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

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Overview

This volume serves as an introductory text or reference on generalized linear models. The range of theoretical topics and applications give this book broad appeal to practicing professionals in a variety of fields and as a textbook for students in regression courses.
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Editorial Reviews

From The Critics
Suitable for graduate students or working engineers, this introduction to generalized linear models (GLMs) features examples of GLMs as applied to a variety of settings. It reviews the types of problems that support the use of GLMs and provides an overviews of the fundamental concepts of the filed. The authors teach at the Virginia Polytechnic Institute and Arizona State University. Annotation c. Book News, Inc., Portland, OR
From the Publisher
"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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Product Details

  • ISBN-13: 9780470454633
  • Publisher: Wiley
  • Publication date: 2/22/2010
  • Series: Wiley Series in Probability and Statistics Series , #791
  • Edition description: New Edition
  • Edition number: 2
  • Pages: 496
  • Sales rank: 933,277
  • Product dimensions: 6.40 (w) x 9.30 (h) x 1.10 (d)

Table of Contents

Preface xi
1 Introduction to Generalized Linear Models 1
1.1 Linear Models 1
1.2 Nonlinear Models 3
1.3 The Generalized Linear Model 4
2 Linear Regression Models 7
2.1 The Linear Regression Model and Its Application 7
2.2 Multiple Regression Models 7
2.2.1 Parameter Estimation with Ordinary Least Squares 7
2.2.2 Properties of the Least Squares Estimator and Estimation of [sigma superscript 2] 15
2.2.3 Hypothesis Testing in Multiple Regression 17
2.2.4 Confidence Intervals in Multiple Regression 25
2.2.5 Prediction of New Response Observations 29
2.2.6 Linear Regression Computer Output 31
2.3 Parameter Estimation Using Maximum Likelihood 32
2.3.1 Parameter Estimation Under the Normal-Theory Assumptions 32
2.3.2 Properties of the Maximum Likelihood Estimators 33
2.4 Model Adequacy Checking 34
2.4.1 Residual Analysis 34
2.4.2 Transformation on the Response Variable Using the Box-Cox Method 39
2.4.3 Scaling Residuals 41
2.4.4 Influence Diagnostics 46
2.5 Parameter Estimation by Weighted Least Squares 48
2.5.1 The Constant Variance Assumption 48
2.5.2 Generalized and Weighted Least Squares 49
2.5.3 Generalized Least Squares and Maximum Likelihood 52
Exercises 52
3 Nonlinear Regression Models 63
3.1 Linear and Nonlinear Regression Models 63
3.1.1 Linear Regression Models 63
3.1.2 Nonlinear Regression Models 64
3.2 Transforming to a Linear Model 65
3.3 Parameter Estimation in a Nonlinear System 69
3.3.1 Nonlinear Least Squares 69
3.3.2 The Geometry of Linear and Nonlinear Least Squares 71
3.3.3 Maximum Likelihood Estimation 71
3.3.4 Linearization and the Gauss-Newton Method 73
3.3.5 Other Parameter Estimation Methods 83
3.3.6 Starting Values 85
3.4 Statistical Inference in Nonlinear Regression 86
3.5 Weighted Nonlinear Regression 90
3.6 Examples of Nonlinear Regression Models 91
Exercises 92
4 Logistic and Poisson Regression Models 100
4.1 Regression Models Where the Variance Is a Function of the Mean 100
4.2 The Logistic Regression Model 101
4.3 Parameter Estimation Using Maximum Likelihood 103
4.4 Different Forms of Statistical Inference Using Logistic Regression 106
4.4.1 Dispersion Properties of Maximum Likelihood Estimators in Logistic Regression 108
4.4.2 Wald Inference Using Logistic Regression 109
4.5 Examples Using Logistic Regression 114
4.6 Other Considerations in Logistic Regression 120
4.6.1 Other Models for Binary Responses 120
