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Donald B Rubin - One of the best experts on this subject based on the ideXlab platform.
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asymptotic theory of rerandomization in treatment control experiments
Proceedings of the National Academy of Sciences of the United States of America, 2018Co-Authors: Xinran Li, Peng Ding, Donald B RubinAbstract:Although complete randomization ensures covariate balance on Average, the chance of observing significant differences between treatment and control covariate distributions increases with many covariates. Rerandomization discards randomizations that do not satisfy a predetermined covariate balance criterion, generally resulting in better covariate balance and more precise estimates of Causal Effects. Previous theory has derived finite sample theory for rerandomization under the assumptions of equal treatment group sizes, Gaussian covariate and outcome distributions, or additive Causal Effects, but not for the general sampling distribution of the difference-in-means estimator for the Average Causal Effect. We develop asymptotic theory for rerandomization without these assumptions, which reveals a non-Gaussian asymptotic distribution for this estimator, specifically a linear combination of a Gaussian random variable and truncated Gaussian random variables. This distribution follows because rerandomization affects only the projection of potential outcomes onto the covariate space but does not affect the corresponding orthogonal residuals. We demonstrate that, compared with complete randomization, rerandomization reduces the asymptotic quantile ranges of the difference-in-means estimator. Moreover, our work constructs accurate large-sample confidence intervals for the Average Causal Effect.
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asymptotic theory of rerandomization in treatment control experiments
arXiv: Statistics Theory, 2016Co-Authors: Xinran Li, Peng Ding, Donald B RubinAbstract:Although complete randomization ensures covariate balance on Average, the chance for observing significant differences between treatment and control covariate distributions increases with many covariates. Rerandomization discards randomizations that do not satisfy a predetermined covariate balance criterion, generally resulting in better covariate balance and more precise estimates of Causal Effects. Previous theory has derived finite sample theory for rerandomization under the assumptions of equal treatment group sizes, Gaussian covariate and outcome distributions, or additive Causal Effects, but not for the general sampling distribution of the difference-in-means estimator for the Average Causal Effect. To supplement existing results, we develop asymptotic theory for rerandomization without these assumptions, which reveals a non-Gaussian asymptotic distribution for this estimator, specifically a linear combination of a Gaussian random variable and a truncated Gaussian random variable. This distribution follows because rerandomization affects only the projection of potential outcomes onto the covariate space but does not affect the corresponding orthogonal residuals. We also demonstrate that, compared to complete randomization, rerandomization reduces the asymptotic sampling variances and quantile ranges of the difference-in-means estimator. Moreover, our work allows the construction of accurate large-sample confidence intervals for the Average Causal Effect, thereby revealing further advantages of rerandomization over complete randomization.
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identification of Causal Effects using instrumental variables
Journal of the American Statistical Association, 1996Co-Authors: Joshua D Angrist, Guido W. Imbens, Donald B RubinAbstract:Abstract We outline a framework for Causal inference in settings where assignment to a binary treatment is ignorable, but compliance with the assignment is not perfect so that the receipt of treatment is nonignorable. To address the problems associated with comparing subjects by the ignorable assignment—an “intention-to-treat analysis”—we make use of instrumental variables, which have long been used by economists in the context of regression models with constant treatment Effects. We show that the instrumental variables (IV) estimand can be embedded within the Rubin Causal Model (RCM) and that under some simple and easily interpretable assumptions, the IV estimand is the Average Causal Effect for a subgroup of units, the compliers. Without these assumptions, the IV estimand is simply the ratio of intention-to-treat Causal estimands with no interpretation as an Average Causal Effect. The advantages of embedding the IV approach in the RCM are that it clarifies the nature of critical assumptions needed for a...
