for Generalized Linear Models......Page 229
5.5.1 The Gamma Family......Page 230
5.5.3 Log Link for the Gamma Distribution......Page 231
5.6 A Class of Link Functions—The Power Function......Page 232
5.7 Inference and Residual Analysis for Generalized Linear Models......Page 233
5.8 Examples with the Gamma Distribution......Page 236
5.9 Using R to Perform GLM Analysis......Page 245
5.9.1 Logistic Regression, Each Response is a Success or Failure......Page 247
5.9.3 Poisson Regression......Page 248
5.10 GLM and Data Transformation......Page 249
5.11.1 The Replicated Case......Page 256
5.11.2 The Unreplicated Case......Page 260
5.12.1 Development of an Alternative Wald Confidence Interval......Page 266
5.12.2 Estimation of Exponential Family Scale Parameter......Page 275
5.12.4 Illustration of Binomial Distribution with a True Identity Link but with Logit Link Assumed......Page 276
5.12.5 Poisson Distribution with a True Identity Link but with Log Link Assumed......Page 278
5.12.6 Gamma Distribution with a True Inverse Link but with Log Link Assumed......Page 279
5.12.8 Impact of Model Misspecification on Confidence Interval Coverage and Precision......Page 280
Exercises......Page 283
6.1 Data Layout for Longitudinal Studies......Page 288
6.2 Impact of the Correlation Matrix R......Page 290
6.3 Iterative Procedure in the Normal Case, Identity Link......Page 291
6.4 Generalized Estimating Equations for More Generalized Linear Models......Page 293
6.4.1 Structure of Vj......Page 294
6.5 Examples......Page 299
6.6 Summary......Page 324
Exercises......Page 327
7. Random Effects in Generalized Linear Models......Page 335
7.1.1 Linear Regression Models......Page 336
7.1.2 General Linear Mixed Effects Models......Page 338
7.1.3 Covariance Matrix, V......Page 342
7.1.4 Parameter Estimation in the General Linear Mixed Model......Page 348
7.1.5 Statistical Inference on Regression Coefficients and Variance Components......Page 350
7.1.6 Conditional and Marginal Means......Page 353
7.1.7 Estimation of the Random Coefficients......Page 354
7.1.8 Examples Revisited......Page 356
7.1.9 Diagnostics......Page 362
7.2 Generalized Linear Mixed Models......Page 370
7.2.1 The Generalized Linear Mixed Model......Page 373
7.2.2 Parameter Estimation in the GLMM......Page 376
7.2.3 Statistical Inference on Regression Coefficients and Variance Components......Page 382
7.2.4 Subject-Specific Versus Population-Averaged Prediction Models......Page 384
7.2.5 Examples Revisited......Page 385
7.2.6 Diagnostics......Page 398
7.3.1 Model Formulation......Page 404
7.3.2 Bayesian Inference......Page 406
7.3.3 Inference on Response Distribution Characteristics......Page 411
Exercises......Page 413
8.1 Introduction......Page 424
8.2.1 Review of Two-Level Factorial and Fractional Factorial Designs......Page 425
8.2.2 Finding Optimal Designs in GLMs......Page 427
8.2.3 The Use of Standard Designs in Generalized Linear Models......Page 437
8.2.4 Orthogonal Designs in GLM: The Variance-Stabilizing Link......Page 440
8.2.5 Use of Other Links......Page 443
8.2.6 Further Comments Concerning the Nature of the Design......Page 452
8.3 GLM Analysis of Screening Experiments......Page 453
Exercises......Page 474
Appendix A.1. Background on Basic Test Statistics......Page 480
Appendix A.2. Background from the Theory of Linear Models......Page 483
Appendix A.3. The Gauss–Markov Theorem, Var(ε) = σ2I......Page 488
Appendix A.4. The Relationship Between Maximum Likelihood Estimation of the Logistic Regression Model and Weighted Least Squares......Page 490
Appendix A.5. Computational Details for GLMs for a Canonical Link......Page 494
Appendix A.6. Computational Details for GLMs for a Noncanonical Link......Page 497
References......Page 500
Index......Page 509
