Applied Regression Analysis and Generalized Linear Models / Edition 2

by John Fox

Overview

Linear models, their variants, and extensions are among the most useful and widely used statistical tools for social research. The Second Edition of Applied Regression Analysis and Generalized Linear Models provides an accessible, in-depth, modern treatment of regression analysis, linear models, and closely related methods.

Author John Fox makes the text as user-friendly as possible: With the exception of three chapters, several sections, and a few shorter passages, the prerequisite for reading the book is a course in basic applied statistics that covers the elements of statistical data analysis and inference. Even relatively advanced topics (such as methods for handling missing data and bootstrapping) are presented in a manner consistent with this prerequisite.

Key Features of the Second Edition

• Covers regression models--such as generalized linear models, limited-dependent-variable-models, mixed models and Cox regression--and methods that are increasingly being used in social science research
• Contains a more robust Web site with extensive appendices of background material (matrices, linear algebra, vector geometry; calculus; probability and estimation); data sets used in the book and for data analytic exercises; and the data-analytic exercises themselves.
• Incorporates real data from the social sciences that is similar to data readers are likely to encounter.

This book should be of interest to students and researchers in the social sciences, as well as other disciplines that employ linear models for data analysis, and in courses on applied regression and linear models where the subject matter ofapplications is not of special concern.

Product Details

ISBN-13:	9780761930426
Publisher:	SAGE Publications
Publication date:	04/16/2008
Edition description:	Second Edition
Pages:	688
Product dimensions:	7.10(w) x 10.10(h) x 1.70(d)

About the Author

John Fox received a BA from the City College of New York and a Ph D from the University of Michigan, both in Sociology. He is Professor Emeritus of Sociology at Mc Master University in Hamilton, Ontario, Canada, where he was previously the Senator William Mc Master Professor of Social Statistics. Prior to coming to Mc Master, he was Professor of Sociology, Professor of Mathematics and Statistics, and Coordinator of the Statistical Consulting Service at York University in Toronto. Professor Fox is the author of many articles and books on applied statistics, including \emph{Applied Regression Analysis and Generalized Linear Models, Third Edition} (Sage, 2016). He is an elected member of the R Foundation, an associate editor of the Journal of Statistical Software, a prior editor of R News and its successor the R Journal, and a prior editor of the Sage Quantitative Applications in the Social Sciences monograph series.

Table of Contents

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

Editorial Reviews

"helps to bridge the divide between introductory and intermediate to advanced methods courses. The book is written in a clear, concise manner and organized in such a way as to help facilitate comprehension of the material...Together [with] the R and S-plus Companion to Applied Regression [has] made a fantastic contribution to the world of quantitative social science methology."

The Political Methodologist - Ryan Baker

"This is an excellent text on regression applications and methods, written with authority, lucidity, and eloquence. "

Joseph Cavanaugh

"helps to bridge the divide between introductory and intermediate to advanced methods courses. The book is written in a clear, concise manner and organized in such a way as to help facilitate comprehension of the material...Together [with] theR and S-plus Companion to Applied Regression [has] made a fantastic contribution to the world of quantitative social science methology. "— Ryan Baker

The Political Methodologist

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

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)

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

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)

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)

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