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identification of Causal Effects using instrumental variables comment
Journal of the American Statistical Association, 1996Co-Authors: Joshua D Angrist, Steve Greenland, Guido W. Imbens, James M Robins, Richard A. Moffitt, James J Heckman, Donald B Rubin, P R RosembaumAbstract:We outline a framework for Causal inference in settings where assignment to a binary treatment is ignorable, but compliance with the assignment is not perfect so that the receipt of treatment is nonignorable. To address the problems associated with comparing subjects by the ignorable assignment-an intention-to-treat analysis-we make use of instrumental variables, which have long been used by economists in the context of regression models with constant treatment Effects. We show that the instrumental variables (IV) estimand can be embedded within the Rubin Causal Model (RCM) and that under some simple and easily interpretable assumptions, the IV estimand is the Average Causal Effect for a subgroup of units, the compliers. Without these assumptions, the IV estimand is simply the ratio of intention-to-treat Causal estimands with no interpretation as an Average Causal Effect. The advantages of embedding the IV approach in the RCM are that it clarifies the nature of critical assumptions needed for a Causal interpretation, and moreover allows us to consider sensitivity of the results to deviations from key assumptions in a straightforward manner. We apply our analysis to estimate the Effect of veteran status in the Vietnam era on mortality, using the lottery number that assigned priority for the draft as an instrument, and we use our results to investigate the sensitivity of the conclusions to critical assumptions.
Guido W. Imbens - One of the best experts on this subject based on the ideXlab platform.
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Design-based Analysis in Difference-In-Differences Settings with Staggered Adoption
2018Co-Authors: Susan Athey, Guido W. ImbensAbstract:In this paper we study estimation of and inference for Average treatment Effects in a setting with panel data. We focus on the setting where units, e.g., individuals, firms, or states, adopt the policy or treatment of interest at a particular point in time, and then remain exposed to this treatment at all times afterwards. We take a design perspective where we investigate the properties of estimators and procedures given assumptions on the assignment process. We show that under random assignment of the adoption date the standard Difference-In-Differences estimator is is an unbiased estimator of a particular weighted Average Causal Effect. We characterize the proeperties of this estimand, and show that the standard variance estimator is conservative.
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identification of Causal Effects using instrumental variables
Journal of the American Statistical Association, 1996Co-Authors: Joshua D Angrist, Guido W. Imbens, Donald B RubinAbstract:Abstract We outline a framework for Causal inference in settings where assignment to a binary treatment is ignorable, but compliance with the assignment is not perfect so that the receipt of treatment is nonignorable. To address the problems associated with comparing subjects by the ignorable assignment—an “intention-to-treat analysis”—we make use of instrumental variables, which have long been used by economists in the context of regression models with constant treatment Effects. We show that the instrumental variables (IV) estimand can be embedded within the Rubin Causal Model (RCM) and that under some simple and easily interpretable assumptions, the IV estimand is the Average Causal Effect for a subgroup of units, the compliers. Without these assumptions, the IV estimand is simply the ratio of intention-to-treat Causal estimands with no interpretation as an Average Causal Effect. The advantages of embedding the IV approach in the RCM are that it clarifies the nature of critical assumptions needed for a...
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identification of Causal Effects using instrumental variables comment
Journal of the American Statistical Association, 1996Co-Authors: Joshua D Angrist, Steve Greenland, Guido W. Imbens, James M Robins, Richard A. Moffitt, James J Heckman, Donald B Rubin, P R RosembaumAbstract:We outline a framework for Causal inference in settings where assignment to a binary treatment is ignorable, but compliance with the assignment is not perfect so that the receipt of treatment is nonignorable. To address the problems associated with comparing subjects by the ignorable assignment-an intention-to-treat analysis-we make use of instrumental variables, which have long been used by economists in the context of regression models with constant treatment Effects. We show that the instrumental variables (IV) estimand can be embedded within the Rubin Causal Model (RCM) and that under some simple and easily interpretable assumptions, the IV estimand is the Average Causal Effect for a subgroup of units, the compliers. Without these assumptions, the IV estimand is simply the ratio of intention-to-treat Causal estimands with no interpretation as an Average Causal Effect. The advantages of embedding the IV approach in the RCM are that it clarifies the nature of critical assumptions needed for a Causal interpretation, and moreover allows us to consider sensitivity of the results to deviations from key assumptions in a straightforward manner. We apply our analysis to estimate the Effect of veteran status in the Vietnam era on mortality, using the lottery number that assigned priority for the draft as an instrument, and we use our results to investigate the sensitivity of the conclusions to critical assumptions.
