Foundations of linear and generalized linear models
 Responsibility
 Alan Agresti (Distinguished Professor Emeritus, University of Florida, Gainesville, FL, Visiting Professor, Harvard University, Cambridge, MA).
 Publication
 Hoboken, New Jersey : Wiley, [2015]
 Copyright notice
 ©2015
 Physical description
 xiii, 444 pages : illustrations ; 25 cm.
 Series
 Wiley series in probability and statistics.
At the library
Science Library (Li and Ma)
Stacks
Call number  Status 

QA299.8 .A37 2015  Unknown 
More options
Description
Creators/Contributors
 Author/Creator
 Agresti, Alan, author.
Contents/Summary
 Bibliography
 Includes bibliographical references (pages 410426) and indexes.
 Contents

 Preface xi
 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
 6
 1.3 Model Matrices and Model Vector Spaces
 10
 1.4 Identifiability and Estimability
 13
 1.5 Example: Using Software to Fit a GLM
 15
 Chapter Notes
 20
 Exercises
 21
 2 Linear Models: Least Squares Theory
 26
 2.1 Least Squares Model Fitting
 27
 2.2 Projections of Data Onto Model Spaces
 33
 2.3 Linear Model Examples: Projections and SS Decompositions
 41
 2.4 Summarizing Variability in a Linear Model
 49
 2.5 Residuals Leverage and Influence
 56
 2.6 Example: Summarizing the Fit of a Linear Model
 62
 2.7 Optimality of Least Squares and Generalized Least Squares
 67
 Chapter Notes
 71
 Exercises
 71
 3 Normal Linear Models: Statistical Inference
 80
 3.1 Distribution Theory for Normal Variates
 81
 3.2 Significance Tests for Normal Linear Models
 86
 3.3 Confidence Intervals and Prediction Intervals for Normal Linear Models
 95
 3.4 Example: Normal Linear Model Inference
 99
 3.5 Multiple Comparisons: Bonferroni Tukey and FDR Methods
 107
 Chapter Notes
 111
 Exercises
 112
 4 Generalized Linear Models: Model Fitting and Inference
 120
 4.1 Exponential Dispersion Family Distributions for a GLM
 120
 4.2 Likelihood and Asymptotic Distributions for GLMs
 123
 4.3 LikelihoodRatio/Wald/Score Methods of Inference for GLM Parameters
 128
 4.4 Deviance of a GLM Model Comparison and Model Checking
 132
 4.5 Fitting Generalized Linear Models
 138
 4.6 Selecting Explanatory Variables for a GLM
 143
 4.7 Example: Building a GLM
 149
 Appendix: GLM Analogs of Orthogonality Results for Linear Models
 156
 Chapter Notes
 158
 Exercises
 159
 5 Models for Binary Data
 165
 5.1 Link Functions for Binary Data
 165
 5.2 Logistic Regression: Properties and Interpretations
 168
 5.3 Inference About Parameters of Logistic Regression Models
 172
 5.4 Logistic Regression Model Fitting
 176
 5.5 Deviance and Goodness of Fit for Binary GLMs
 179
 5.6 Probit and Complementary Log Log Models
 183
 5.7 Examples: Binary Data Modeling
 186
 Chapter Notes
 193
 Exercises
 194
 6 Multinomial Response Models
 202
 6.1 Nominal Responses: BaselineCategory Logit Models
 203
 6.2 Ordinal Responses: Cumulative Logit and Probit Models
 209
 6.3 Examples: Nominal and Ordinal Responses
 216
 Chapter Notes
 223
 Exercises
 223
 7 Models for Count Data
 228
 7.1 Poisson GLMs for Counts and Rates
 229
 7.2 Poisson/Multinomial Models for Contingency Tables
 235
 7.3 Negative Binomial GLMS
 247
 7.4 Models for ZeroInflated Data
 250
 7.5 Example: Modeling Count Data
 254
 Chapter Notes
 259
 Exercises
 260
 8 QuasiLikelihood Methods
 268
 8.1 Variance Inflation for Overdispersed Poisson and Binomial GLMs
 269
 8.2 BetaBinomial Models and QuasiLikelihood Alternatives
 272
 8.3 QuasiLikelihood and Model Misspecification
 278
 Chapter Notes
 282
 Exercises
 282
 9 Modeling Correlated Responses
 286
 9.1 Marginal Models and Models with Random Effects
 287
 9.2 Normal Linear Mixed Models
 294
 9.3 Fitting and Prediction for Normal Linear Mixed Models
 302
 9.4 Binomial and Poisson GLMMs
 307
 9.5 GLMM Fitting Inference and Prediction
 311
 9.6 Marginal Modeling and Generalized Estimating Equations
 314
 9.7 Example: Modeling Correlated Survey Responses
 319
 Chapter Notes
 322
 Exercises
 324
 10 Bayesian Linear and Generalized Linear Modeling
 333
 10.1 The Bayesian Approach to Statistical Inference
 333
 10.2 Bayesian Linear Models
 340
 10.3 Bayesian Generalized Linear Models
 347
 10.4 Empirical Bayes and Hierarchical Bayes Modeling
 351
 Chapter Notes
 357
 Exercises
 359
 11 Extensions of Generalized Linear Models
 364
 11.1 Robust Regression and Regularization Methods for Fitting Models
 365
 11.2 Modeling With Large p
 375
 11.3 Smoothing Generalized Additive Models and Other GLM Extensions
 378
 Chapter Notes
 386
 Exercises
 388
 Appendix A Supplemental Data Analysis Exercises
 391
 Appendix B Solution Outlines for Selected Exercises
 396
 References
 410
 Author Index
 427
 Example Index
 433
 Subject Index 435.
 (source: Nielsen Book Data)
 Summary

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 linearstatistical models. The book presents a broad, indepth 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 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 ofLinear 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.
(source: Nielsen Book Data)
Subjects
Bibliographic information
 Publication date
 2015
 Copyright date
 2015
 Series
 Wiley series in probability and statistics
 ISBN
 9781118730034 (hardback)
 1118730038 (hardback)