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Samprit Chatterjee. Handbook of Regression Analysis With Applications in R
Table of Contents
List of Tables
List of Illustrations
Guide
Pages
WILEY SERIES IN PROBABILITY AND STATISTICS
Handbook of Regression Analysis With Applications in R
Preface to the Second Edition
Preface to the First Edition. How to Use This Book
CHAPTER ONE Multiple Linear Regression
1.1 Introduction
1.2 Concepts and Background Material. 1.2.1 THE LINEAR REGRESSION MODEL
1.2.2 ESTIMATION USING LEAST SQUARES
1.2.3 ASSUMPTIONS
1.3 Methodology
1.3.1 INTERPRETING REGRESSION COEFFICIENTS
1.3.2 MEASURING THE STRENGTH OF THE REGRESSION RELATIONSHIP
1.3.3 HYPOTHESIS TESTS AND CONFIDENCE INTERVALS FOR β
1.3.4 FITTED VALUES AND PREDICTIONS
1.3.5 CHECKING ASSUMPTIONS USING RESIDUAL PLOTS
1.4 Example — Estimating Home Prices
1.5 Summary
KEY TERMS
CHAPTER TWO Model Building
2.1 Introduction
2.2 Concepts and Background Material
2.2.1 USING HYPOTHESIS TESTS TO COMPARE MODELS
2.2.2 COLLINEARITY
2.3 Methodology
2.3.1 MODEL SELECTION
2.3.2 EXAMPLE — ESTIMATING HOME PRICES (CONTINUED)
2.4 Indicator Variables and Modeling Interactions
2.4.1 EXAMPLE — ELECTRONIC VOTING AND THE 2004 PRESIDENTIAL ELECTION
2.5 Summary
KEY TERMS
CHAPTER THREE Diagnostics for Unusual Observations
3.1 Introduction
3.2 Concepts and Background Material
3.3 Methodology. 3.3.1 RESIDUALS AND OUTLIERS
3.3.2 LEVERAGE POINTS
3.3.3 INFLUENTIAL POINTS AND COOK'S DISTANCE
3.4 Example — Estimating Home Prices (continued)
3.5 Summary
KEY TERMS
CHAPTER FOUR Transformations and Linearizable Models
4.1 Introduction
4.2 Concepts and Background Material: The Log‐Log Model
4.3 Concepts and Background Material: Semilog Models
4.3.1 LOGGED RESPONSE VARIABLE
4.3.2 LOGGED PREDICTOR VARIABLE
4.4 Example — Predicting Movie Grosses After One Week
4.5 Summary
KEY TERMS
CHAPTER FIVE Time Series Data and Autocorrelation
5.1 Introduction
5.2 Concepts and Background Material
5.3 Methodology: Identifying Autocorrelation
5.3.1 THE DURBIN‐WATSON STATISTIC
5.3.2 THE AUTOCORRELATION FUNCTION (ACF)
5.3.3 RESIDUAL PLOTS AND THE RUNS TEST
5.4 Methodology: Addressing Autocorrelation. 5.4.1 DETRENDING AND DESEASONALIZING
5.4.2 EXAMPLE — E‐COMMERCE RETAIL SALES
5.4.3 LAGGING AND DIFFERENCING
5.4.4 EXAMPLE — STOCK INDEXES
5.4.5 GENERALIZED LEAST SQUARES (GLS): THE COCHRANE‐ORCUTT PROCEDURE
5.4.6 EXAMPLE — TIME INTERVALS BETWEEN OLD FAITHFUL GEYSER ERUPTIONS
5.5 Summary
KEY TERMS
CHAPTER SIX Analysis of Variance
6.1 Introduction
6.2 Concepts and Background Material. 6.2.1 ONE‐WAY ANOVA
6.2.2 TWO‐WAY ANOVA
6.3 Methodology
6.3.1 CODINGS FOR CATEGORICAL PREDICTORS
6.3.2 MULTIPLE COMPARISONS