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Two-Stage Least Squares Estimation of Average Causal Effects in Models with Variable Treatment Intensity
Journal of the American Statistical Association, 1995Co-Authors: Joshua D Angrist, Guido W. ImbensAbstract:Abstract Two-stage least squares (TSLS) is widely used in econometrics to estimate parameters in systems of linear simultaneous equations and to solve problems of omitted-variables bias in single-equation estimation. We show here that TSLS can also be used to estimate the Average Causal Effect of variable treatments such as drug dosage, hours of exam preparation, cigarette smoking, and years of schooling. The Average Causal Effect in which we are interested is a conditional expectation of the difference between the outcomes of the treated and what these outcomes would have been in the absence of treatment. Given mild regularity assumptions, the probability limit of TSLS is a weighted Average of per-unit Average Causal Effects along the length of an appropriately defined Causal response function. The weighting function is illustrated in an empirical example based on the relationship between schooling and earnings.
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Average Causal response with variable treatment intensity
1995Co-Authors: Joshua D Angrist, Guido W. ImbensAbstract:In evaluation research, an Average Causal Effect is usually defined as the expected difference between the outcomes of the treated, and what these outcomes would have been in the absence of treatment. This definition of Causal Effects makes sense for binary treatments only. In this paper, we extend the definition of Average Causal Effects to the case of variable treatments such as drug dosage, hours of exam preparation, cigarette smoking, and years of schooling. We show that given mild regularity assumptions, instrumental variables independence assumptions identify a weighted Average of per-unit Causal Effects along the length of an appropriately defined Causal response function. Conventional instrumental variables and Two-Stage Least Squares procedures can be interpreted as estimating the Average Causal response to a variable treatment.
Joshua D Angrist - One of the best experts on this subject based on the ideXlab platform.
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identification of Causal Effects using instrumental variables
Journal of the American Statistical Association, 1996Co-Authors: Joshua D Angrist, Guido W. Imbens, Donald B RubinAbstract:Abstract We outline a framework for Causal inference in settings where assignment to a binary treatment is ignorable, but compliance with the assignment is not perfect so that the receipt of treatment is nonignorable. To address the problems associated with comparing subjects by the ignorable assignment—an “intention-to-treat analysis”—we make use of instrumental variables, which have long been used by economists in the context of regression models with constant treatment Effects. We show that the instrumental variables (IV) estimand can be embedded within the Rubin Causal Model (RCM) and that under some simple and easily interpretable assumptions, the IV estimand is the Average Causal Effect for a subgroup of units, the compliers. Without these assumptions, the IV estimand is simply the ratio of intention-to-treat Causal estimands with no interpretation as an Average Causal Effect. The advantages of embedding the IV approach in the RCM are that it clarifies the nature of critical assumptions needed for a...
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identification of Causal Effects using instrumental variables comment
Journal of the American Statistical Association, 1996Co-Authors: Joshua D Angrist, Steve Greenland, Guido W. Imbens, James M Robins, Richard A. Moffitt, James J Heckman, Donald B Rubin, P R RosembaumAbstract:We outline a framework for Causal inference in settings where assignment to a binary treatment is ignorable, but compliance with the assignment is not perfect so that the receipt of treatment is nonignorable. To address the problems associated with comparing subjects by the ignorable assignment-an intention-to-treat analysis-we make use of instrumental variables, which have long been used by economists in the context of regression models with constant treatment Effects. We show that the instrumental variables (IV) estimand can be embedded within the Rubin Causal Model (RCM) and that under some simple and easily interpretable assumptions, the IV estimand is the Average Causal Effect for a subgroup of units, the compliers. Without these assumptions, the IV estimand is simply the ratio of intention-to-treat Causal estimands with no interpretation as an Average Causal Effect. The advantages of embedding the IV approach in the RCM are that it clarifies the nature of critical assumptions needed for a Causal interpretation, and moreover allows us to consider sensitivity of the results to deviations from key assumptions in a straightforward manner. We apply our analysis to estimate the Effect of veteran status in the Vietnam era on mortality, using the lottery number that assigned priority for the draft as an instrument, and we use our results to investigate the sensitivity of the conclusions to critical assumptions.
