An R Companion to Applied Regression Third Edition To the memory of my parents, Joseph and Diana —J. F. For my teachers, and especially Fred Mosteller, who I think would have liked this book —S. W. An R Companion to Applied Regression Third Edition John Fox McMaster University Sanford Weisberg University of Minnesota Los Angeles London New Delhi Singapore Washington DC Melbourne Copyright © 2019 by SAGE Publications, Inc. All rights reserved. No part of this book may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording, or by any information storage and retrieval system, without permission in writing from the publisher. FOR INFORMATION: SAGE Publications, Inc. 2455 Teller Road Thousand Oaks, California 91320 E-mail: [email protected] SAGE Publications Ltd. 1 Oliver’s Yard 55 City Road London, EC1Y 1SP United Kingdom SAGE Publications India Pvt. Ltd. B 1/I 1 Mohan Cooperative Industrial Area Mathura Road, New Delhi 110 044 India SAGE Publications Asia-Pacific Pte. Ltd. 3 Church Street #10-04 Samsung Hub Singapore 049483 ISBN: 978-1-5443-3647-3 Printed in the United States of America This book is printed on acid-free paper. Acquisitions Editor: Helen Salmon Editorial Assistant: Megan O’Heffernan Production Editor: Kelly DeRosa Copy Editor: Gillian Dickens Typesetter: QuADS Prepress (P) Ltd Proofreader: Jen Grubba Cover Designer: Anthony Paular Marketing Manager: Susannah Goldes Contents Preface What Is R? Obtaining and Installing R and RStudio Installing R on a Windows System Installing R on a macOS System Installing RStudio Installing and Using R Packages Optional: Customizing R Optional: Installing LATEX Using This Book Chapter Synopses Typographical Conventions New in the Third Edition The Website for the R Companion Beyond the R Companion Acknowledgments About the Authors 1 Getting Started With R and RStudio 1.1 Projects in RStudio 1.2 R Basics 1.2.1 Interacting With R Through the Console 1.2.2 Editing R Commands in the Console 1.2.3 R Functions 1.2.4 Vectors and Variables 1.2.5 Nonnumeric Vectors 1.2.6 Indexing Vectors 1.2.7 User-Defined Functions 1.3 Fixing Errors and Getting Help 1.3.1 When Things Go Wrong 1.3.2 Getting Help and Information 1.4 Organizing Your Work in R and RStudio and Making It Reproducible 1.4.1 Using the RStudio Editor With R Script Files 1.4.2 Writing R Markdown Documents 1.5 An Extended Illustration: Duncan’s Occupational-Prestige Regression 1.5.1 Examining the Data 1.5.2 Regression Analysis 1.5.3 Regression Diagnostics 1.6 R Functions for Basic Statistics 1.7 Generic Functions and Their Methods* 2 Reading and Manipulating Data 2.1 Data Input 2.1.1 Accessing Data From a Package 2.1.2 Entering a Data Frame Directly 2.1.3 Reading Data From Plain-Text Files 2.1.4 Files and Paths 2.1.5 Exporting or Saving a Data Frame to a File 2.1.6 Reading and Writing Other File Formats 2.2 Other Approaches to Reading and Managing Data Sets in R 2.3 Working With Data Frames 2.3.1 How the R Interpreter Finds Objects 2.3.2 Missing Data 2.3.3 Modifying and Transforming Data 2.3.4 Binding Rows and Columns 2.3.5 Aggregating Data Frames 2.3.6 Merging Data Frames 2.3.7 Reshaping Data 2.4 Working With Matrices, Arrays, and Lists 2.4.1 Matrices 2.4.2 Arrays 2.4.3 Lists 2.4.4 Indexing 2.5 Dates and Times 2.6 Character Data 2.7 Large Data Sets in R* 2.7.1 How Large Is “Large”? 