Handbook of Regression Analysis With Applications in R

Handbook and reference guide for students and practitioners of statistical regression-based analyses in R

Handbook of Regression Analysis with Applications in R, Second Edition is a comprehensive and up-to-date guide to conducting complex regressions in the R statistical programming language. The authors' thorough treatment of "classical" regression analysis in the first edition is complemented here by their discussion of more advanced topics including time-to-event survival data and longitudinal and clustered data.

The book further pays particular attention to methods that have become prominent in the last few decades as increasingly large data sets have made new techniques and applications possible. These include:

• Regularization methods
• Smoothing methods
• Tree-based methods

In the new edition of the Handbook, the data analyst's toolkit is explored and expanded. Examples are drawn from a wide variety of real-life applications and data sets. All the utilized R code and data are available via an author-maintained website.

Of interest to undergraduate and graduate students taking courses in statistics and regression, the Handbook of Regression Analysis will also be invaluable to practicing data scientists and statisticians.

Samprit Chatterjee, PhD, is Professor Emeritus of Statistics at New York University. A Fellow of the American Statistical Association, Dr. Chatterjee has been a Fulbright scholar in both Kazakhstan and Mongolia. He is the coauthor of multiple editions of Regression Analysis By Example, Sensitivity Analysis in Linear Regression, A Casebook for a First Course in Statistics and Data Analysis, and the first edition of Handbook of Regression Analysis, all published by Wiley.

Jeffrey S. Simonoff, PhD, is Professor of Statistics at the Leonard N. Stern School of Business of New York University. He is a Fellow of the American Statistical Association, a Fellow of the Institute of Mathematical Statistics, and an Elected Member of the International Statistical Institute. He has authored, coauthored, or coedited more than one hundred articles and seven books on the theory and applications of statistics.

