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Bias of the regression estimator for experiments using clustered random assignment

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  • Middleton, Joel A.

Abstract

This paper shows that regression may be biased for cluster randomized experiments. For one application bias tends to zero when the number of clusters is large but for another, regression is not consistent. Results underscore Freedman's [Freedman D.A., 2008. On regression adjustments to experimental data. Advances in Applied Mathematics 40, 180-193] insight that randomization does not justify regression assumptions.

Suggested Citation

  • Middleton, Joel A., 2008. "Bias of the regression estimator for experiments using clustered random assignment," Statistics & Probability Letters, Elsevier, vol. 78(16), pages 2654-2659, November.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:16:p:2654-2659
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    References listed on IDEAS

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    1. John M. Williamson & Somnath Datta & Glen A. Satten, 2003. "Marginal Analyses of Clustered Data When Cluster Size Is Informative," Biometrics, The International Biometric Society, vol. 59(1), pages 36-42, March.
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    Cited by:

    1. Fangzhou Su & Peng Ding, 2021. "Model‐assisted analyses of cluster‐randomized experiments," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 83(5), pages 994-1015, November.
    2. Rogers, Todd T & Middleton, Joel A., 2012. "Are Ballot Initiative Outcomes Influenced by the Campaigns of Independent Groups? A Precinct-Randomized Field Experiment," Scholarly Articles 9830357, Harvard Kennedy School of Government.
    3. Samii, Cyrus & Aronow, Peter M., 2012. "On equivalencies between design-based and regression-based variance estimators for randomized experiments," Statistics & Probability Letters, Elsevier, vol. 82(2), pages 365-370.
    4. Rogers, Todd & Middleton, Joel A., 2012. "Are Ballot Initiative Outcomes Influenced by the Campaigns of Independent Groups? A Precinct-Randomized Field Experiment," Working Paper Series rwp12-049, Harvard University, John F. Kennedy School of Government.
    5. Eckles Dean & Karrer Brian & Ugander Johan, 2017. "Design and Analysis of Experiments in Networks: Reducing Bias from Interference," Journal of Causal Inference, De Gruyter, vol. 5(1), pages 1-23, March.
    6. Aronow Peter M. & Middleton Joel A., 2013. "A Class of Unbiased Estimators of the Average Treatment Effect in Randomized Experiments," Journal of Causal Inference, De Gruyter, vol. 1(1), pages 135-154, June.
    7. Eckles Dean & Karrer Brian & Ugander Johan, 2017. "Design and Analysis of Experiments in Networks: Reducing Bias from Interference," Journal of Causal Inference, De Gruyter, vol. 5(1), pages 1-23, March.
    8. Zach Branson & Tirthankar Dasgupta, 2020. "Sampling‐based Randomised Designs for Causal Inference under the Potential Outcomes Framework," International Statistical Review, International Statistical Institute, vol. 88(1), pages 101-121, April.
    9. Joel A. Middleton, 2021. "Unifying Design-based Inference: On Bounding and Estimating the Variance of any Linear Estimator in any Experimental Design," Papers 2109.09220, arXiv.org.
    10. Middleton Joel A. & Aronow Peter M., 2015. "Unbiased Estimation of the Average Treatment Effect in Cluster-Randomized Experiments," Statistics, Politics and Policy, De Gruyter, vol. 6(1-2), pages 39-75, December.
    11. Kai Jäger, 2020. "When Do Campaign Effects Persist for Years? Evidence from a Natural Experiment," American Journal of Political Science, John Wiley & Sons, vol. 64(4), pages 836-851, October.

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