6.3.3 LEVENE'S TEST AND WEIGHTED LEAST SQUARES
6.3.4 MEMBERSHIP IN MULTIPLE GROUPS
6.4 Example — DVD Sales of Movies
6.5 Higher‐Way ANOVA
6.6 Summary
KEY TERMS
CHAPTER SEVEN Analysis of Covariance
7.1 Introduction
7.2 Methodology. 7.2.1 CONSTANT SHIFT MODELS
7.2.2 VARYING SLOPE MODELS
7.3 Example — International Grosses of Movies
7.4 Summary
KEY TERMS
CHAPTER EIGHT Logistic Regression
8.1 Introduction
8.2 Concepts and Background Material
8.2.1 THE LOGIT RESPONSE FUNCTION
8.2.2 BERNOULLI AND BINOMIAL RANDOM VARIABLES
8.2.3 PROSPECTIVE AND RETROSPECTIVE DESIGNS
8.3 Methodology
8.3.1 MAXIMUM LIKELIHOOD ESTIMATION
8.3.2 INFERENCE, MODEL COMPARISON, AND MODEL SELECTION
8.3.3 GOODNESS‐OF‐FIT
8.3.4 MEASURES OF ASSOCIATION AND CLASSIFICATION ACCURACY
8.3.5 DIAGNOSTICS
8.4 Example — Smoking and Mortality
8.5 Example — Modeling Bankruptcy
8.6 Summary
KEY TERMS
CHAPTER NINE Multinomial Regression
9.1 Introduction
9.2 Concepts and Background Material
9.2.1 NOMINAL RESPONSE VARIABLE
9.2.2 ORDINAL RESPONSE VARIABLE
9.3 Methodology. 9.3.1 ESTIMATION
9.3.2 INFERENCE, MODEL COMPARISONS, AND STRENGTH OF FIT
9.3.3 LACK OF FIT AND VIOLATIONS OF ASSUMPTIONS
9.4 Example — City Bond Ratings
9.5 Summary
KEY TERMS
CHAPTER TEN Count Regression
10.1 Introduction
10.2 Concepts and Background Material
10.2.1 THE POISSON RANDOM VARIABLE
10.2.2 GENERALIZED LINEAR MODELS
10.3 Methodology. 10.3.1 ESTIMATION AND INFERENCE
10.3.2 OFFSETS
10.4 Overdispersion and Negative Binomial Regression
10.4.1 QUASI‐LIKELIHOOD
10.4.2 NEGATIVE BINOMIAL REGRESSION
10.5 Example — Unprovoked Shark Attacks in Florida
10.6 Other Count Regression Models
10.7 Poisson Regression and Weighted Least Squares
10.7.1 EXAMPLE — INTERNATIONAL GROSSES OF MOVIES (CONTINUED)
10.8 Summary
KEY TERMS
CHAPTER ELEVEN Models for Time‐to‐Event (Survival) Data
11.1 Introduction
11.2 Concepts and Background Material. 11.2.1 THE NATURE OF SURVIVAL DATA
11.2.2 ACCELERATED FAILURE TIME MODELS
11.2.3 THE PROPORTIONAL HAZARDS MODEL
11.3 Methodology. 11.3.1 THE KAPLAN‐MEIER ESTIMATOR AND THE LOG‐RANK TEST. 11.3.1.1 The Kaplan‐Meier Estimator
11.3.1.2 The Log‐Rank Test
11.3.1.3 Example — The Survival of Broadway Shows
11.3.2 PARAMETRIC (LIKELIHOOD) ESTIMATION
11.3.3 SEMIPARAMETRIC (PARTIAL LIKELIHOOD) ESTIMATION
11.3.4 THE BUCKLEY‐JAMES ESTIMATOR
11.4 Example — The Survival of Broadway Shows (continued)
11.5 Left‐Truncated/Right‐Censored Data and Time‐Varying Covariates. 11.5.1 LEFT‐TRUNCATED/RIGHT‐CENSORED DATA
11.5.2 EXAMPLE — THE SURVIVAL OF BROADWAY SHOWS (CONTINUED)
11.5.3 TIME‐VARYING COVARIATES
11.5.4 EXAMPLE — FEMALE HEADS OF GOVERNMENT
11.6 Summary
KEY TERMS
CHAPTER TWELVE Nonlinear Regression
