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85
Multivariate Matching Methods That are Monotonic Imbalance Bounding ∗
, 2009
"... We introduce a new “Monotonic Imbalance Bounding ” (MIB) class of matching methods for causal inference that satisfies several important insample properties. MIB generalizes and extends in several new directions the only existing class, “Equal Percent Bias Reducing ” (EPBR), which is designed to sa ..."
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Cited by 39 (1 self)
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We introduce a new “Monotonic Imbalance Bounding ” (MIB) class of matching methods for causal inference that satisfies several important insample properties. MIB generalizes and extends in several new directions the only existing class, “Equal Percent Bias Reducing ” (EPBR), which is designed to satisfy weaker properties and only in expectation. We also offer strategies to obtain specific members of the MIB class, and present a member of this class, called Coarsened Exact Matching, whose properties we analyze from this new perspective. ∗Open source R and Stata software to implement the methods described herein (called CEM) is available at
Propensity Scores: An Introduction and Experimental Test.” Evaluation Review 29:530–58
, 2005
"... ..."
Attributing Effects to A Cluster Randomized GetOutTheVote Campaign.” Working Paper
, 2008
"... In a landmark study of political participation, A. Gerber and D. Green (2000) experimentally compared the effectiveness of various getoutthevote interventions. The study was wellpowered, conducted not in a lab but under field conditions, in the midst of a Congressional campaign; it used random ..."
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Cited by 29 (7 self)
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In a landmark study of political participation, A. Gerber and D. Green (2000) experimentally compared the effectiveness of various getoutthevote interventions. The study was wellpowered, conducted not in a lab but under field conditions, in the midst of a Congressional campaign; it used random assignment, in a field where randomization had been rare. As Fisher (1935) showed long ago, inferences from randomized designs can be essentially assumptionfree, making them uniquely suited to settle scientific debates. This study, however, prompted a contentious new debate after Imai (2005) tested and rejected the randomization model for Gerber and Green’s data. His alternate methodology reaches substantive conclusions contradicting those of Gerber and Green. It has since become clear that the experiment’s apparent lapses can be ascribed to clustered treatment assignment, rather than failures of randomization; it had randomized households, not individuals. What remains to be clarified is how this structure could have been accommodated by an analysis as sparing with
Optimal full matching and related designs via network flows
 Journal of Computational and Graphical Statistics
, 2006
"... In the matched analysis of an observational study, confounding on covariates X is addressed by comparing members of a distinguished group (Z = 1) to controls (Z =0) only when they belong to the same matched set. The better matchings, therefore, are those whose matched sets exhibit both dispersion in ..."
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Cited by 27 (4 self)
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In the matched analysis of an observational study, confounding on covariates X is addressed by comparing members of a distinguished group (Z = 1) to controls (Z =0) only when they belong to the same matched set. The better matchings, therefore, are those whose matched sets exhibit both dispersion in Z and uniformity in X. For dispersion in Z, pair matching is best, creating matched sets that are equally balanced between the groups; but actual data place limits, often severe limits, on matched pairs’ uniformity in X. At the other extreme is full matching, the matched sets of which are as uniform in X as can be, while often so poorly dispersed in Z as to sacrifice efficiency. This article presents an algorithm for exploring the intermediate territory. Given requirements on matched sets ’ uniformity in X and dispersion in Z, the algorithm first decides the requirements ’ feasibility. In feasible cases, it furnishes a match that is optimal for Xuniformity among matches with Zdispersion as stipulated. To illustrate, we describe the algorithm’s use in a study comparing womens ’ to mens ’ working conditions; and we compare our method to a commonly used alternative, greedy matching, which is neither optimal nor as flexible but is algorithmically much simpler. The comparison finds meaningful advantages, in terms of both bias and efficiency, for our more studied approach.
Entropy Balancing for Causal Effects: A Multivariate Reweighting Method to Produce Balanced Samples in Observational Studies
"... This paper proposes entropy balancing, a data preprocessing method to achieve covariate balance in observational studies with binary treatments. Entropy balancing relies on a maximum entropy reweighting scheme that calibrates unit weights so that the reweighted treatment and control group satisfy a ..."
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Cited by 19 (0 self)
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This paper proposes entropy balancing, a data preprocessing method to achieve covariate balance in observational studies with binary treatments. Entropy balancing relies on a maximum entropy reweighting scheme that calibrates unit weights so that the reweighted treatment and control group satisfy a potentially large set of prespecified balance conditions that incorporate information about known sample moments. Entropy balancing thereby exactly adjusts inequalities in representation with respect to the first, second, and possibly higher moments of the covariate distributions. These balance improvements can reduce model dependence for the subsequent estimation of treatment effects. The method assures that balance improves on all covariate moments included in the reweighting. It also obviates the need for continual balance checking and iterative searching over propensity score models that may stochastically balance the covariate moments. We demonstrate the use of entropy balancing with Monte Carlo simulations and empirical applications. 1
Combining propensity score matching and groupbased trajectory analysis in an observational study
 Psychological Methods
, 2007
"... In a nonrandomized or observational study, propensity scores may be used to balance observed covariates and trajectory groups may be used to control baseline or pretreatment measures of outcome. The trajectory groups also aid in characterizing classes of subjects for whom no good matches are availab ..."
