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| Preface | |
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| Introduction to Regression Modeling | |
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| Chapter Overview | |
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| Mathematical and Statistical Models | |
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| Linear Regression Models | |
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| Generalized Linear Model | |
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| Model Evaluation | |
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| Regression Models and Causal Inference | |
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| What Is a Cause? | |
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| When Does a Regression Coefficient Have a Causal Interpretation? | |
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| Recommendations | |
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| Datasets Used in This Volume | |
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| National Survey of Families and Households Datasets | |
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| Datasets from the NVAWS | |
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| Other Datasets | |
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| Statistical Review | |
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| Simple Linear Regression | |
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| Chapter Overview | |
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| Linear Relationships | |
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| Simple Linear Regression Model | |
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| Regression Assumptions | |
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| Interpreting the Regression Equation | |
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| Estimation Using Sample Data | |
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| Rationale for OLS | |
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| Mathematics of OLS | |
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| Inferences in Simple Linear Regression | |
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| Tests about the Population Slope | |
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| Testing the Intercept | |
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| Confidence Intervals for [beta subscript 0] and [beta subscript 1] | |
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| Additional Examples | |
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| Assessing Empirical Consistency of the Model | |
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| Conforming to Assumptions | |
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| Formal Test of Empirical Consistency | |
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| Stochastic Regressors | |
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| Estimation of [beta subscript 0] and [beta subscript 1] via Maximum Likelihood | |
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| Exercises | |
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| Introduction to Multiple Regression | |
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| Chapter Overview | |
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| Employing Multiple Predictors | |
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| Advantages and Rationale for MULR | |
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| Example | |
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| Controlling for a Third Variable | |
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| MULR Model | |
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| Inferences in MULR | |
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| Omitted-Variable Bias | |
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| Modeling Interaction Effects | |
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| Evaluating Empirical Consistency | |
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| Examination of Residuals | |
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| Partial Regression Leverage Plots | |
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| Exercises | |
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| Multiple Regression with Categorical Predictors: ANOVA and ANCOVA Models | |
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| Chapter Overview | |
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| Models with Exclusively Categorical Predictors | |
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| Dummy Coding | |
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| Effect Coding | |
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| Two-Way ANOVA in Regression | |
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| Interaction between Categorical Predictors | |
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| Models with Both Categorical and Continuous Predictors | |
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| Adjusted Means | |
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| Interaction between Categorical and Continuous Predictors | |
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| Comparing Models across Groups, Revisited | |
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| Exercises | |
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| Modeling Nonlinearity | |
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| Chapter Overview | |
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| Nonlinearity Defined | |
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| Common Nonlinear Functions of X | |
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| Quadratic Functions of X | |
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| Applications of the Quadratic Model | |
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| Testing Departures from Linearity | |
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| Interpreting Quadratic Models | |
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| Nonlinear Interaction | |
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| Nonlinear Regression | |
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| Estimating the Multiplicative Model | |
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| Estimating the Nonlinear Model | |
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| Exercises | |
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| Advanced Issues in Multiple Regression | |
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| Chapter Overview | |
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| Multiple Regression in Matrix Notation | |
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| The Model | |
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| OLS Estimates | |
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| Regression Model in Standardized Form | |
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| Heteroscedasticity and Weighted Least Squares | |
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| Properties of the WLS Estimator | |
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| Consequences of Heteroscedasticity | |
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| Testing for Heteroscedasticity | |
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| Example: Regression of Coital Frequency | |
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| WLS in Practice: Two-Step Procedure | |
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| Testing Slope Homogeneity with WLS | |
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| Gender Differences in Salary Models, Revisited | |
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| WLS with Sampling Weights: WOLS | |
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| Omitted-Variable Bias in a Multivariable Framework | |
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| Mathematics of Omitted-Variable Bias | |
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| Bias in the Cross-Product Term | |
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| Example: Bias in Models for Faculty Salary | |
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| Regression Diagnostics I: Influential Observations | |
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| Building Blocks of Influence: Outliers and Leverage | |
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| Measuring Influence | |
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| Illustration of Influence Diagnosis | |
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| Regression Diagnostics II: Multicollinearity | |
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| Linear Dependencies in the Design Matrix | |
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| Consequences of Collinearity | |
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| Diagnosing Collinearity | |
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| Illustration | |
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| Alternatives to OLS When Regressors Are Collinear | |
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| Exercises | |
