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Applied Regression Analysis and Generalized Linear Models
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Applied Regression Analysis and Generalized Linear Models

Third Edition
April 2015 | 816 pages | SAGE Publications, Inc
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Combining a modern, data-analytic perspective with a focus on applications in the social sciences, the Third Edition of Applied Regression Analysis and Generalized Linear Models provides in-depth coverage of regression analysis, generalized linear models, and closely related methods, such as bootstrapping and missing data. Updated throughout, this Third Edition includes new chapters on mixed-effects models for hierarchical and longitudinal data. Although the text is largely accessible to readers with a modest background in statistics and mathematics, author John Fox also presents more advanced material in optional sections and chapters throughout the book. 

Accompanying website resources: An instructor website for the book is available at edge.sagepub.com/fox3e containing all answers to the end-of-chapter exercises. Answers to odd-numbered questions, as well as datasets and other student resources are available on the author's website at: https://www.john-fox.ca/AppliedRegression/index.html.

NEW! Bonus chapters available on the author's website at the URL above!
Chapter 25 on Bayesian Estimation of Regression Models, and
Chapter 26 on Causal Inferences from Observational Data: Directed Acyclic Graphs and Potential Outcomes

 
Preface
 
About the Author
 
1. Statistical Models and Social Science
1.1 Statistical Models and Social Reality

 
1.2 Observation and Experiment

 
1.3 Populations and Samples

 
 
I. DATA CRAFT
 
2. What Is Regression Analysis?
2.1 Preliminaries

 
2.2 Naive Nonparametric Regression

 
2.3 Local Averaging

 
 
3. Examining Data
3.1 Univariate Displays

 
3.2 Plotting Bivariate Data

 
3.3 Plotting Multivariate Data

 
 
4. Transforming Data
4.1 The Family of Powers and Roots

 
4.2 Transforming Skewness

 
4.3 Transforming Nonlinearity

 
4.4 Transforming Nonconstant Spread

 
4.5 Transforming Proportions

 
4.6 Estimating Transformations as Parameters*

 
 
II. LINEAR MODELS AND LEAST SQUARES
 
5. Linear Least-Squares Regression
5.1 Simple Regression

 
5.2 Multiple Regression

 
 
6. Statistical Inference for Regression
6.1 Simple Regression

 
6.2 Multiple Regression

 
6.3 Empirical Versus Structural Relations

 
6.4 Measurement Error in Explanatory Variables*

 
 
7. Dummy-Variable Regression
7.1 A Dichotomous Factor

 
7.2 Polytomous Factors

 
7.3 Modeling Interactions

 
 
8. Analysis of Variance
8.1 One-Way Analysis of Variance

 
8.2 Two-Way Analysis of Variance

 
8.3 Higher-Way Analysis of Variance

 
8.4 Analysis of Covariance

 
8.5 Linear Contrasts of Means

 
 
9. Statistical Theory for Linear Models*
9.1 Linear Models in Matrix Form

 
9.2 Least-Squares Fit

 
9.3 Properties of the Least-Squares Estimator

 
9.4 Statistical Inference for Linear Models

 
9.5 Multivariate Linear Models

 
9.6 Random Regressors

 
9.7 Specification Error

 
9.8 Instrumental Variables and Two-Stage Least Squares

 
 
10. The Vector Geometry of Linear Models*
10.1 Simple Regression

 
10.2 Multiple Regression

 
10.3 Estimating the Error Variance

 
10.4 Analysis-of-Variance Models

 
 
III. LINEAR-MODEL DIAGNOSTICS
 
11. Unusual and Influential Data
11.1 Outliers, Leverage, and Influence

 
11.2 Assessing Leverage: Hat-Values

 
11.3 Detecting Outliers: Studentized Residuals

 
11.4 Measuring Influence

 
11.5 Numerical Cutoffs for Diagnostic Statistics

 
11.6 Joint Influence

 
11.7 Should Unusual Data Be Discarded?

 
11.8 Some Statistical Details*

 
 
12. Non-Normality, Nonconstant Error Variance, Nonlinearity
12.1 Non-Normally Distributed Errors

 
12.2 Nonconstant Error Variance

 
12.3 Nonlinearity

 
12.4 Discrete Data

 
12.5 Maximum-Likelihood Methods*

 
12.6 Structural Dimension

 
 
13. Collinearity and Its Purported Remedies
13.1 Detecting Collinearity

 
13.2 Coping With Collinearity: No Quick Fix

 
 
IV. GENERALIZED LINEAR MODELS
 
14. Logit and Probit Models for Categorical Response Variables
14.1 Models for Dichotomous Data

 
14.2 Models for Polytomous Data

 
14.3 Discrete Explanatory Variables and Contingency Tables

 
 
15. Generalized Linear Models
15.1 The Structure of Generalized Linear Models

 
15.2 Generalized Linear Models for Counts

 
15.3 Statistical Theory for Generalized Linear Models*

 
15.4 Diagnostics for Generalized Linear Models

 
15.5 Analyzing Data From Complex Sample Surveys

 
 
V. EXTENDING LINEAR AND GENERALIZED LINEAR MODELS
 
16. Time-Series Regression and Generalized Leasr Squares*
16.1 Generalized Least-Squares Estimation

 
16.2 Serially Correlated Errors

 
16.3 GLS Estimation With Autocorrelated Errors

 
16.4 Correcting OLS Inference for Autocorrelated Errors

 
16.5 Diagnosing Serially Correlated Errors

 
16.6 Concluding Remarks

 
 
