scholarly journals Regression Adjustments for Estimating the Global Treatment Effect in Experiments with Interference

2019 ◽  
Vol 7 (2) ◽  
Author(s):  
Alex Chin
Keyword(s):  
Treatment Effect ◽  
Variance Estimation ◽  
Rural China ◽  
Engineering Problem ◽  
Average Treatment Effect ◽  
Standard Theory ◽  
Randomized Experiments ◽  
Exposure Modeling ◽  
Flexible Machine ◽  
Regression Adjustment

AbstractStandard estimators of the global average treatment effect can be biased in the presence of interference. This paper proposes regression adjustment estimators for removing bias due to interference in Bernoulli randomized experiments. We use a fitted model to predict the counterfactual outcomes of global control and global treatment. Our work differs from standard regression adjustments in that the adjustment variables are constructed from functions of the treatment assignment vector, and that we allow the researcher to use a collection of any functions correlated with the response, turning the problem of detecting interference into a feature engineering problem. We characterize the distribution of the proposed estimator in a linear model setting and connect the results to the standard theory of regression adjustments under SUTVA. We then propose an estimator that allows for flexible machine learning estimators to be used for fitting a nonlinear interference functional form. We propose conducting statistical inference via bootstrap and resampling methods, which allow us to sidestep the complicated dependences implied by interference and instead rely on empirical covariance structures. Such variance estimation relies on an exogeneity assumption akin to the standard unconfoundedness assumption invoked in observational studies. In simulation experiments, our methods are better at debiasing estimates than existing inverse propensity weighted estimators based on neighborhood exposure modeling. We use our method to reanalyze an experiment concerning weather insurance adoption conducted on a collection of villages in rural China.

scholarly journals Regression-adjusted average treatment effect estimates in stratified randomized experiments

Biometrika ◽  
2020 ◽  
Vol 107 (4) ◽  
pp. 935-948
Author(s):  
Hanzhong Liu ◽  
Yuehan Yang
Keyword(s):  
Treatment Effect ◽  
Asymptotic Variance ◽  
Average Treatment Effect ◽  
Randomized Experiments ◽  
Asymptotically Normal ◽  
Variance Estimators ◽  
Average Treatment ◽  
Effect Estimation ◽  
Regression Adjustment ◽  
And Control

Summary Linear regression is often used in the analysis of randomized experiments to improve treatment effect estimation by adjusting for imbalances of covariates in the treatment and control groups. This article proposes a randomization-based inference framework for regression adjustment in stratified randomized experiments. We re-establish, under mild conditions, the finite-population central limit theorem for a stratified experiment, and we prove that both the stratified difference-in-means estimator and the regression-adjusted average treatment effect estimator are consistent and asymptotically normal; the asymptotic variance of the latter is no greater and typically less than that of the former. We also provide conservative variance estimators that can be used to construct large-sample confidence intervals for the average treatment effect.

OLS and 2SLS in Randomized and Conditionally Randomized Experiments

2018 ◽  
Vol 238 (3-4) ◽  
pp. 243-293 ◽  
Author(s):  
Jason Ansel ◽  
Han Hong ◽  
and Jessie Li
Keyword(s):  
Treatment Effect ◽  
Average Treatment Effect ◽  
Randomized Experiments ◽  
Adaptive Randomization ◽  
Working Paper ◽  
Average Treatment ◽  
Local Average Treatment Effect ◽  
Effect Parameter ◽  
Multiple Treatments ◽  
Local Average

Abstract We investigate estimation and inference of the (local) average treatment effect parameter when a binary instrumental variable is generated by a randomized or conditionally randomized experiment. Under i.i.d. sampling, we show that adding covariates and their interactions with the instrument will weakly improve estimation precision of the (local) average treatment effect, but the robust OLS (2SLS) standard errors will no longer be valid. We provide an analytic correction that is easy to implement and demonstrate through Monte Carlo simulations and an empirical application the interacted estimator’s efficiency gains over the unadjusted estimator and the uninteracted covariate adjusted estimator. We also generalize our results to covariate adaptive randomization where the treatment assignment is not i.i.d., thus extending the recent contributions of Bugni, F., I.A. Canay, A.M. Shaikh (2017a), Inference Under Covariate-Adaptive Randomization. Working Paper and Bugni, F., I.A. Canay, A.M. Shaikh (2017b), Inference Under Covariate-Adaptive Randomization with Multiple Treatments. Working Paper to allow for the case of non-compliance.

A Class of Unbiased Estimators of the Average Treatment Effect in Randomized Experiments

2013 ◽  
Vol 1 (1) ◽  
pp. 135-154 ◽  
Author(s):  
Peter M. Aronow ◽  
Joel A. Middleton
Keyword(s):  
Treatment Effect ◽  
Average Treatment Effect ◽  
Covariate Adjustment ◽  
Randomized Experiments ◽  
Treatment Assignment ◽  
Unbiased Estimators ◽  
Average Treatment

AbstractWe derive a class of design-based estimators for the average treatment effect that are unbiased whenever the treatment assignment process is known. We generalize these estimators to include unbiased covariate adjustment using any model for outcomes that the analyst chooses. We then provide expressions and conservative estimators for the variance of the proposed estimators.