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Cited by 18 (2 self)
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In a nonrandomized or observational study, propensity scores may be used to balance observed covariates and trajectory groups may be used to control baseline or pretreatment measures of outcome. The trajectory groups also aid in characterizing classes of subjects for whom no good matches are available and to define substantively interesting groups between which treatment effects may vary. These and related methods are illustrated using data from a Montrealbased study. The effects on subsequent violence of gang joining at age 14 are studied while controlling for measured characteristics of boys prior to age 14. The boys are divided into trajectory groups based on violence from ages 11 to 13. Within trajectory group, joiners are optimally matched to a variable number of controls using propensity scores, Mahalanobis distances, and a combinatorial optimization algorithm. Use of variable ratio matching results in greater efficiency than pair matching and also greater bias reduction than matching at a fixed ratio. The possible impact of failing to adjust for an important but unmeasured covariate is examined using sensitivity analysis.
Bayesian Nonparametric Modeling for Causal Inference
, 2007
"... Researchers have long struggled to identify causal effects in nonexperimental settings. Many recentlyproposed strategies assume ignorability of the treatment assignment mechanism and require fitting two models – one for the assignment mechanism and one for the response surface. We propose a strate ..."
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Cited by 16 (2 self)
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Researchers have long struggled to identify causal effects in nonexperimental settings. Many recentlyproposed strategies assume ignorability of the treatment assignment mechanism and require fitting two models – one for the assignment mechanism and one for the response surface. We propose a strategy that instead focuses on very flexibly modeling just the response surface using a Bayesian nonparametric modeling procedure, Bayesian Additive Regression Trees (BART). BART has several advantages: it is far simpler to use than many recent competitors, requires less guesswork in model fitting, handles a large number of predictors, yields coherent uncertainty intervals, fluidly handles continuous treatment variables and missing data for the outcome variable. BART produces more efficient estimates in the nonlinear situations tested in our simulations compared to propensity score matching, propensityweighted estimators, and regression adjustment. Further, it is highly competitive in linear settings with the “correct” model, linear regression.
Best Practices in QuasiExperimental Designs: Matching Methods for Causal Inference
 in Best Practices in Quantitative Social Science, Edited by Jason Osborne. Thousand Oaks, CA: Sage
, 2007
"... any studies in social science that aim to estimate the effect of an intervention suffer from treatment selection bias, where the units who receive the treatment may have different characteristics from those in the control condition. These preexisting differences between the groups must be controlled ..."
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Cited by 14 (0 self)
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any studies in social science that aim to estimate the effect of an intervention suffer from treatment selection bias, where the units who receive the treatment may have different characteristics from those in the control condition. These preexisting differences between the groups must be controlled to obtain approximately unbiased estimates of the effects of interest. For example, in a study estimating the effect of bullying on high school graduation, students who were bullied are likely to be very different from students who were not bullied on a wide range of characteristics, such as socioeconomic status and academic performance, even before the bullying began. It is crucial to try to
Comparative effectiveness of matching methods for causal inference
, 2011
"... Matching methods for causal inference selectively prune observations from the data in order to reduce model dependence. They are successful when simultaneously maximizing balance (between the treated and control groups on the pretreatment covariates) and the number of observations remaining in the ..."
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Cited by 13 (2 self)
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Matching methods for causal inference selectively prune observations from the data in order to reduce model dependence. They are successful when simultaneously maximizing balance (between the treated and control groups on the pretreatment covariates) and the number of observations remaining in the data set. However, existing matching methods either fix the matched sample size ex ante and attempt to reduce imbalance as a result of the procedure (e.g., propensity score and Mahalanobis distance matching) or fix imbalance ex ante and attempt to lose as few observations as possible ex post (e.g., coarsened exact matching and calpierbased approaches). As an alternative, we offer a simple graphical approach that addresses both criteria simultaneously and lets the user choose a matching solution from the imbalancesample size frontier. In the process of applying our approach, we also discover that propensity score matching (PSM) often approximates random matching, both in real applications and in data simulated by the processes that fit PSM theory. Moreover, contrary to conventional wisdom, random matching is not benign: it (and thus often PSM) can degrade inferences relative to not matching at all. Other methods we study do not have these or other problems we describe. However, with our easytouse graphical approach, users can focus on choosing a matching solution for a particular application rather than whatever method happened to be used to generate it. ∗Our thanks to Stefano Iacus and Giuseppe Porro for always helpful insights, suggestions, and collaboration