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 linear statistical models. The book presents a broad, in-depth 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 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
- 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 Likelihood-Ratio/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: Quasi-Likelihood 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
You might also like
book
Linear Models and Time-Series Analysis
A comprehensive and timely edition on an emerging new trend in time series Linear Models and …
book
Mathematical Statistics for Applied Econometrics
An Introductory Econometrics Text Mathematical Statistics for Applied Econometrics covers the basics of statistical inference in …
book
Mathematical Statistics and Stochastic Processes
Generally, books on mathematical statistics are restricted to the case of independent identically distributed random variables. …
book
Bayesian Analysis of Stochastic Process Models
Bayesian analysis of complex models based on stochastic processes has in recent years become a growing …