2.7.2 Reading and Saving Large Data Sets 2.8 Complementary Reading and References 3 Exploring and Transforming Data 3.1 Examining Distributions 3.1.1 Histograms 3.1.2 Density Estimation 3.1.3 Quantile-Comparison Plots 3.1.4 Boxplots 3.2 Examining Relationships 3.2.1 Scatterplots 3.2.2 Parallel Boxplots 3.2.3 More on the plot() Function 3.3 Examining Multivariate Data 3.3.1 Three-Dimensional Plots 3.3.2 Scatterplot Matrices 3.4 Transforming Data 3.4.1 Logarithms: The Champion of Transformations 3.4.2 Power Transformations 3.4.3 Transformations and Exploratory Data Analysis 3.4.4 Transforming Restricted-Range Variables 3.4.5 Other Transformations 3.5 Point Labeling and Identification 3.5.1 The identify() Function 3.5.2 Automatic Point Labeling 3.6 Scatterplot Smoothing 3.7 Complementary Reading and References 4 Fitting Linear Models 4.1 The Linear Model 4.2 Linear Least-Squares Regression 4.2.1 Simple Linear Regression 4.2.2 Multiple Linear Regression 4.2.3 Standardized Regression Coefficients 4.3 Predictor Effect Plots 4.4 Polynomial Regression and Regression Splines 4.4.1 Polynomial Regression 4.4.2 Regression Splines* 4.5 Factors in Linear Models 4.5.1 A Linear Model With One Factor: One-Way Analysis of Variance 4.5.2 Additive Models With Numeric Predictors and Factors 4.6 Linear Models With Interactions 4.6.1 Interactions Between Numeric Predictors and Factors 4.6.2 Shortcuts for Writing Linear-Model Formulas 4.6.3 Multiple Factors 4.6.4 Interactions Between Numeric Predictors* 4.7 More on Factors 4.7.1 Dummy Coding 4.7.2 Other Factor Codings 4.7.3 Ordered Factors and Orthogonal-Polynomial Contrasts 4.7.4 User-Specified Contrasts* 4.7.5 Suppressing the Intercept in a Model With Factors* 4.8 Too Many Regressors* 4.9 The Arguments of the lm() Function 4.9.1 formula 4.9.2 data 4.9.3 subset 4.9.4 weights 4.9.5 na.action 4.9.6 method, model, x, y, qr* 4.9.7 singular.ok* 4.9.8 contrasts 4.9.9 offset 4.10 Complementary Reading and References 5 Coefficient Standard Errors, Confidence Intervals, and Hypothesis Tests 5.1 Coefficient Standard Errors 5.1.1 Conventional Standard Errors of Least-Squares Regression Coefficients 5.1.2 Robust Regression Coefficient Standard Errors 5.1.3 Using the Bootstrap to Compute Standard Errors 5.1.4 The Delta Method for Standard Errors of Nonlinear Functions* 5.2 Confidence Intervals 5.2.1 Wald Confidence Intervals 5.2.2 Bootstrap Confidence Intervals 5.2.3 Confidence Regions and Data Ellipses* 5.3 Testing Hypotheses About Regression Coefficients 5.3.1 Wald Tests 5.3.2 Likelihood-Ratio Tests and the Analysis of Variance 5.3.3 Sequential Analysis of Variance 5.3.4 The Anova() Function 5.3.5 Testing General Linear Hypotheses* 5.4 Complementary Reading and References 6 Fitting Generalized Linear Models 6.1 Review of the Structure of GLMs 6.2 The glm() Function in R 6.3 GLMs for Binary Response Data 6.3.1 Example: Women’s Labor Force Participation 6.3.2 Example: Volunteering for a Psychological Experiment 6.3.3 Predictor Effect Plots for Logistic Regression 6.3.4 Analysis of Deviance and Hypothesis Tests for Logistic Regression 6.3.5 Fitted and Predicted Values 6.4 Binomial Data 6.5 Poisson GLMs for Count Data 6.6 Loglinear Models for Contingency Tables 6.6.1 Two-Dimensional Tables 6.6.2 Three-Dimensional Tables 6.6.3 Sampling Plans for Loglinear Models 6.6.4 Response Variables 6.7 Multinomial Response Data 6.8 Nested Dichotomies 6.9 The Proportional-Odds Model 6.9.1 Testing for Proportional Odds 6.10 Extensions 6.10.1 More on the Anova () Function 6.10.2 Gamma Models 6.10.3 Quasi-Likelihood Estimation 6.10.4 Overdispersed Binomial and Poisson Models 6.11 Arguments to glm() 6.11.1 weights 6.11.2 start, etastart, mustart 6.11.3 offset 6.11.4 control 6.11.5 model, method, x, y 6.12 Fitting GLMs by Iterated Weighted Least Squares* 6.13 Complementary Reading and References 7 Fitting Mixed-Effects Models 7.1 Background: The Linear Model Revisited 7.1.1 The Linear Model in Matrix Form* 7.2 Linear Mixed-Effects Models 7.2.1 Matrix Form of the Linear Mixed-Effects Model* 7.2.2 An Application to Hierarchical Data 7.2.3 Wald Tests for Linear Mixed-Effects Models 7.2.4 Examining the Random Effects: Computing BLUPs 7.2.5 An Application to Longitudinal Data 7.2.6 Modeling the Errors