17. Nonlinear Regression
17.1 Polynomial Regression

 
17.2 Piece-wise Polynomials and Regression Splines

 
17.3 Transformable Nonlinearity

 
17.4 Nonlinear Least Squares*

 
 
18. Nonparametric Regression
18.1 Nonparametric Simple Regression: Scatterplot Smoothing

 
18.2 Nonparametric Multiple Regression

 
18.3 Generalized Nonparametric Regression

 
 
19. Robust Regression*
19.1 M Estimation

 
19.2 Bounded-Influence Regression

 
19.3 Quantile Regression

 
19.4 Robust Estimation of Generalized Linear Models

 
19.5 Concluding Remarks

 
 
20. Missing Data in Regression Models
20.1 Missing Data Basics

 
20.2 Traditional Approaches to Missing Data

 
20.3 Maximum-Likelihood Estimation for Data Missing at Random*

 
20.4 Bayesian Multiple Imputation

 
20.5 Selection Bias and Censoring

 
 
21. Bootstrapping Regression Models
21.1 Bootstrapping Basics

 
21.2 Bootstrap Confidence Intervals

 
21.3 Bootstrapping Regression Models

 
21.4 Bootstrap Hypothesis Tests*

 
21.5 Bootstrapping Complex Sampling Designs

 
21.6 Concluding Remarks

 
 
22. Model Selection, Averaging, and Validation
22.1 Model Selection

 
22.2 Model Averaging*

 
22.3 Model Validation

 
 
VI. MIXED-EFFECT MODELS
 
23. Linear Mixed-Effects Models for Hierarchical and Longitudinal Data
23.1 Hierarchical and Longitudinal Data

 
23.2 The Linear Mixed-Effects Model

 
23.3 Modeling Hierarchical Data

 
23.4 Modeling Longitudinal Data

 
23.5 Wald Tests for Fixed Effects

 
23.6 Likelihood-Ratio Tests of Variance and Covariance Components

 
23.7 Centering Explanatory Variables, Contextual Effects, and Fixed-Effects Models

 
23.8 BLUPs

 
23.9 Statistical Details*

 
 
24. Generalized Linear and Nonlinear Mixed-Effects Models
24.1 Generalized Linear Mixed Models

 
24.2 Nonlinear Mixed Models

 
 
Appendix A
 
References
 
Author Index
 
Subject Index
 
Data Set Index

Supplements

Companion Website
The companion website features data sets, data analysis exercises, Appendixes B,C,D, and errata.

The strength of this text is the unified presentation of several regression topics that provides the student with a global perspective on regression analysis.  The student is well served with this unified approach as it facilitates deeper research on any one topic with more advanced texts.

E. C. Hedberg, Arizona State University

This text is a one-stop shop for me for my first year stats sequence for students in our program. Those wanting the technical detail will be satisfied; those wanting an excellent explanation of these methods using real-world examples and approachable language will also be satisfied.

Corey S. Sparks, The University of Texas at San Antonio

I have enjoyed using previous editions of this text and look forward to using this edition. It covers all key topics, and quite a few advanced ones, in one well-written text.

Michael S. Lynch, University of Georgia

PRAISE FOR THE PREVIOUS EDITIONS

In summary, this is an excellent text on regression applications and methods, written with authority, lucidity, and eloquence. The second edition provides substantive and topical updates, and makes the book suitable for courses designed to emphasize both the classical and the modern aspects of regression.


Journal of the American Statistical Association (review of the second edition)

PRAISE FOR THE PREVIOUS EDITIONS

Even though the book is written with social scientists as the target audience, the depth of material and how it is conveyed give it far broader appeal. Indeed, I recommend it as a useful learning text and resource for researchers and students in any field that applies regression or linear models (that is, most everyone), including courses for undergraduate statistics majors…. The author is to be commended for giving us this book, which I trust will find a wide and enduring readership.


Journal of the American Statistical Association (review of the first edition)

PRAISE FOR THE PREVIOUS EDITIONS

[T]his wonderfully comprehensive book focuses on regression analysis and linear models… We enthusiastically recommend this book—having used it in class, we know that it is thorough and well-liked by students.

Chance (review of the first edition)

I loved it and students did too (well, as much as they will!)

Dr Erin M Hodgess
Computer Mathematical Sci Dept, Univ Of Houston-Downtown
May 10, 2016
Report this review

The book covers regression only and not all the topics in regression. I need a book that covers both regression methods and design of experiments methods.

Mr Ahmed Almaskut
Human Kinetics, University Of Ottawa
June 25, 2015
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Key features

NEW TO THIS EDITION:

  • A new Part IV on mixed-effects models for hierarchical and longitudinal data with chapters on linear mixed-effects models (Chapter 23) and nonlinear and generalized linear mixed-effects models (Chapter 24) provides readers with a basis for applying these models in practice, as well as for reading more extensive treatments of the subject.
  • A revised presentation of analysis-of-variance models includes a simplified treatment that allows readers to skip the more complex aspects of the topic if they wish.
  • An introduction to instrumental-variables estimation and two-stage least-squares regression has been added.
  • The book now includes a brief introduction to design-based inference for regression models fit to data from complex survey samples.
  • References have been updated.

KEY FEATURES:

  • The book is a valuable resource for graduate students and researchers in the social sciences (particularly sociology, political science, and psychology) and other disciplines that employ linear, generalized-linear, and related models for data analysis.
  • Each chapter ends with a summary and exercises.
  • An extensive website includes: appendices with background information on matrices, linear algebra, vector geometry, calculus, probability and estimation; datasets used in the book and for data-analytic exercises; and the data-analytic exercises themselves. 

Sample Materials & Chapters

Chapter 7

Chapter 21

For instructors

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