| |

| |

Preface | |

| |

| |

| |

Introduction to Regression Modeling | |

| |

| |

Chapter Overview | |

| |

| |

Mathematical and Statistical Models | |

| |

| |

Linear Regression Models | |

| |

| |

Generalized Linear Model | |

| |

| |

Model Evaluation | |

| |

| |

Regression Models and Causal Inference | |

| |

| |

What Is a Cause? | |

| |

| |

When Does a Regression Coefficient Have a Causal Interpretation? | |

| |

| |

Recommendations | |

| |

| |

Datasets Used in This Volume | |

| |

| |

National Survey of Families and Households Datasets | |

| |

| |

Datasets from the NVAWS | |

| |

| |

Other Datasets | |

| |

| |

| |

Statistical Review | |

| |

| |

| |

Simple Linear Regression | |

| |

| |

Chapter Overview | |

| |

| |

Linear Relationships | |

| |

| |

Simple Linear Regression Model | |

| |

| |

Regression Assumptions | |

| |

| |

Interpreting the Regression Equation | |

| |

| |

Estimation Using Sample Data | |

| |

| |

Rationale for OLS | |

| |

| |

Mathematics of OLS | |

| |

| |

Inferences in Simple Linear Regression | |

| |

| |

Tests about the Population Slope | |

| |

| |

Testing the Intercept | |

| |

| |

Confidence Intervals for [beta subscript 0] and [beta subscript 1] | |

| |

| |

Additional Examples | |

| |

| |

Assessing Empirical Consistency of the Model | |

| |

| |

Conforming to Assumptions | |

| |

| |

Formal Test of Empirical Consistency | |

| |

| |

Stochastic Regressors | |

| |

| |

Estimation of [beta subscript 0] and [beta subscript 1] via Maximum Likelihood | |