4.6.2 Lack-of-Fit Tests in Logistic Regression 122
4.7 The Concept of Overdispersion in Logistic Regression 125
4.7.1 Variation Between Binomial Parameters or Correlation Between Binomial Observations 126
4.7.2 Effect of Overdispersion on Results 127
4.7.3 Adjustments for Overdispersion 128
4.8 Introduction to Poisson Regression 131
4.9 Maximum Likelihood Estimators for Poisson Regression 132
4.10 Applications in Poisson Regression 133
4.11 Examples Using Poisson Regression 136
4.12 Classification Variables and Extensions to the Anova Model 148
Exercises 149
5 The Family of Generalized Linear Models 157
5.1 The Exponential Family of Distributions 157
5.2 Formal Structure for the Class of Generalized Linear Models 160
5.3 Likelihood Equations for Generalized Linear Models 162
5.4 Quasi-likelihood 167
5.5 Other Important Distributions for Generalized Linear Models 168
5.5.1 The Gamma "Family" 169
5.5.2 Canonical Link Function for the Gamma Distribution 170
5.5.3 Log Link for the Gamma Distribution 171
5.6 A Class of Link Functions--The Power Function 172
5.7 Inference and Residual Analysis for Generalized Linear Models 173
5.8 Examples with the Gamma Distribution 176
Exercises 190
6 Generalized Estimating Equations 195
6.1 Data Layout for Longitudinal Studies 195
6.2 Impact of the Correlation Matrix R 197
6.3 Iterative Procedure in the Normal Case, Identity Link 198
6.4 Generalized Estimating Equations for More Generalized Linear Models 200
6.4.1 Structure of V[subscript j] 201
6.4.2 Iterative Computation of Elements in R 206
6.5 Examples 207
6.6 Summary 229
Exercises 229
7 Further Advances and Applications in GLM 236
7.1 Introduction 236
7.2 Experimental Designs for Generalized Linear Models 237
7.2.1 Review of Two-Level Factorial and Fractional Factorial Designs 237
7.2.2 Difficulty in Finding Optimal Designs in GLMs 239
7.2.3 The Use of Standard Designs in Generalized Linear Models 241
7.2.4 Orthogonal Designs in GLM: The Variance-Stabilizing Link 243
7.2.5 Use of Other Links 246
7.2.6 Further Comments Concerning the Nature of the Design 250
7.3 Quality of Asymptotic Results and Related Issues 253
7.3.1 Development of a Wald Confidence Interval 254
7.3.2 Estimation of Exponential Family Scale Parameter 261
7.3.3 Impact of Link Misspecification on Confidence Interval Coverage and Precision 262
7.3.4 Illustration of Binomial Distribution with a True Identity Link but with Logit Link Assumed 263
7.3.5 Poisson Distribution with a True Identity Link but with Log Link Assumed 265
7.3.6 Gamma Distribution with a True Inverse Link but with Log Link Assumed 266
7.3.7 Summary of Link Misspecification on Confidence Interval Coverage and Precision 267
7.3.8 Impact of Model Misspecification on Confidence Interval Coverage and Precision 267
7.4 GLM Analysis of Screening Experiments 270
7.5 GLM and Data Transformation 281
7.6 Modeling Both a Process Mean and Process Variance Using GLM 288
7.6.1 When Replication Is Present 288
7.6.2 Case of Unreplicated Experiments 294
7.7 Generalized Additive Models 297
7.7.1 Nonparametric Regression in One Regressor 297
7.7.2 Generalized Additive Models 304
Exercises 309
Appendices
Appendix A.1 Background on Basic Test Statistics 314
Appendix A.2 Background from the Theory of Linear Models 317
Appendix A.3 The Gauss-Markov Theorem, var([varepsilon]) = [sigma superscript 2]I 322
Appendix A.4 The Relationship Between Maximum Likelihood Estimation of the Logistic Regression Model and Weighted Least Squares 324
Appendix A.5 Computational Details for GLMs for a Canonical Link 328
Appendix A.6 Computational Details for GLMs for a Noncanonical Link 331
References 334
Index 339
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