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114
Matching methods for causal inference: A review and a look forward.
 Statistical science.
, 2010
"... Abstract When estimating causal effects using observational data, it is desirable to replicate a randomized experiment as closely as possible by obtaining treated and control groups with similar covariate distributions. This goal can often be achieved by choosing wellmatched samples of the origina ..."
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Abstract When estimating causal effects using observational data, it is desirable to replicate a randomized experiment as closely as possible by obtaining treated and control groups with similar covariate distributions. This goal can often be achieved by choosing wellmatched samples of the original treated and control groups, thereby reducing bias due to the covariates. Since the 1970's, work on matching methods has examined how to best choose treated and control subjects for comparison. Matching methods are gaining popularity in fields such as economics, epidemiology, medicine, and political science. However, until now the literature and related advice has been scattered across disciplines. Researchers who are interested in using matching methodsor developing methods related to matchingdo not have a single place to turn to learn about past and current research. This paper provides a structure for thinking about matching methods and guidance on their use, coalescing the existing research (both old and new) and providing a summary of where the literature on matching methods is now and where it should be headed.
Discriminative learning under covariate shift
 The Journal of Machine Learning Research
"... We address classification problems for which the training instances are governed by an input distribution that is allowed to differ arbitrarily from the test distribution—problems also referred to as classification under covariate shift. We derive a solution that is purely discriminative: neither tr ..."
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We address classification problems for which the training instances are governed by an input distribution that is allowed to differ arbitrarily from the test distribution—problems also referred to as classification under covariate shift. We derive a solution that is purely discriminative: neither training nor test distribution are modeled explicitly. The problem of learning under covariate shift can be written as an integrated optimization problem. Instantiating the general optimization problem leads to a kernel logistic regression and an exponential model classifier for covariate shift. The optimization problem is convex under certain conditions; our findings also clarify the relationship to the known kernel mean matching procedure. We report on experiments on problems of spam filtering, text classification, and landmine detection.
New evidence on the finite sample properties of propensity score reweighting and matching estimators. Unpublished manuscript
, 2011
"... Currently available asymptotic results in the literature suggest that matching estimators have higher variance than reweighting estimators. The extant literature comparing the finite sample properties of matching to specific reweighting estimators, however, has concluded that reweighting performs fa ..."
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Cited by 30 (0 self)
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Currently available asymptotic results in the literature suggest that matching estimators have higher variance than reweighting estimators. The extant literature comparing the finite sample properties of matching to specific reweighting estimators, however, has concluded that reweighting performs far worse than even the simplest matching estimator. We resolve these puzzling conclusions. Specifically we show that the findings from the finite sample analyses are not inconsistent with asymptotic analysis, but are very specific to particular choices regarding the implementation of reweighting, and fail to generalize to settings likely to be encountered in actual empirical practice.
An Introduction to Propensity Score Methods for Reducing the Effects of Confounding in Observational Studies
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Doubly Robust Policy Evaluation and Learning
"... We study decision making in environments where the reward is only partially observed, but can be modeled as a function of an action and an observed context. This setting, known as contextual bandits, encompasses a wide variety of applications including healthcare policy and Internet advertising. A ..."
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Cited by 25 (7 self)
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We study decision making in environments where the reward is only partially observed, but can be modeled as a function of an action and an observed context. This setting, known as contextual bandits, encompasses a wide variety of applications including healthcare policy and Internet advertising. A central task is evaluation of a new policy given historic data consisting of contexts, actions and received rewards. The key challenge is that the past data typically does not faithfully represent proportions of actions taken by a new policy. Previous approaches rely either on models of rewards or models of the past policy. The former are plagued by a large bias whereas the latter have a large variance. In this work, we leverage the strength and overcome the weaknesses of the two approaches by applying the doubly robust technique to the problems of policy evaluation and optimization. We prove that this approach yields accurate value estimates when we have either a good (but not necessarily consistent) model of rewards or a good (but not necessarily consistent) model of past policy. Extensive empirical comparison demonstrates that the doubly robust approach uniformly improves over existing techniques, achieving both lower variance in value estimation and better policies. As such, we expect the doubly robust approach to become common practice. 1.
