1. What the Book Is About
2. New in the Second Edition
3. Acknowledgments
1. Introduction
1.1 Observational Studies
1.2 History and Development
1.3 Randomized Experiments
1.3.1 Fisher's Randomized Experiment
1.3.2 Types of Randomized Experiments and Statistical Tests
1.3.3 Critiques of Social Experimentation
1.4 Why and When a Propensity Score Analysis Is Needed
1.5 Computing Software Packages
1.6 Plan of the Book
2. Counterfactual Framework and Assumptions
2.1 Causality, Internal Validity, and Threats
2.2 Counterfactuals and the Neyman-Rubin Counterfactual Framework
2.3 The Ignorable Treatment Assignment Assumption
2.4 The Stable Unit Treatment Value Assumption
2.5 Methods for Estimating Treatment Effects
2.5.1 Design of Observational Study
2.5.2 The Seven Models
2.5.3 Other Balancing Methods
2.5.4 Instrumental Variables Estimator
2.5.5 Regression Discontinuity Designs
2.6 The Underlying Logic of Statistical Inference
2.7 Types of Treatment Effects
2.8 Treatment Effect Heterogeneity
2.8.1 The Importance of Studying Treatment Effect Heterogeneity
2.8.2 Checking the Plausability of the Unconfoundedness Assumption
2.8.3 A Methodological Note About the Hausman Test of Endogeneity
2.8.4 Tests of Treatment Effect Heterogeneity
2.8.5 Example
2.9 Heckman's Econometric Model of Causality
2.10 Conclusion
3. Conventional Methods for Data Balancing
3.1 Why Is Data Balancing Necessary? A Heuristic Example
3.2 Three Methods for Data Balancing
3.2.1 The Ordinary Least Squares Regression
3.2.2 Matching
3.2.3 Stratification
3.3 Design of the Data Simulation
3.4 Results of the Data Simulation
3.5 Implications of the Data Simulation
3.6 Key Issues Regarding the Application of OLS Regression
3.7 Conclusion
4. Sample Selection and Related Models
4.1 The Sample Selection Model
4.1.1 Truncation, Censoring, and Incidental Truncation
4.1.2 Why Is It Important to Model Sample Selection?
4.1.3 Moments of an Incidentally Truncated Bivariate Normal Distribution
4.1.4 The Heckman Model and Its Two-Step Estimator
4.2 Treatment Effect Model
4.3 Overview of the Stata Programs and Main Features of
treatreg
4.4 Examples
4.4.1 Application of the Treatment Effect model to Analysis of Observational Data
4.4.2 Evaluation of Treatment Effects from a Program With a Group Randomization Design
4.4.3 Running the Treatment Effect Model After Multiple Imputations of Missing Data
4.5 Conclusion
5. Propensity Score Matching and Related Models
5.1 Overview
5.2 The Problem of Dimensionality and the Properties of Propensity Scores
5.3 Estimating Propensity Scores
5.3.1 Binary Logistic Regression
5.3.2 Strategies to Specify a Correct Model—Predicting Propensity Scores
5.3.3 Hirano and Imbens's Method for Specifying Predictors Relying on Predetermined Critical t Values
5.3.4 Generalized Boosted Modeling
5.4 Matching
5.4.1 Greedy Matching
5.4.2 Optimal Matching
5.4.3 Fine Balance
5.5 Postmatching Analysis
5.5.1 Multivariate Analysis After Greedy Matching
5.5.2 Computing Indices of Covariate Imbalance
5.5.3 Outcome Analysis Using the Hodges-Lehmann Aligned Rank Test After Optimal Matching
5.5.4 Regression Adjustment Based on Sample Created by Optimal Pair Matching
5.5.5 Regression Adjustment Using Hodges-Lehmann Aligned Rank Scores After Optimal Matching
5.6 Propensity Score Matching With Multilevel Data
5.6.1 Overview of Statistical Approaches to Multilevel Data
5.6.2 Perspectives Extending the Propensity Score Analysis to the Multilevel Modeling
5.6.3 Estimation of the Propensity Scores Under the Context of Multilevel Modeling
5.6.4 Multilevel Outcome Analysis
5.7 Overview of the Stata and R Programs
5.8 Examples
5.8.1 Greedy Matching and Subsequent Analysis of Hazard Rates
5.8.2 Optimal Matching
5.8.3 Post-Full Matching Analysis Using the Hodges-Lehmann Aligned Rank Test
5.8.4 Post-Pair Matching Analysis Using Regression of Difference Scores
5.8.5 Multilevel Propensity Score Analysis
5.8.6 Comparison of Rand-gbm and Stata's boost Algorithms
5.9 Conclusion
6. Propensity Score Subclassification