Preface to the Second Edition xiii

Preface to the First Edition xvii

Part I The Multiple Linear Regression Model

1 Multiple Linear Regression 3

1.1 Introduction 3

1.2 Concepts and Background Material 4

1.2.1 The Linear Regression Model 4

1.2.2 Estimation Using Least Squares 5

1.2.3 Assumptions 8

1.3 Methodology 9

1.3.1 Interpreting Regression Coefficients 9

1.3.2 Measuring the Strength of the Regression Relationship 11

1.3.3 Hypothesis Tests and Confidence Intervals for _ 12

1.3.4 Fitted Values and Predictions 14

1.3.5 Checking Assumptions Using Residual Plots 15

1.4 Example — Estimating Home Prices 16

1.5 Summary 19

2 Model Building 23

2.1 Introduction 23

2.2 Concepts and Background Material 24

2.2.1 Using Hypothesis Tests to Compare Models 24

2.2.2 Collinearity 26

2.3 Methodology 29

2.3.1 Model Selection 29

2.3.2 Example—Estimating Home Prices (continued) 31

2.4 Indicator Variables and Modeling Interactions 39

2.4.1 Example—Electronic Voting and the 2004 Presidential Election 41

2.5 Summary 46

Part II Addressing Violations of Assumptions

3 Diagnostics for Unusual Observations 53

3.1 Introduction 53

3.2 Concepts and Background Material 54

3.3 Methodology 56

3.3.1 Residuals and Outliers 56

3.3.2 Leverage Points 57

3.3.3 Influential Points and Cook’s Distance 58

3.4 Example — Estimating Home Prices (continued) 60

3.5 Summary 64

4 Transformations and Linearizable Models 67

4.1 Introduction 67

4.2 Concepts and Background Material: The Log-Log Model 69

4.3 Concepts and Background Material: Semilog Models 69

4.3.1 Logged Response Variable 70

4.3.2 Logged Predictor Variable 70

4.4 Example — Predicting Movie Grosses After One Week 71

4.5 Summary 78

5 Time Series Data and Autocorrelation 81

5.1 Introduction 81

5.2 Concepts and Background Material 83

5.3 Methodology: Identifying Autocorrelation 85

5.3.1 The Durbin-Watson Statistic 86

5.3.2 The Autocorrelation Function (ACF) 87

5.3.3 Residual Plots and the Runs Test 87

5.4 Methodology: Addressing Autocorrelation 88

5.4.1 Detrending and Deseasonalizing 88

5.4.2 Example — e-Commerce Retail Sales 89

5.4.3 Lagging and Differencing 95

5.4.4 Example — Stock Indexes 96

5.4.5 Generalized Least Squares (GLS): The Cochrane- Orcutt Procedure 102

5.4.6 Example — Time Intervals Between Old Faithful Geyser Eruptions 104

5.5 Summary 107

Part III Categorical Predictors

6 Analysis of Variance 113

6.1 Introduction 113

6.2 Concepts and Background Material 114

6.2.1 One-Way ANOVA 114

6.2.2 Two-Way ANOVA 115

6.3 Methodology 117

6.3.1 Codings for Categorical Predictors 117

6.3.2 Multiple Comparisons 122

6.3.3 Levene’s Test and Weighted Least Squares 124

6.3.4 Membership in Multiple Groups 127

6.4 Example — DVD Sales of Movies 129

6.5 Higher-Way ANOVA 134

6.6 Summary 136

7 Analysis of Covariance 139

7.1 Introduction 139

7.2 Methodology 139

7.2.1 Constant Shift Models 139

7.2.2 Varying Slope Models 141

7.3 Example — International Grosses of Movies 141

7.4 Summary 145

Part IV Non-Gaussian Regression Models

8 Logistic Regression 149

8.1 Introduction 149

8.2 Concepts and Background Material 151

8.2.1 The Logit Response Function 151

8.2.2 Bernoulli and Binomial Random Variables 152

8.2.3 Prospective and Retrospective Designs 153

8.3 Methodology 156

8.3.1 Maximum Likelihood Estimation 156

8.3.2 Inference, Model Comparison, and Model Selection 157

8.3.3 Goodness-of-Fit 159

8.3.4 Measures of Association and Classification Accuracy 161

8.3.5 Diagnostics 163

8.4 Example — Smoking and Mortality 163

8.5 Example — Modeling Bankruptcy 167

8.6 Summary 173

9 Multinomial Regression 177

9.1 Introduction 177

9.2 Concepts and Background Material 178

9.2.1 Nominal Response Variable 178

9.2.2 Ordinal Response Variable 180

9.3 Methodology 182

9.3.1 Estimation 182

9.3.2 Inference, Model Comparisons, and Strength of Fit 183

9.3.3 Lack of Fit and Violations of Assumptions 184

9.4 Example — City Bond Ratings 185

9.5 Summary 189

10 Count Regression 191

10.1 Introduction 191

10.2 Concepts and Background Material 192

10.2.1 The Poisson Random Variable 192

10.2.2 Generalized Linear Models 193

10.3 Methodology 194

10.3.1 Estimation and Inference 194

10.3.2 Offsets 195

10.4 Overdispersion and Negative Binomial Regression 196

10.4.1 Quasi-likelihood 197

10.4.2 Negative Binomial Regression 198

10.5 Example — Unprovoked Shark Attacks in Florida 198

10.6 Other Count Regression Models 205

10.7 Poisson Regression and Weighted Least Squares 209

10.7.1 Example—International Grosses of Movies (continued) 210

10.8 Summary 212

11 Models for Time-to-Event (Survival) Data 215

11.1 Introduction 216

11.2 Concepts and Background Material 217

11.2.1 The Nature of Survival Data 217

11.2.2 Accelerated Failure Time Models 218

11.2.3 The Proportional Hazards Model 219

11.3 Methodology 220

11.3.1 The Kaplan-Meier Estimator and the Log-Rank Test 220

11.3.2 Parametric (Likelihood) Estimation 225

11.3.3 Semiparametric (Partial Likelihood) Estimation 227

11.3.4 The Buckley-James Estimator 229

11.4 Example—The Survival of Broadway Shows (continued) 230

11.5 LTRC Data and Time-Varying Covariates 238

11.5.1 Left-Truncated/Right-Censored Data 238

11.5.2 Example—The Survival of Broadway Shows (continued) 239

11.5.3 Time-Varying Covariates 240

11.5.4 Example — Female Heads of Government 241

11.6 Summary 244

Part V Other Regression Models

12 Nonlinear Regression 249

12.1 Introduction 249

12.2 Concepts and Background Material 250

12.3 Methodology 252

12.3.1 Nonlinear Least Squares Estimation 252

12.3.2 Inference for Nonlinear Regression Models 253

12.4 Example — Michaelis-Menten Enzyme Kinetics 254

12.5 Summary 259

13 Models for Longitudinal and Nested Data 261

13.1 Introduction 261

13.2 Concepts and Background Material 263

13.2.1 Nested Data and ANOVA 263

13.2.2 Longitudinal Data and Time Series 264

13.2.3 Fixed Effects Versus Random Effects 265

13.3 Methodology 266

13.3.1 The Linear Mixed Effects Model 266

13.3.2 The Generalized Linear Mixed Effects Model 268

13.3.3 Generalized Estimating Equations 269

13.3.4 Nonlinear Mixed Effects Models 269

13.4 Example — Tumor Growth in a Cancer Study 270

13.5 Example—Unprovoked Shark Attacks in theUnited States 276

13.6 Summary 282

14 Regularization Methods and Sparse Models 285

14.1 Introduction 285

14.2 Concepts and Background Material 286

14.2.1 The Bias–Variance Tradeoff 286

14.2.2 Large Numbers of Predictors and Sparsity 287

14.3 Methodology 288

14.3.1 Forward Stepwise Regression 288

14.3.2 Ridge Regression 289

14.3.3 The Lasso 290

14.3.4 Other Regularization Methods 291

14.3.5 Choosing the Regularization Parameter(s) 292

14.3.6 More Structured Regression Problems 293

14.3.7 Cautions About Regularization Methods 294

14.4 Example — Human Development Index 295

14.5 Summary 298

Part VI Nonparametric and Semiparametric Models

15 Smoothing and Additive Models 303

15.1 Introduction 303

15.2 Concepts and Background Material 304

15.2.1 The Bias–Variance Tradeoff 304

15.2.2 Smoothing and Local Regression 305

15.3 Methodology 306

15.3.1 Local Polynomial Regression 306

15.3.2 Choosing the Bandwidth 307

15.3.3 Smoothing Splines 308

15.3.4 Multiple Predictors, the Curse of Dimensionality, and Additive Models 308

15.4 Example — Prices of German Used Automobiles 309

15.5 Local and Penalized Likelihood Regression 312

15.5.1 Example — The Bechdel Rule and Hollywood Movies 313

15.6 Using Smoothing to Identify Interactions 316

15.6.1 Example—Estimating Home Prices (continued) 318

15.7 Summary 318

16 Tree-Based Models 323

16.1 Introduction 324

16.2 Concepts and Background Material 324

16.2.1 Recursive Partitioning 324

16.2.2 Types of Trees 327

16.3 Methodology 328

16.3.1 CART 328

16.3.2 Conditional Inference Trees 329

16.3.3 Ensemble Methods 330

16.4 Examples 332

16.4.1 Estimating Home Prices (continued) 332

16.4.2 Example — Courtesy in Airplane Travel 332

16.5 Trees for Other Types of Data 337

16.5.1 Trees for Nested and Longitudinal Data 337

16.5.2 Survival Trees 338

16.6 Summary 343

Index 355

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