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Foundations of Linear and Generalized Linear Models

Book Description

A valuable overview of the most important ideas and results in statistical modeling

Written by a highly-experienced author, Foundations of Linear and Generalized Linear Models is a clear and comprehensive guide to the key concepts and results of linearstatistical models. The book presents a broad, in-depth overview of the most commonly usedstatistical models by discussing the theory underlying the models, R software applications,and examples with crafted models to elucidate key ideas and promote practical modelbuilding.

The book begins by illustrating the fundamentals of linear models, such as how the model-fitting projects the data onto a model vector subspace and how orthogonal decompositions of the data yield information about the effects of explanatory variables. Subsequently, the book covers the most popular generalized linear models, which include binomial and multinomial logistic regression for categorical data, and Poisson and negative binomial loglinear models for count data. Focusing on the theoretical underpinnings of these models, Foundations of Linear and Generalized Linear Models also features:

  • An introduction to quasi-likelihood methods that require weaker distributional assumptions, such as generalized estimating equation methods

  • An overview of linear mixed models and generalized linear mixed models with random effects for clustered correlated data, Bayesian modeling, and extensions to handle problematic cases such as high dimensional problems

  • Numerous examples that use R software for all text data analyses

  • More than 400 exercises for readers to practice and extend the theory, methods, and data analysis

  • A supplementary website with datasets for the examples and exercises

  • An invaluable textbook for upper-undergraduate and graduate-level students in statistics and biostatistics courses, Foundations of Linear and Generalized Linear Models is also an excellent reference for practicing statisticians and biostatisticians, as well as anyone who is interested in learning about the most important statistical models for analyzing data.

    Table of Contents

    1. Preface
      1. Purpose of this Book
      2. Use as a Textbook
      3. Acknowledgments
    2. Chapter 1: Introduction to Linear and Generalized Linear Models
      1. 1.1 Components of A Generalized Linear Model
      2. 1.2 Quantitative/Qualitative Explanatory Variables and Interpreting Effects
      3. 1.3 Model Matrices and Model Vector Spaces
      4. 1.4 Identifiability and Estimability
      5. 1.5 Example: Using Software to Fit A GLM
      6. Chapter Notes
      7. Exercises
      8. Notes
    3. Chapter 2: Linear Models: Least Squares Theory
      1. 2.1 Least Squares Model Fitting
      2. 2.2 Projections of Data Onto Model Spaces
      3. 2.3 Linear Model Examples: Projections and SS Decompositions
      4. 2.4 Summarizing Variability in a Linear Model
      5. 2.5 Residuals, Leverage, and Influence
      6. 2.6 Example: Summarizing the Fit of a Linear Model
      7. 2.7 Optimality of Least Squares and Generalized Least Squares
      8. Chapter Notes
      9. Exercises
      10. Notes
    4. Chapter 3: Normal Linear Models: Statistical Inference
      1. 3.1 Distribution Theory for Normal Variates
      2. 3.2 Significance Tests for Normal Linear Models
      3. 3.3 Confidence Intervals and Prediction Intervals for Normal Linear Models
      4. 3.4 Example: Normal Linear Model Inference
      5. 3.5 Multiple Comparisons: Bonferroni, Tukey, and FDR Methods
      6. Chapter Notes
      7. EXERCISES
      8. Notes
    5. Chapter 4: Generalized Linear Models: Model Fitting and Inference
      1. 4.1 Exponential Dispersion Family Distributions for a GLM
      2. 4.2 Likelihood and Asymptotic Distributions for GLMs
      3. 4.3 Likelihood-Ratio/Wald/Score Methods of Inference for GLM Parameters
      4. 4.4 Deviance of a GLM, Model Comparison, and Model Checking
      5. 4.5 Fitting Generalized Linear Models
      6. 4.6 Selecting Explanatory Variables for a GLM
      7. 4.7 Example: Building a GLM
      8. Appendix: GLM Analogs of Orthogonality Results for Linear Models
      9. Chapter Notes
      10. Exercises
      11. Notes
    6. Chapter 5: Models for Binary Data
      1. 5.1 Link Functions for Binary Data
      2. 5.2 Logistic Regression: Properties and Interpretations
      3. 5.3 Inference About Parameters of Logistic Regression Models
      4. 5.4 Logistic Regression Model Fitting
      5. 5.5 Deviance and Goodness of Fit for Binary GLMs
      6. 5.6 Probit and Complementary Log–Log Models
      7. 5.7 Examples: Binary Data Modeling
      8. Chapter Notes
      9. Exercises
      10. Notes
    7. Chapter 6: Multinomial Response Models
      1. 6.1 Nominal Responses: Baseline-Category Logit Models
      2. 6.2 Ordinal Responses: Cumulative Logit and Probit Models
      3. 6.3 Examples: Nominal and Ordinal Responses
      4. Chapter Notes
      5. Exercises
      6. Notes
    8. Chapter 7: Models for Count Data
      1. 7.1 Poisson GLMs for Counts and Rates
      2. 7.2 Poisson/Multinomial Models for Contingency Tables
      3. 7.3 Negative Binomial GLMS
      4. 7.4 Models for Zero-Inflated Data
      5. 7.5 Example: Modeling Count Data
      6. Chapter Notes
      7. Exercises
      8. Notes
    9. Chapter 8: Quasi-Likelihood Methods
      1. 8.1 Variance Inflation for Overdispersed Poisson and Binomial GLMs
      2. 8.2 Beta-Binomial Models and Quasi-Likelihood Alternatives
      3. 8.3 Quasi-Likelihood and Model Misspecification
      4. Chapter Notes
      5. Exercises
      6. Notes
    10. Chapter 9: Modeling Correlated Responses
      1. 9.1 Marginal Models and Models with Random Effects
      2. 9.2 Normal Linear Mixed Models
      3. 9.3 Fitting and Prediction for Normal Linear Mixed Models
      4. 9.4 Binomial and Poisson GLMMs
      5. 9.5 GLMM Fitting, Inference, and Prediction
      6. 9.6 Marginal Modeling and Generalized Estimating Equations
      7. 9.7 Example: Modeling Correlated Survey Responses
      8. Chapter Notes
      9. Exercises
      10. Notes
    11. Chapter 10: Bayesian Linear and Generalized Linear Modeling
      1. 10.1 The Bayesian Approach to Statistical Inference
      2. 10.2 Bayesian Linear Models
      3. 10.3 Bayesian Generalized Linear Models
      4. 10.4 Empirical Bayes and Hierarchical Bayes Modeling
      5. Chapter Notes
      6. Exercises
      7. Notes
    12. Chapter 11: Extensions of Generalized Linear Models
      1. 11.1 Robust Regression and Regularization Methods for Fitting Models
      2. 11.2 Modeling With Large <i xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:svg="http://www.w3.org/2000/svg">P</i>
      3. 11.3 Smoothing, Generalized Additive Models, and Other GLM Extensions
      4. Chapter Notes
      5. Exercises
      6. Notes
    13. Appendix A: Supplemental Data Analysis Exercises
      1. Notes
    14. Appendix B: Solution Outlines for Selected Exercises
      1. Chapter 1
      2. Chapter 2
      3. Chapter 3
      4. Chapter 4
      5. Chapter 5
      6. Chapter 6
      7. Chapter 7
      8. Chapter 8
      9. Chapter 9
      10. Chapter 10
      11. Chapter 11
    15. References
    16. Author Index
    17. Example Index
    18. Subject Index
    19. Wiley Series
    20. End User License Agreement