6.1 Overview
6.2 The Overlap Assumption and Methods to Address Its Violation
6.3 Structural Equation Modeling With Propensity Score Subclassification
6.3.1 The Need for Integrating SEM and Propensity Score Modeling Into One Analysis
6.3.2 Kaplan's (1999) Work to Integrate Propensity Score Subclassification With SEM
6.3.3 Conduct SEM With Propensity Score Subclassification
6.4 The Stratification-Multilevel Method
6.5 Examples
6.5.1 Stratification After Greedy Matching
6.5.2 Subclassification Followed by a Cox Proportional Hazards Model
6.5.3 Propensity Score Subclassification in Conjunction with SEM
6.6 Conclusion
7. Propensity Score Weighting
7.1 Overview
7.2 Weighting Estimators
7.2.1 Formulas for Creating Weights to Estimate ATE and ATT
7.2.2 A Corrected Version of Weights Estimating ATE
7.2.3 Steps in Propensity Score Weighting
7.3 Examples
7.3.1 Propensity Score Weighting With a Multiple Regression Outcome Analysis
7.3.2 Propensity Score Weighting With a Cox Proportional Hazards Model
7.3.3 Propensity Score Weighting With an SEM
7.3.4 Comparison of Models and Conclusions of the Study of the Impact of Poverty on Child Academic Achievement
7.4 Conclusion
8. Matching Estimators
8.1 Overview
8.2 Methods of Matching Estimators
8.2.1 Simple Matching Estimators
8.2.2 Bias-Corrected Matching Estimator
8.2.3 Variance Estimator Assuming Homoscedasticity
8.2.4 Variance Estimator Allowing for Heteroscedasticity
8.2.5 Large Sample Properties and Correction
8.3 Overview of the Stata Program
nnmatch
8.4 Examples
8.4.1 Matching With Bias-Corrected and Robust Variance Estimators
8.4.2 Efficacy Subset Analysis With Matching Estimators
8.5 Conclusion
9. Propensity Score Analysis With Nonparametric Regression
9.1 Overview
9.2 Methods of Propensity Score Analysis With Nonparametric Regression
9.2.1 The Kernel-Based Matching Estimators
9.2.2 Review of the Basic Concepts of Local Linear Regression (lowess)
9.2.3 Asymptotic and Finite-Sample Properties of Kernel and Local Linear Matching
9.3 Overview of the Stata Programs
psmatch2 and
bootstrap
9.4 Examples
9.4.1 Analysis of Difference-in-Differences
9.4.2 Application of Kernel-Based Matching to One-Point Data
9.5 Conclusion
10. Propensity Score Analysis of Categorical or Continuous Treatments: Dosage Analyses
10.1 Overview
10.2 Modeling Doses With a Single Scalar Balancing Score Estimated by an Ordered Logistic Regression
10.3 Modeling Doses With Multiple Balancing Scores Estimated by a Multinomial Logit Model
10.4 The Generalized Propensity Score Estimator
10.5 Overview of the Stata
gpscore Program
10.6 Examples
10.6.1 Modeling Doses of Treatment With Multiple Balancing Scores Estimated by a Multinomial Logit Model
10.6.2 Modeling Doses of Treatment With the Generalized Propensity Score Estimator
10.7 Conclusion
11. Selection Bias and Sensitivity Analysis
11.1 Selection Bias: An Overview
11.1.1 Sources of Selection Bias
11.1.2 Overt Bias Versus Hidden Bias
11.1.3 Consequences of Selection Bias
11.1.4 Strategies to Correct for Selection Bias
11.2 A Monte Carlo Study Comparing Corrective Models
11.2.1 Design of the Monte Carlo Study
11.2.2 Results of the Monte Carlo Study
11.2.3 Implications
11.3 Rosenbaum's Sensitivity Analysis
11.3.1 The Basic Idea
11.3.2 Illustration of Wilcoxon's Signed Rank Test for Sensitivity Analysis of a Matched Pair Study
11.4 Overview of the Stata Program
rbounds
11.5 Examples
11.5.1 Sensitivity Analysis of the Effects of Lead Exposure
11.5.2 Sensitivity Analysis for the Study Using Pair Matching
11.6 Conclusion
12. Concluding Remarks
12.1 Common Pitfalls in Observational Studies: A Checklist for Critical Review
12.2 Approximating Experiments With Propensity Score Approaches
12.2.1 Criticism of Propensity Score Methods
12.2.2 Regression and Propensity Score Approaches: Do They Provide Similar Results?
12.2.3 Criticism of Sensitivity Analysis (Γ)
12.2.4 Group Randomized Trials
12.3 Other Advances in Modeling Causality
12.4 Directions for Future Development