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Two-Stage Least Squares Estimation of Average Causal Effects in Models with Variable Treatment Intensity
Journal of the American Statistical Association, 1995Co-Authors: Joshua D Angrist, Guido W. ImbensAbstract:Abstract Two-stage least squares (TSLS) is widely used in econometrics to estimate parameters in systems of linear simultaneous equations and to solve problems of omitted-variables bias in single-equation estimation. We show here that TSLS can also be used to estimate the Average Causal Effect of variable treatments such as drug dosage, hours of exam preparation, cigarette smoking, and years of schooling. The Average Causal Effect in which we are interested is a conditional expectation of the difference between the outcomes of the treated and what these outcomes would have been in the absence of treatment. Given mild regularity assumptions, the probability limit of TSLS is a weighted Average of per-unit Average Causal Effects along the length of an appropriately defined Causal response function. The weighting function is illustrated in an empirical example based on the relationship between schooling and earnings.
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Average Causal response with variable treatment intensity
1995Co-Authors: Joshua D Angrist, Guido W. ImbensAbstract:In evaluation research, an Average Causal Effect is usually defined as the expected difference between the outcomes of the treated, and what these outcomes would have been in the absence of treatment. This definition of Causal Effects makes sense for binary treatments only. In this paper, we extend the definition of Average Causal Effects to the case of variable treatments such as drug dosage, hours of exam preparation, cigarette smoking, and years of schooling. We show that given mild regularity assumptions, instrumental variables independence assumptions identify a weighted Average of per-unit Causal Effects along the length of an appropriately defined Causal response function. Conventional instrumental variables and Two-Stage Least Squares procedures can be interpreted as estimating the Average Causal response to a variable treatment.
Peng Ding - One of the best experts on this subject based on the ideXlab platform.
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asymptotic theory of rerandomization in treatment control experiments
Proceedings of the National Academy of Sciences of the United States of America, 2018Co-Authors: Xinran Li, Peng Ding, Donald B RubinAbstract:Although complete randomization ensures covariate balance on Average, the chance of observing significant differences between treatment and control covariate distributions increases with many covariates. Rerandomization discards randomizations that do not satisfy a predetermined covariate balance criterion, generally resulting in better covariate balance and more precise estimates of Causal Effects. Previous theory has derived finite sample theory for rerandomization under the assumptions of equal treatment group sizes, Gaussian covariate and outcome distributions, or additive Causal Effects, but not for the general sampling distribution of the difference-in-means estimator for the Average Causal Effect. We develop asymptotic theory for rerandomization without these assumptions, which reveals a non-Gaussian asymptotic distribution for this estimator, specifically a linear combination of a Gaussian random variable and truncated Gaussian random variables. This distribution follows because rerandomization affects only the projection of potential outcomes onto the covariate space but does not affect the corresponding orthogonal residuals. We demonstrate that, compared with complete randomization, rerandomization reduces the asymptotic quantile ranges of the difference-in-means estimator. Moreover, our work constructs accurate large-sample confidence intervals for the Average Causal Effect.
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Bridging Finite and Super Population Causal Inference
Journal of Causal Inference, 2017Co-Authors: Peng Ding, Luke MiratrixAbstract:There are two general views in Causal analysis of experimental data: the super population view that the units are an independent sample from some hypothetical infinite population, and the finite population view that the potential outcomes of the experimental units are fixed and the randomness comes solely from the treatment assignment. These two views differs conceptually and mathematically, resulting in different sampling variances of the usual difference-in-means estimator of the Average Causal Effect. Practically, however, these two views result in identical variance estimators. By recalling a variance decomposition and exploiting a completeness-type argument, we establish a connection between these two views in completely randomized experiments. This alternative formulation could serve as a template for bridging finite and super population Causal inference in other scenarios.
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Identification and estimation of Causal Effects with confounders subject to instrumental missingness
arXiv: Methodology, 2017Co-Authors: Shu Yang, Linbo Wang, Peng DingAbstract:Drawing Causal inference from unconfounded observational studies is of great importance, which, however, is jeopardized if the confounders are subject to missingness. Generally, it is impossible to identify Causal Effects if the confounders are missing not at random. In this paper, we propose a novel framework to nonparametrically identify the Causal Effects with confounders missing not at random, but subject to instrumental missingness, that is, the missing data mechanism is independent of the outcome, given the treatment and possibly missing confounder values. The Average Causal Effect is then estimated using a nonparametric two-stage least squares estimator based on series approximation.
