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

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.