Handbook of Regression Analysis With Applications in R: (Wiley Series in Probability and Statistics)

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.

Table of Contents:
Preface to the Second Edition xv Preface to the First Edition xix 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 10 1.3.3 Hypothesis Tests and Confidence Intervals for β 12 1.3.4 Fitted Values and Predictions 13 1.3.5 Checking Assumptions Using Residual Plots 14 1.4 Example —Estimating Home Prices 15 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 38 2.4.1 Example—Electronic Voting and the 2004 Presidential Election 40 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 63 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 77 5 Time Series Data and Autocorrelation 79 5.1 Introduction 79 5.2 Concepts and Background Material 81 5.3 Methodology: Identifying Autocorrelation 83 5.3.1 The Durbin-Watson Statistic 83 5.3.2 The Autocorrelation Function (ACF) 84 5.3.3 Residual Plots and the Runs Test 85 5.4 Methodology: Addressing Autocorrelation 86 5.4.1 Detrending and Deseasonalizing 86 5.4.2 Example— e-Commerce Retail Sales 87 5.4.3 Lagging and Differencing 93 5.4.4 Example— Stock Indexes 94 5.4.5 Generalized Least Squares (GLS): The Cochrane-Orcutt Procedure 99 5.4.6 Example— Time Intervals Between Old Faithful Geyser Eruptions 100 5.5 Summary 104 Part III Categorical Predictors 6 Analysis of Variance 109 6.1 Introduction 109 6.2 Concepts and Background Material 110 6.2.1 One-Way ANOVA 110 6.2.2 Two-Way ANOVA 111 6.3 Methodology 113 6.3.1 Codings for Categorical Predictors 113 6.3.2 Multiple Comparisons 118 6.3.3 Levene’s Test and Weighted Least Squares 120 6.3.4 Membership in Multiple Groups 123 6.4 Example—DVD Sales of Movies 125 6.5 Higher-Way ANOVA 130 6.6 Summary 132 7 Analysis of Covariance 135 7.1 Introduction 135 7.2 Methodology 136 7.2.1 Constant Shift Models 136 7.2.2 Varying Slope Models 137 7.3 Example —International Grosses of Movies 137 7.4 Summary 142 Part IV Non-Gaussian Regression Models 8 Logistic Regression 145 8.1 Introduction 145 8.2 Concepts and Background Material 147 8.2.1 The Logit Response Function 148 8.2.2 Bernoulli and Binomial Random Variables 149 8.2.3 Prospective and Retrospective Designs 149 8.3 Methodology 152 8.3.1 Maximum Likelihood Estimation 152 8.3.2 Inference, Model Comparison, and Model Selection 153 8.3.3 Goodness-of-Fit 155 8.3.4 Measures of Association and Classification Accuracy 157 8.3.5 Diagnostics 159 8.4 Example— Smoking and Mortality 159 8.5 Example— Modeling Bankruptcy 163 8.6 Summary 168 9 Multinomial Regression 173 9.1 Introduction 173 9.2 Concepts and Background Material 174 9.2.1 Nominal Response Variable 174 9.2.2 Ordinal Response Variable 176 9.3 Methodology 178 9.3.1 Estimation 178 9.3.2 Inference, Model Comparisons, and Strength of Fit 178 9.3.3 Lack of Fit and Violations of Assumptions 180 9.4 Example— City Bond Ratings 180 9.5 Summary 184 10 Count Regression 187 10.1 Introduction 187 10.2 Concepts and Background Material 188 10.2.1 The Poisson Random Variable 188 10.2.2 Generalized Linear Models 189 10.3 Methodology 190 10.3.1 Estimation and Inference 190 10.3.2 Offsets 191 10.4 Overdispersion and Negative Binomial Regression 192 10.4.1 Quasi-likelihood 192 10.4.2 Negative Binomial Regression 193 10.5 Example— Unprovoked Shark Attacks in Florida 194 10.6 Other Count Regression Models 201 10.7 Poisson Regression and Weighted Least Squares 203 10.7.1 Example— International Grosses of Movies (continued) 204 10.8 Summary 206 11 Models for Time-to-Event (Survival) Data 209 11.1 Introduction 210 11.2 Concepts and Background Material 211 11.2.1 The Nature of Survival Data 211 11.2.2 Accelerated Failure Time Models 212 11.2.3 The Proportional Hazards Model 214 11.3 Methodology 214 11.3.1 The Kaplan-Meier Estimator and the Log-Rank Test 214 11.3.2 Parametric (Likelihood) Estimation 219 11.3.3 Semiparametric (Partial Likelihood) Estimation 221 11.3.4 The Buckley-James Estimator 223 11.4 Example—The Survival of Broadway Shows (continued) 223 11.5 Left-Truncated/Right-Censored Data and Time-Varying Covariates 230 11.5.1 Left-Truncated/Right-Censored Data 230 11.5.2 Example—The Survival of Broadway Shows (continued) 233 11.5.3 Time-Varying Covariates 233 11.5.4 Example—Female Heads of Government 235 11.6 Summary 238 Part V Other Regression Models 12 Nonlinear Regression 243 12.1 Introduction 243 12.2 Concepts and Background Material 244 12.3 Methodology 246 12.3.1 Nonlinear Least Squares Estimation 246 12.3.2 Inference for Nonlinear Regression Models 247 12.4 Example —Michaelis-Menten Enzyme Kinetics 248 12.5 Summary 252 13 Models for Longitudinal and Nested Data 255 13.1 Introduction 255 13.2 Concepts and Background Material 257 13.2.1 Nested Data and ANOVA 257 13.2.2 Longitudinal Data and Time Series 258 13.2.3 Fixed Effects Versus Random Effects 259 13.3 Methodology 260 13.3.1 The Linear Mixed Effects Model 260 13.3.2 The Generalized Linear Mixed Effects Model 262 13.3.3 Generalized Estimating Equations 262 13.3.4 Nonlinear Mixed Effects Models 263 13.4 Example —Tumor Growth in a Cancer Study 264 13.5 Example —Unprovoked Shark Attacks in the United States 269 13.6 Summary 275 14 Regularization Methods and Sparse Models 277 14.1 Introduction 277 14.2 Concepts and Background Material 278 14.2.1 The Bias–Variance Tradeoff 278 14.2.2 Large Numbers of Predictors and Sparsity 279 14.3 Methodology 280 14.3.1 Forward Stepwise Regression 280 14.3.2 Ridge Regression 281 14.3.3 The Lasso 281 14.3.4 Other Regularization Methods 283 14.3.5 Choosing the Regularization Parameter(s) 284 14.3.6 More Structured Regression Problems 285 14.3.7 Cautions About Regularization Methods 286 14.4 Example— Human Development Index 287 14.5 Summary 289 Part VI Nonparametric and Semiparametric Models 15 Smoothing and Additive Models 295 15.1 Introduction 296 15.2 Concepts and Background Material 296 15.2.1 The Bias–Variance Tradeoff 296 15.2.2 Smoothing and Local Regression 297 15.3 Methodology 298 15.3.1 Local Polynomial Regression 298 15.3.2 Choosing the Bandwidth 298 15.3.3 Smoothing Splines 299 15.3.4 Multiple Predictors, the Curse of Dimensionality, and Additive Models 300 15.4 Example— Prices of German Used Automobiles 301 15.5 Local and Penalized Likelihood Regression 304 15.5.1 Example— The Bechdel Rule and Hollywood Movies 305 15.6 Using Smoothing to Identify Interactions 307 15.6.1 Example— Estimating Home Prices (continued) 308 15.7 Summary 310 16 Tree-Based Models 313 16.1 Introduction 314 16.2 Concepts and Background Material 314 16.2.1 Recursive Partitioning 314 16.2.2 Types of Trees 317 16.3 Methodology 318 16.3.1 CART 318 16.3.2 Conditional Inference Trees 319 16.3.3 Ensemble Methods 320 16.4 Examples 321 16.4.1 Estimating Home Prices (continued) 321 16.4.2 Example—Courtesy in Airplane Travel 322 16.5 Trees for Other Types of Data 327 16.5.1 Trees for Nested and Longitudinal Data 327 16.5.2 Survival Trees 328 16.6 Summary 332 Bibliography 337 Index 343