Finite Sample Properties of Semiparametric Estimators of Average Treatment Effects,” Unpublished Working
, 2008
"... We explore the finite sample properties of several semiparametric estimators of average treatment effects, including propensity score reweighting, matching, double robust, and control function estimators. When there is good overlap in the distribution of propensity scores for treatment and control u ..."
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Cited by 23 (5 self)
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We explore the finite sample properties of several semiparametric estimators of average treatment effects, including propensity score reweighting, matching, double robust, and control function estimators. When there is good overlap in the distribution of propensity scores for treatment and control units, reweighting estimators are preferred on bias grounds and attain the semiparametric efficiency bound even for samples of size 100. Pair matching exhibits similarly good performance in terms of bias, but has notably higher variance. Local linear and ridge matching are competitive with reweighting in terms of bias and variance, but only once n = 500. Nearestneighbor, kernel, and blocking matching are not competitive. When overlap is close to failing, none of the estimators examined perform well and √ nasymptotics may be a poor guide to finite sample performance. Trimming rules, commonly used in the face of problems with overlap, are effective only in settings with homogeneous treatment effects. JEL Classification: C14, C21, C52.
Weighting Regressions by Propensity Scores
"... Regressions can be weighted by propensity scores in order to reduce bias. However, weighting is likely to increase random error in the estimates, and to bias the estimated standard errors downward, even when selection mechanisms are well understood. Moreover, in some cases, weighting will increase t ..."
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Cited by 20 (3 self)
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Regressions can be weighted by propensity scores in order to reduce bias. However, weighting is likely to increase random error in the estimates, and to bias the estimated standard errors downward, even when selection mechanisms are well understood. Moreover, in some cases, weighting will increase the bias in estimated causal parameters. If investigators have a good causal model, it seems better just to fit the model without weights. If the causal model is improperly specified, there can be significant problems in retrieving the situation by weighting, although weighting may help under some circumstances.
The impact of gang formation on local patterns of crime
 Journal of Research in Crime and Delinquency
, 2007
"... Research has demonstrated that even after controlling for individual level attributes, individuals who join gangs commit more crimes than do nongang members. Furthermore, the offending level of gang members is higher when they report being active members of the gang. Therefore, gang membership clear ..."
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Cited by 18 (2 self)
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Research has demonstrated that even after controlling for individual level attributes, individuals who join gangs commit more crimes than do nongang members. Furthermore, the offending level of gang members is higher when they report being active members of the gang. Therefore, gang membership clearly facilitates offending above and beyond individual level characteristics. But what impact does the onset of gangs have on aggregate crime patterns? By exploring levels and patterns of crime in an “emergent gang city” (Pittsburgh, Pennsylvania), the authors test whether the individual level finding linking gang membership to increased offending equates to more crime at the aggregate, citywide level. They also explore the impact that gang formation has on local patterns of crime. Gangs tend to be territorial, but although many qualitative accounts describe the crimegang relationship within the community, few empirical studies have explored how gangs shape the spatial distribution of crime in and around their territory.
A systematic review of propensity score methods in the social sciences
 Multivariate Behavioral Research
, 2011
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The importance of covariate selection in controlling for selection bias in observational studies
 Psychological Methods
, 2010
"... The assumption of strongly ignorable treatment assignment is required for eliminating selection bias in observational studies. To meet this assumption, researchers often rely on a strategy of selecting covariates that they think will control for selection bias. Theory indicates that the most importa ..."
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Cited by 14 (2 self)
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The assumption of strongly ignorable treatment assignment is required for eliminating selection bias in observational studies. To meet this assumption, researchers often rely on a strategy of selecting covariates that they think will control for selection bias. Theory indicates that the most important covariates are those highly correlated with both the real selection process and the potential outcomes. However, when planning a study, it is rarely possible to identify such covariates with certainty. In this article, we report on an extensive reanalysis of a withinstudy comparison that contrasts a randomized experiment and a quasiexperiment. Various covariate sets were used to adjust for initial group differences in the quasiexperiment that was characterized by selfselection into treatment. The adjusted effect sizes were then compared with the experimental ones to identify which individual covariates, and which conceptually grouped sets of covariates, were responsible for the high degree of bias reduction achieved in the adjusted quasiexperiment. Such results provide strong clues about preferred strategies for identifying the covariates most likely to reduce bias when planning a study and when the true selection process is not known.