| |

| |

Exercises | |

| |

| |

| |

Introduction to Multiple Regression | |

| |

| |

Chapter Overview | |

| |

| |

Employing Multiple Predictors | |

| |

| |

Advantages and Rationale for MULR | |

| |

| |

Example | |

| |

| |

Controlling for a Third Variable | |

| |

| |

MULR Model | |

| |

| |

Inferences in MULR | |

| |

| |

Omitted-Variable Bias | |

| |

| |

Modeling Interaction Effects | |

| |

| |

Evaluating Empirical Consistency | |

| |

| |

Examination of Residuals | |

| |

| |

Partial Regression Leverage Plots | |

| |

| |

Exercises | |

| |

| |

| |

Multiple Regression with Categorical Predictors: ANOVA and ANCOVA Models | |

| |

| |

Chapter Overview | |

| |

| |

Models with Exclusively Categorical Predictors | |

| |

| |

Dummy Coding | |

| |

| |

Effect Coding | |

| |

| |

Two-Way ANOVA in Regression | |

| |

| |

Interaction between Categorical Predictors | |

| |

| |

Models with Both Categorical and Continuous Predictors | |

| |

| |

Adjusted Means | |

| |

| |

Interaction between Categorical and Continuous Predictors | |

| |

| |

Comparing Models across Groups, Revisited | |

| |

| |

Exercises | |

| |

| |

| |

Modeling Nonlinearity | |

| |

| |

Chapter Overview | |

| |

| |

Nonlinearity Defined | |

| |

| |

Common Nonlinear Functions of X | |

| |

| |

Quadratic Functions of X | |

| |

| |

Applications of the Quadratic Model | |

| |

| |

Testing Departures from Linearity | |

| |

| |

Interpreting Quadratic Models | |

| |

| |

Nonlinear Interaction | |

| |

| |

Nonlinear Regression | |

| |

| |

Estimating the Multiplicative Model | |

| |

| |

Estimating the Nonlinear Model | |

| |

| |

Exercises | |

| |

| |

| |

Advanced Issues in Multiple Regression | |

| |

| |

Chapter Overview | |

| |

| |

Multiple Regression in Matrix Notation | |

| |

| |

The Model | |

| |

| |

OLS Estimates | |

| |

| |

Regression Model in Standardized Form | |

| |

| |

Heteroscedasticity and Weighted Least Squares | |

| |

| |

Properties of the WLS Estimator | |

| |

| |

Consequences of Heteroscedasticity | |

| |

| |

Testing for Heteroscedasticity | |

| |

| |

Example: Regression of Coital Frequency | |

| |

| |

WLS in Practice: Two-Step Procedure | |

| |

| |

Testing Slope Homogeneity with WLS | |

| |

| |

Gender Differences in Salary Models, Revisited | |

| |

| |

WLS with Sampling Weights: WOLS | |

| |

| |

Omitted-Variable Bias in a Multivariable Framework | |

| |

| |

Mathematics of Omitted-Variable Bias | |

| |

| |

Bias in the Cross-Product Term | |

| |

| |

Example: Bias in Models for Faculty Salary | |

| |

| |

Regression Diagnostics I: Influential Observations | |

| |

| |

Building Blocks of Influence: Outliers and Leverage | |

| |

| |

Measuring Influence | |

| |

| |

Illustration of Influence Diagnosis | |

| |

| |

Regression Diagnostics II: Multicollinearity | |

| |

| |

Linear Dependencies in the Design Matrix | |

| |

| |

Consequences of Collinearity | |

| |

| |

Diagnosing Collinearity | |

| |

| |

Illustration | |

| |

| |

Alternatives to OLS When Regressors Are Collinear | |

| |

| |

Exercises | |

| |

| |

| |

Regression with a Binary Response | |

| |

| |

Chapter Overview | |

| |

| |

Linear Probability Model | |

| |

| |

Example | |

| |

| |

Problems with the LPM | |

| |

| |

Nonlinear Probability Models | |

| |

| |

Latent-Variable Motivation of Probit and Logistic Regression | |

| |

| |

Estimation | |

| |

| |

Inferences in Logit and Probit | |

| |

| |

Logit and Probit Analyses of Violence | |

| |

| |

Empirical Consistency and Discriminatory Power in Logistic Regression | |

| |

| |

Empirical Consistency | |

| |

| |

Discriminatory Power | |

| |

| |

Exercises | |

| |

| |

| |

Advanced Topics in Logistic Regression | |

| |

| |

Chapter Overview | |

| |

| |

Modeling Interaction | |

| |

| |

Comparing Models across Groups | |

| |

| |

Examining Variable-Specific Interaction Effects | |

| |

| |

Targeted Centering | |

| |

| |

Modeling Nonlinearity in the Regressors | |

| |

| |

Testing for Nonlinearity | |

| |

| |

Targeted Centering in Quadratic Models | |

| |

| |

Testing Coefficient Changes in Logistic Regression | |

| |

| |

Variance-Covariance Matrix of Coefficient Differences | |

| |

| |

Discriminatory Power and Empirical Consistency of Model 2 | |

| |

| |

Multinomial Models | |

| |

| |

Unordered Categorical Variables | |

| |

| |

Modeling (M - 1) Log Odds | |

| |

| |

Ordered Categorical Variables | |

| |

| |

Exercises | |

| |

| |

| |

Truncated and Censored Regression Models | |

| |

| |

Chapter Overview | |

| |

| |

Truncation and Censoring Defined | |

| |

| |

Truncation | |

| |

| |

Censoring | |

| |

| |

Simulation | |

| |

| |

Truncated Regression Model | |

| |

| |

Estimation | |

| |

| |

Simulated Data Example | |

| |

| |

Application: Scores on the First Exam | |

| |

| |

Censored Regression Model | |

| |

| |

Social Science Applications | |

| |

| |

Mean Functions | |

| |

| |

Estimation | |

| |

| |

Interpretation of Parameters | |

| |

| |

Analog of R[superscript 2] | |

| |

| |

Alternative Specification | |

| |

| |

Simulated Data Example | |

| |

| |

Applications of the Tobit Model | |

| |

| |

Sample-Selection Models | |

| |

| |

Conceptual Framework | |

| |

| |

Estimation | |

| |

| |

Nuances | |

| |

| |

Simulation | |

| |

| |

Applications of the Sample-Selection Model | |

| |

| |

Caveats Regarding Heckman's Two-Step Procedure | |

| |

| |

Exercises | |

| |

| |

| |

Regression Models for an Event Count | |

| |

| |

Chapter Overview | |

| |

| |

Densities for Count Responses | |

| |

| |

Poisson Density | |

| |

| |

Negative Binomial Density | |

| |

| |

Modeling Count Responses with Poisson Regression | |

| |

| |

Problems with OLS | |

| |

| |

Poisson Regression Model | |

| |

| |

Truncated PRM | |

| |

| |

Censoring and Sample Selection | |

| |

| |

Count-Data Models That Allow for Overdispersion | |

| |

| |

Negative Binomial Regression Model | |

| |

| |

Zero-Inflated Models | |

| |

| |

Hurdle Models | |

| |

| |

Exercises | |

| |

| |

| |

Introduction to Survival Analysis | |

| |

| |

Chapter Overview | |

| |

| |

Nature of Survival Data | |

| |

| |

Key Concepts in Survival Analysis | |

| |

| |

Nature of Event Histories | |

| |

| |

Critical Functions of Time: Density, Survival, Hazard | |

| |

| |

Example: Dissolution of Intimate Unions | |

| |

| |

Regression Models in Survival Analysis | |

| |

| |

Accelerated Failure-Time Model | |

| |

| |

Cox Regression Model | |

| |

| |

Adjusting for Left Truncation | |

| |

| |

Estimating Survival Functions in Cox Regression | |

| |

| |

Time-Varying Covariates | |

| |

| |

Handling Nonproportional Effects | |

| |

| |

Stratified Models | |

| |

| |

Assessing Model Fit | |

| |

| |

Exercises | |

| |

| |

| |

Multistate, Multiepisode, and Interval-Censored Models in Survival Analysis | |

| |

| |

Chapter Overview | |

| |

| |

Multistate Models | |

| |

| |

Modeling Type-Specific Hazard Rates | |

| |

| |

Example: Transitions Out of Cohabitation | |

| |

| |

Alternative Modeling Strategies | |

| |

| |

Multiepisode Models | |

| |

| |

Example: Unemployment Spells | |

| |

| |

Nonindependence of Survival Times | |

| |

| |

Model Variation across Spells | |

| |

| |

Modeling Interval-Censored Data | |

| |

| |

Discrete-Time Hazard Model and Estimation | |

| |

| |

Converting to Person-Period Data | |

| |

| |

Discrete-Time Analysis: Examples | |

| |

| |

Exercises | |

| |

| |

| |

Mathematics Tutorials | |

| |

| |

| |

Answers to Selected Exercises | |

| |

| |

References | |

| |

| |

Index | |