Unbiased Estimation of the Average Treatment Effect in Cluster-Randomized Experiments

2015 ◽  
Vol 6 (1-2) ◽  
Author(s):  
Joel A. Middleton ◽  
Peter M. Aronow
Keyword(s):  
Treatment Effect ◽  
Average Treatment Effect ◽  
Unbiased Estimation ◽  
Random Allocation ◽  
Randomized Experiments ◽  
Average Treatment ◽  
Randomized Field Experiment ◽  
The Difference ◽  
Biased Estimators ◽  
Cluster Randomized

AbstractMany estimators of the average treatment effect, including the difference-in-means, may be biased when clusters of units are allocated to treatment. This bias remains even when the number of units within each cluster grows asymptotically large. In this paper, we propose simple, unbiased, location-invariant, and covariate-adjusted estimators of the average treatment effect in experiments with random allocation of clusters, along with associated variance estimators. We then analyze a cluster-randomized field experiment on voter mobilization in the US, demonstrating that the proposed estimators have precision that is comparable, if not superior, to that of existing, biased estimators of the average treatment effect.

scholarly journals High-dimensional regression adjustments in randomized experiments

2016 ◽  
Vol 113 (45) ◽  
pp. 12673-12678 ◽  
Author(s):  
Stefan Wager ◽  
Wenfei Du ◽  
Jonathan Taylor ◽  
Robert J. Tibshirani
Keyword(s):  
Treatment Effect ◽  
Average Treatment Effect ◽  
High Dimensional ◽  
Randomized Experiments ◽  
Finite Sample ◽  
Simple Method ◽  
Average Treatment ◽  
Population Average ◽  
High Dimensional Regression ◽  
Effect Estimation

We study the problem of treatment effect estimation in randomized experiments with high-dimensional covariate information and show that essentially any risk-consistent regression adjustment can be used to obtain efficient estimates of the average treatment effect. Our results considerably extend the range of settings where high-dimensional regression adjustments are guaranteed to provide valid inference about the population average treatment effect. We then propose cross-estimation, a simple method for obtaining finite-sample–unbiased treatment effect estimates that leverages high-dimensional regression adjustments. Our method can be used when the regression model is estimated using the lasso, the elastic net, subset selection, etc. Finally, we extend our analysis to allow for adaptive specification search via cross-validation and flexible nonparametric regression adjustments with machine-learning methods such as random forests or neural networks.

Propensity score weighting analysis and treatment effect discovery

2018 ◽  
Vol 28 (8) ◽  
pp. 2439-2454 ◽  
Author(s):  
Huzhang Mao ◽  
Liang Li ◽  
Tom Greene
Keyword(s):  
Propensity Score ◽  
Treatment Effect ◽  
Statistical Power ◽  
Variance Estimation ◽  
Propensity Score Analysis ◽  
Inverse Probability Weighting ◽  
Average Treatment Effect ◽  
Probability Weighting ◽  
Inverse Probability ◽  
Average Treatment

Inverse probability weighting can be used to estimate the average treatment effect in propensity score analysis. When there is lack of overlap in the propensity score distributions between the treatment groups under comparison, some weights may be excessively large, causing numerical instability and bias in point and variance estimation. We study a class of modified inverse probability weighting estimators that can be used to avoid this problem. These weights cause the estimand to deviate from the average treatment effect. We provide some justification for this deviation from the perspective of treatment effect discovery. We show that when lack of overlap occurs, the modified weights can achieve substantial gains in statistical power compared with inverse probability weighting and other propensity score methods. We develop analytical variance estimates that properly adjust for the sampling variability of the estimated propensity scores, and augment the modified inverse probability weighting estimator with outcome models for improved efficiency, a property that resembles double robustness. Results from extensive simulations and a real data application support our conclusions. The proposed methodology is implemented in R package PSW.

scholarly journals Regression adjustment in completely randomized experiments with a diverging number of covariates

Biometrika ◽  
2020 ◽  
Author(s):  
Lihua Lei ◽  
Peng Ding
Keyword(s):  
Asymptotic Properties ◽  
Average Treatment Effect ◽  
Covariate Adjustment ◽  
Randomized Experiments ◽  
Asymptotically Normal ◽  
Matrix Concentration ◽  
Simple Difference ◽  
Regression Adjustment ◽  
Weaker Conditions ◽  
Theoretical Results

Abstract Randomized experiments have become important tools in empirical research. In a completely randomized treatment-control experiment, the simple difference in means of the outcome is unbiased for the average treatment effect, and covariate adjustment can further improve the efficiency without assuming a correctly specified outcome model. In modern applications, experimenters often have access to many covariates, motivating the need for a theory of covariate adjustment under the asymptotic regime with a diverging number of covariates. We study the asymptotic properties of covariate adjustment under the potential outcomes model and propose a bias-corrected estimator that is consistent and asymptotically normal under weaker conditions. Our theory is purely randomization-based without imposing any parametric outcome model assumptions. To prove the theoretical results, we develop novel vector and matrix concentration inequalities for sampling without replacement.

scholarly journals A Generalized Regression-adjustment Estimator for Average Treatment Effects from Panel Data

2016 ◽  
Vol 16 (4) ◽  
pp. 826-836 ◽  
Author(s):  
David M. Drukker
Keyword(s):  
Panel Data ◽  
Random Effects ◽  
Treatment Effect ◽  
Average Treatment Effect ◽  
Potential Outcomes ◽  
Treatment Assignment ◽  
Average Treatment ◽  
Average Treatment Effects ◽  
Regression Adjustment ◽  
Simple Regression

I illustrate that the simple regression-adjustment estimator is inconsistent for the average treatment effect when the random effects affecting treatment assignment are correlated with the random effects that affect the potential outcomes. I present a simple parametric estimator that is consistent in this case.

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