Handbook of Regression Analysis with Applications in R

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