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Propensity Score Analysis

Propensity Score Analysis
Statistical Methods and Applications

Second Edition

July 2014 | 448 pages | SAGE Publications, Inc

Fully updated to reflect the most recent changes in the field, the Second Edition of Propensity Score Analysis provides an accessible, systematic review of the origins, history, and statistical foundations of propensity score analysis, illustrating how it can be used for solving evaluation and causal-inference problems. With a strong focus on practical applications, the authors explore various strategies for employing PSA, discuss the use of PSA with alternative types of data, and delineate the limitations of PSA under a variety of constraints. Unlike existing textbooks on program evaluation and causal inference, this book delves into statistical concepts, formulas, and models within the context of a robust and engaging focus on application.

List of Tables
List of Figures
About the Authors
Chapter 1: Introduction
Observational Studies

History and Development

Randomized Experiments

Why and When a Propensity Score Analysis Is Needed

Computing Software Packages

Plan of the Book

Chapter 2: Counterfactual Framework and Assumptions
Causality, Internal Validity, and Threats

Counterfactuals and the Neyman-Rubin Counterfactual Framework

The Ignorable Treatment Assignment Assumption

The Stable Unit Treatment Value Assumption

Methods for Estimating Treatment Effects

The Underlying Logic of Statistical Inference

Types of Treatment Effects

Treatment Effect Heterogeneity

Heckman’s Econometric Model of Causality


Chapter 3: Conventional Methods for Data Balancing
Why Is Data Balancing Necessary? A Heuristic Example

Three Methods for Data Balancing

Design of the Data Simulation

Results of the Data Simulation

Implications of the Data Simulation

Key Issues Regarding the Application of OLS Regression


Chapter 4: Sample Selection and Related Models
The Sample Selection Model

Treatment Effect Model

Overview of the Stata Programs and Main Features of treatreg



Chapter 5: Propensity Score Matching and Related Models

The Problem of Dimensionality and the Properties of Propensity Scores

Estimating Propensity Scores


Postmatching Analysis

Propensity Score Matching With Multilevel Data

Overview of the Stata and R Programs



Chapter 6: Propensity Score Subclassification

The Overlap Assumption and Methods to Address Its Violation

Structural Equation Modeling With Propensity Score Subclassification

The Stratification-Multilevel Method



Chapter 7: Propensity Score Weighting

Weighting Estimators



Chapter 8: Matching Estimators

Methods of Matching Estimators

Overview of the Stata Program nnmatch



Chapter 9: Propensity Score Analysis With Nonparametric Regression

Methods of Propensity Score Analysis With Nonparametric Regression

Overview of the Stata Programs psmatch2 and bootstrap



Chapter 10: Propensity Score Analysis of Categorical or Continuous Treatments

Modeling Doses With a Single Scalar Balancing Score Estimated by an Ordered Logistic Regression

Modeling Doses With Multiple Balancing Scores Estimated by a Multinomial Logit Model

The Generalized Propensity Score Estimator

Overview of the Stata gpscore Program



Chapter 11: Selection Bias and Sensitivity Analysis
Selection Bias: An Overview

A Monte Carlo Study Comparing Corrective Models

Rosenbaum’s Sensitivity Analysis

Overview of the Stata Program rbounds



Chapter 12: Concluding Remarks
Common Pitfalls in Observational Studies: A Checklist for Critical Review

Approximating Experiments With Propensity Score Approaches

Other Advances in Modeling Causality

Directions for Future Development



Companion Website
The site contains programming syntax for all the examples found in the book, by chapter and section.

    Over the past 35 years, methods of program evaluation have undergone a significant change, and the researchers have recognized the need to develop more efficient approaches for assessing treatment effects from studies based on observational data and for evaluations based on quasi-experimental designs.

    Written by experts, this volume is updated and fully reflects the current changes to the field. It offers a systematic review of the history, origins, and statistical foundations of propensity score analysis,  and more.

NeoPopRealism Journal
NeoPopRealism Journal
Key features


  • Propensity score sub-classification and propensity score weighting are treated as separate models to give thorough attention to each.
  • Newly expanded coverage of analyzing treatment dosage in the context of propensity score modeling broadens the scope of application for readers.
  • New coverage of modeling heterogeneous treatment effects includes two nonparametric tests and a discussion of modeling issues to ensure students are on the cutting edge.
  • Expanded content on propensity score analysis with multilevel data includes new discussions of four multilevel models for estimating propensity scores and two strategies for controlling clustering effects in outcome analysis.
  • The principles and issues related to running propensity score models with sub-classification and weighting are covered in depth.
  • The authors demonstrate new software and include clear illustrations for analyzing treatment dosage with GPS.




  • The authors present key information on model derivations and summarize complex statistical arguments—omitting their proofs to challenge readers to apply their learning.
  • Each method, and its empirical examples, is linked to specific Stata programs for seamless integration of learning and application. 
  • Two conceptual frameworks—the Neyman-Rubin counterfactual framework and the Heckman econometric model of causality—provide a foundation for understanding key topics.
  • Examples in every chapter demonstrate real challenges found in social and health sciences research.
  • Data simulation is used to illustrate key points. 
  • New statistical approaches necessary for understanding the seven evaluation methods are included.

The most significant change of the second edition is discussion of propensity score subclassification, propensity score weighting, and dosage analysis from Chapter 5 to separate chapters. These methods are closely related to the Rosenbaum and Rubin’s (1983) seminal study of the development of propensity scores—it is for this reason that Chapter 5 of the first edition pooled these methods together. Because subclassification and weighting methods have been widely applied in recent research and have become recommended models for addressing challenging data issues (Imbens & Wooldridge, 2009), we decided to give each topic a separate treatment. There is an increasing need in social behavioral and health research to model treatment dosage and to extend the propensity score approach from the binary treatment conditions context to categorical and/or continuous treatment conditions contexts. Given these considerations, we treated dosage analysis in the second edition as a separate chapter. As a result, Chapter 5 now focuses on propensity score matching methods alone, including greedy matching and optimal matching.

Sample Materials & Chapters

Chapter 1

Chapter 2

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