Book description
A valuable overview of the most important ideas and results in statistical modeling
Written by a highlyexperienced author, Foundations of Linear and Generalized Linear Models is a clear and comprehensive guide to the key concepts and results of linear statistical models. The book presents a broad, indepth overview of the most commonly used statistical 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 modelfitting 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 quasilikelihood 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 upperundergraduate and graduatelevel 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
 Preface
 Chapter 1: Introduction to Linear and Generalized Linear Models

Chapter 2: Linear Models: Least Squares Theory
 2.1 Least Squares Model Fitting
 2.2 Projections of Data Onto Model Spaces
 2.3 Linear Model Examples: Projections and SS Decompositions
 2.4 Summarizing Variability in a Linear Model
 2.5 Residuals, Leverage, and Influence
 2.6 Example: Summarizing the Fit of a Linear Model
 2.7 Optimality of Least Squares and Generalized Least Squares
 Chapter Notes
 Exercises
 Notes

Chapter 3: Normal Linear Models: Statistical Inference
 3.1 Distribution Theory for Normal Variates
 3.2 Significance Tests for Normal Linear Models
 3.3 Confidence Intervals and Prediction Intervals for Normal Linear Models
 3.4 Example: Normal Linear Model Inference
 3.5 Multiple Comparisons: Bonferroni, Tukey, and FDR Methods
 Chapter Notes
 EXERCISES
 Notes

Chapter 4: Generalized Linear Models: Model Fitting and Inference
 4.1 Exponential Dispersion Family Distributions for a GLM
 4.2 Likelihood and Asymptotic Distributions for GLMs
 4.3 LikelihoodRatio/Wald/Score Methods of Inference for GLM Parameters
 4.4 Deviance of a GLM, Model Comparison, and Model Checking
 4.5 Fitting Generalized Linear Models
 4.6 Selecting Explanatory Variables for a GLM
 4.7 Example: Building a GLM
 Appendix: GLM Analogs of Orthogonality Results for Linear Models
 Chapter Notes
 Exercises
 Notes

Chapter 5: Models for Binary Data
 5.1 Link Functions for Binary Data
 5.2 Logistic Regression: Properties and Interpretations
 5.3 Inference About Parameters of Logistic Regression Models
 5.4 Logistic Regression Model Fitting
 5.5 Deviance and Goodness of Fit for Binary GLMs
 5.6 Probit and Complementary Log–Log Models
 5.7 Examples: Binary Data Modeling
 Chapter Notes
 Exercises
 Notes
 Chapter 6: Multinomial Response Models
 Chapter 7: Models for Count Data
 Chapter 8: QuasiLikelihood Methods

Chapter 9: Modeling Correlated Responses
 9.1 Marginal Models and Models with Random Effects
 9.2 Normal Linear Mixed Models
 9.3 Fitting and Prediction for Normal Linear Mixed Models
 9.4 Binomial and Poisson GLMMs
 9.5 GLMM Fitting, Inference, and Prediction
 9.6 Marginal Modeling and Generalized Estimating Equations
 9.7 Example: Modeling Correlated Survey Responses
 Chapter Notes
 Exercises
 Notes
 Chapter 10: Bayesian Linear and Generalized Linear Modeling
 Chapter 11: Extensions of Generalized Linear Models
 Appendix A: Supplemental Data Analysis Exercises
 Appendix B: Solution Outlines for Selected Exercises
 References
 Author Index
 Example Index
 Subject Index
 Wiley Series
 End User License Agreement
Product information
 Title: Foundations of Linear and Generalized Linear Models
 Author(s):
 Release date: February 2015
 Publisher(s): Wiley
 ISBN: 9781118730034
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