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| Regression with a Binary Response | |
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| Chapter Overview | |
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| Linear Probability Model | |
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| Example | |
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| Problems with the LPM | |
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| Nonlinear Probability Models | |
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| Latent-Variable Motivation of Probit and Logistic Regression | |
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| Estimation | |
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| Inferences in Logit and Probit | |
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| Logit and Probit Analyses of Violence | |
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| Empirical Consistency and Discriminatory Power in Logistic Regression | |
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| Empirical Consistency | |
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| Discriminatory Power | |
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| Exercises | |
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| Advanced Topics in Logistic Regression | |
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| Chapter Overview | |
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| Modeling Interaction | |
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| Comparing Models across Groups | |
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| Examining Variable-Specific Interaction Effects | |
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| Targeted Centering | |
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| Modeling Nonlinearity in the Regressors | |
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| Testing for Nonlinearity | |
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| Targeted Centering in Quadratic Models | |
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| Testing Coefficient Changes in Logistic Regression | |
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| Variance-Covariance Matrix of Coefficient Differences | |
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| Discriminatory Power and Empirical Consistency of Model 2 | |
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| Multinomial Models | |
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| Unordered Categorical Variables | |
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| Modeling (M - 1) Log Odds | |
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| Ordered Categorical Variables | |
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| Exercises | |
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| Truncated and Censored Regression Models | |
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| Chapter Overview | |
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| Truncation and Censoring Defined | |
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| Truncation | |
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| Censoring | |
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| Simulation | |
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| Truncated Regression Model | |
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| Estimation | |
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| Simulated Data Example | |
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| Application: Scores on the First Exam | |
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| Censored Regression Model | |
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| Social Science Applications | |
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| Mean Functions | |
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| Estimation | |
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| Interpretation of Parameters | |
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| Analog of R[superscript 2] | |
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| Alternative Specification | |
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| Simulated Data Example | |
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| Applications of the Tobit Model | |
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| Sample-Selection Models | |
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| Conceptual Framework | |
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| Estimation | |
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| Nuances | |
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| Simulation | |
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| Applications of the Sample-Selection Model | |
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| Caveats Regarding Heckman's Two-Step Procedure | |
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| Exercises | |
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| Regression Models for an Event Count | |
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| Chapter Overview | |
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| Densities for Count Responses | |
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| Poisson Density | |
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| Negative Binomial Density | |
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| Modeling Count Responses with Poisson Regression | |
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| Problems with OLS | |
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| Poisson Regression Model | |
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| Truncated PRM | |
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| Censoring and Sample Selection | |
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| Count-Data Models That Allow for Overdispersion | |
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| Negative Binomial Regression Model | |
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| Zero-Inflated Models | |
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| Hurdle Models | |
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| Exercises | |
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| Introduction to Survival Analysis | |
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| Chapter Overview | |
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| Nature of Survival Data | |
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| Key Concepts in Survival Analysis | |
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| Nature of Event Histories | |
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| Critical Functions of Time: Density, Survival, Hazard | |
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| Example: Dissolution of Intimate Unions | |
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| Regression Models in Survival Analysis | |
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| Accelerated Failure-Time Model | |
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| Cox Regression Model | |
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| Adjusting for Left Truncation | |
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| Estimating Survival Functions in Cox Regression | |
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| Time-Varying Covariates | |
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| Handling Nonproportional Effects | |
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| Stratified Models | |
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| Assessing Model Fit | |
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| Exercises | |
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| Multistate, Multiepisode, and Interval-Censored Models in Survival Analysis | |
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| Chapter Overview | |
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| Multistate Models | |
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| Modeling Type-Specific Hazard Rates | |
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| Example: Transitions Out of Cohabitation | |
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| Alternative Modeling Strategies | |
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| Multiepisode Models | |
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| Example: Unemployment Spells | |
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| Nonindependence of Survival Times | |
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| Model Variation across Spells | |
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| Modeling Interval-Censored Data | |
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| Discrete-Time Hazard Model and Estimation | |
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| Converting to Person-Period Data | |
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| Discrete-Time Analysis: Examples | |
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| Exercises | |
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| Mathematics Tutorials | |
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| Answers to Selected Exercises | |
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| References | |
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| Index | |