12.1 Introduction
12.2 Concepts and Background Material
12.3 Methodology
12.3.1 NONLINEAR LEAST SQUARES ESTIMATION
12.3.2 INFERENCE FOR NONLINEAR REGRESSION MODELS
12.4 Example — Michaelis‐Menten Enzyme Kinetics
12.5 Summary
KEY TERMS
CHAPTER THIRTEEN Models for Longitudinal and Nested Data
13.1 Introduction
13.2 Concepts and Background Material
13.2.1 NESTED DATA AND ANOVA
13.2.2 LONGITUDINAL DATA AND TIME SERIES
13.2.3 FIXED EFFECTS VERSUS RANDOM EFFECTS
13.3 Methodology. 13.3.1 THE LINEAR MIXED EFFECTS MODEL
13.3.2 THE GENERALIZED LINEAR MIXED EFFECTS MODEL
13.3.3 GENERALIZED ESTIMATING EQUATIONS
13.3.4 NONLINEAR MIXED EFFECTS MODELS
13.4 Example — Tumor Growth in a Cancer Study
13.5 Example — Unprovoked Shark Attacks in the United States
13.6 Summary
KEY TERMS
CHAPTER FOURTEEN Regularization Methods and Sparse Models
14.1 Introduction
14.2 Concepts and Background Material
14.2.1 THE BIAS–VARIANCE TRADEOFF
14.2.2 LARGE NUMBERS OF PREDICTORS AND SPARSITY
14.3 Methodology. 14.3.1 FORWARD STEPWISE REGRESSION
14.3.2 RIDGE REGRESSION
14.3.3 THE LASSO
14.3.4 OTHER REGULARIZATION METHODS
14.3.5 CHOOSING THE REGULARIZATION PARAMETER(S)
14.3.6 MORE STRUCTURED REGRESSION PROBLEMS
14.3.7 CAUTIONS ABOUT REGULARIZATION METHODS
14.4 Example — Human Development Index
14.5 Summary
KEY TERMS
CHAPTER FIFTEEN Smoothing and Additive Models
15.1 Introduction
15.2 Concepts and Background Material. 15.2.1 THE BIAS–VARIANCE TRADEOFF
15.2.2 SMOOTHING AND LOCAL REGRESSION
15.3 Methodology. 15.3.1 LOCAL POLYNOMIAL REGRESSION
15.3.2 CHOOSING THE BANDWIDTH
15.3.3 SMOOTHING SPLINES
15.3.4 MULTIPLE PREDICTORS, THE CURSE OF DIMENSIONALITY, AND ADDITIVE MODELS
15.4 Example — Prices of German Used Automobiles
15.5 Local and Penalized Likelihood Regression
15.5.1 EXAMPLE — THE BECHDEL RULE AND HOLLYWOOD MOVIES
15.6 Using Smoothing to Identify Interactions
15.6.1 EXAMPLE — ESTIMATING HOME PRICES (CONTINUED)
15.7 Summary
KEY TERMS
CHAPTER SIXTEEN Tree‐Based Models
16.1 Introduction
16.2 Concepts and Background Material. 16.2.1 RECURSIVE PARTITIONING
16.2.2 TYPES OF TREES
16.2.2.1 Regression Trees
16.2.2.2 Classification Trees
16.3 Methodology. 16.3.1 CART
16.3.2 CONDITIONAL INFERENCE TREES
16.3.3 ENSEMBLE METHODS
16.4 Examples. 16.4.1 ESTIMATING HOME PRICES (CONTINUED)
16.4.2 EXAMPLE — COURTESY IN AIRPLANE TRAVEL
16.5 Trees for Other Types of Data. 16.5.1 TREES FOR NESTED AND LONGITUDINAL DATA
16.5.1.1 Example — Wages of Young People
16.5.2 SURVIVAL TREES
16.5.2.1 Example — The Survival of Broadway Shows (continued)
16.5.2.2 Example — Female Heads of Government (continued)
16.6 Summary
KEY TERMS
Bibliography
Index
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