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asymptotic theory of rerandomization in treatment control experiments
arXiv: Statistics Theory, 2016Co-Authors: Xinran Li, Peng Ding, Donald B RubinAbstract:Although complete randomization ensures covariate balance on Average, the chance for observing significant differences between treatment and control covariate distributions increases with many covariates. Rerandomization discards randomizations that do not satisfy a predetermined covariate balance criterion, generally resulting in better covariate balance and more precise estimates of Causal Effects. Previous theory has derived finite sample theory for rerandomization under the assumptions of equal treatment group sizes, Gaussian covariate and outcome distributions, or additive Causal Effects, but not for the general sampling distribution of the difference-in-means estimator for the Average Causal Effect. To supplement existing results, we develop asymptotic theory for rerandomization without these assumptions, which reveals a non-Gaussian asymptotic distribution for this estimator, specifically a linear combination of a Gaussian random variable and a truncated Gaussian random variable. This distribution follows because rerandomization affects only the projection of potential outcomes onto the covariate space but does not affect the corresponding orthogonal residuals. We also demonstrate that, compared to complete randomization, rerandomization reduces the asymptotic sampling variances and quantile ranges of the difference-in-means estimator. Moreover, our work allows the construction of accurate large-sample confidence intervals for the Average Causal Effect, thereby revealing further advantages of rerandomization over complete randomization.
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Exact confidence intervals for the Average Causal Effect on a binary outcome.
Statistics in Medicine, 2016Co-Authors: Peng DingAbstract:Based on the physical randomization of completely randomized experiments, in a recent article in Statistics in Medicine, Rigdon and Hudgens propose two approaches to obtaining exact confidence intervals for the Average Causal Effect on a binary outcome. They construct the first confidence interval by combining, with the Bonferroni adjustment, the prediction sets for treatment Effects among treatment and control groups, and the second one by inverting a series of randomization tests. With sample size n, their second approach requires performing O(n4 )randomization tests. We demonstrate that the physical randomization also justifies other ways to constructing exact confidence intervals that are more computationally efficient. By exploiting recent advances in hypergeometric confidence intervals and the stochastic order information of randomization tests, we propose approaches that either do not need to invoke Monte Carlo or require performing at most O(n2) randomization tests. We provide technical details and R code in the Supporting Information.
Ioannis N Psaromiligkos - One of the best experts on this subject based on the ideXlab platform.
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evaluating Average Causal Effect using wireless sensor networks
International Conference on Acoustics Speech and Signal Processing, 2004Co-Authors: Mark Coates, Ioannis N PsaromiligkosAbstract:Sensor networks have exciting potential applications in agriculture and medicine, where after the application of treatment, it is beneficial not merely to track the response but to assess the Causal impact of the treatment reception. We describe a distributed algorithm for the evaluation of the Average Causal Effect of treatment reception upon response. Our procedure applies the expectation-maximization algorithm across a graphical model of the system, using local message-passing techniques. The key collaborative step in the algorithm is simple message aggregation and averaging, which we perform over a tree network topology. Finally, for completeness purposes, we describe a simple framework for the construction and maintenance of the tree topology that provides a robust mechanism for executing the algorithm using spread-spectrum or ultra-wideband communication.
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ICASSP (3) - Evaluating Average Causal Effect using wireless sensor networks
2004 IEEE International Conference on Acoustics Speech and Signal Processing, 1Co-Authors: Mark Coates, Ioannis N PsaromiligkosAbstract:Sensor networks have exciting potential applications in agriculture and medicine, where after the application of treatment, it is beneficial not merely to track the response but to assess the Causal impact of the treatment reception. We describe a distributed algorithm for the evaluation of the Average Causal Effect of treatment reception upon response. Our procedure applies the expectation-maximization algorithm across a graphical model of the system, using local message-passing techniques. The key collaborative step in the algorithm is simple message aggregation and averaging, which we perform over a tree network topology. Finally, for completeness purposes, we describe a simple framework for the construction and maintenance of the tree topology that provides a robust mechanism for executing the algorithm using spread-spectrum or ultra-wideband communication.
