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Reasoning about Interference Between Units: A General Framework

Published online by Cambridge University Press:  04 January 2017

Jake Bowers ,
Mark M. Fredrickson  and
Costas Panagopoulos
Jake Bowers*
Affiliation:
Department of Political Science, University of Illinois, Urbana-Champaign, Urbana, IL
Mark M. Fredrickson
Affiliation:
University of Illinois, Urbana-Champaign, Urbana, IL
Costas Panagopoulos
Affiliation:
Department of Political Science, Fordham University, New York City, NY
*
e-mail: jwbowers@illinois.edu (corresponding author)
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Abstract

If an experimental treatment is experienced by both treated and control group units, tests of hypotheses about causal effects may be difficult to conceptualize, let alone execute. In this article, we show how counterfactual causal models may be written and tested when theories suggest spillover or other network-based interference among experimental units. We show that the “no interference” assumption need not constrain scholars who have interesting questions about interference. We offer researchers the ability to model theories about how treatment given to some units may come to influence outcomes for other units. We further show how to test hypotheses about these causal effects, and we provide tools to enable researchers to assess the operating characteristics of their tests given their own models, designs, test statistics, and data. The conceptual and methodological framework we develop here is particularly applicable to social networks, but may be usefully deployed whenever a researcher wonders about interference between units. Interference between units need not be an untestable assumption; instead, interference is an opportunity to ask meaningful questions about theoretically interesting phenomena.

Type
Regular Articles
Information
Political Analysis , Volume 21 , Issue 1 , Winter 2013 , pp. 97 - 124
Copyright
Copyright © The Author 2013. Published by Oxford University Press on behalf of the Society for Political Methodology 

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Footnotes

Authors' note: Thanks are due to the participants in the Student-Faculty Workshop in the Department of Political Science at the University of Illinois at Urbana-Champaign, at the Experiments in Governance and Politics Workshop at MIT (EGAP-6), our panel at MPSA 2012, SLAMM 2012, and Polmeth 2012. We especially appreciate the in-depth comments provided by Peter Aronow, John Freeman, Matthew Hayes, Luke Keele, Cyrus Samii, Cara Wong, and the anonymous reviewers.

References

Aronow, M. Peter. 2012. A general method for detecting interference between units in randomized experiments. Sociological Methods & Research 41(3): 3–16.CrossRefGoogle Scholar
Aronow, M. Peter, and Samii, Cyrus. 2012a. Estimating average causal effects under general interference. Working paper.Google Scholar
Aronow, M. Peter, and Samii, Cyrus. 2012b. Large sample coverage properties of inverted exact test intervals for randomized experiments. Working paper.Google Scholar
Barnard, G. A. 1947. Significance tests for 2 × 2 tables. Biometrika 34 (1–2): 123–38.Google Scholar
Berger, R. L., and Boos, D. D. 1994. P-values maximized over a confidence set for the nuisance parameter. Journal of the American Statistical Association 89(427): 1012–1016.Google Scholar
Brady, Henry E. 2008. Causation and explanation in social science. In Oxford handbook of political methodology, eds. Box-Steffensmeier, J. M., Brady, H. E., and Collier, D., 217–70. Oxford, UK: Oxford University Press.Google Scholar
Chen, J., Humphreys, M., and Modi, V. 2010. Technology diffusion and social networks: Evidence from a field experiment in Uganda. Paper presented at EGAP 4 at New York University.Google Scholar
Cox, David R. 1958. The planning of experiments. New York: John Wiley.Google Scholar
Fisher, R. A. 1935. The design of experiments. Edinburgh: Oliver and Boyd.Google Scholar
Fredrickson, Mark M., and Bowers, Jake. 2012. Reproduction archive for “reasoning about interference between units: A general framework.” http://hdl.3andle.net/1902.1/18933.Google Scholar
Hansen, B. Ben, and Bowers, Jake. 2008. Covariate balance in simple, stratified, and clustered comparative studies. Statistical Science 23(2): 219–36.Google Scholar
Hansen, B. Ben, and Bowers, Jake. 2009. Attributing effects to a cluster randomized get-out-the-vote campaign. Journal of the American Statistical Association 104(487): 873–85.Google Scholar
Hollander, Myles. 1999. Nonparametric statistical methods. 2nd ed. New York: Wiley-Interscience.Google Scholar
Hong, G., and Raudenbush, S. W. 2006. Evaluating kindergarten retention policy. Journal of the American Statistical Association 101(475): 901–10.CrossRefGoogle Scholar
Hudgens, M. G., and Halloran, M. E. 2008. Toward causal inference with interference. Journal of the American Statistical Association 103(482): 832–42.Google Scholar
Ichino, N., and Schündeln, M. 2012a. Deterring or displacing electoral irregularities? Spillover effects of observers in a randomized field experiment in Ghana. Working paper.Google Scholar
Ichino, N., and Schündeln, M. 2012b. Deterring or displacing electoral irregularities? Spillover effects of observers in a randomized field experiment in Ghana. Journal of Politics 74(1): 292–307.Google Scholar
Imbens, G., and Rubin, D. 2009. Causal inference in statistics. Unpublished book manuscript. Forthcoming at Cambridge University Press.Google Scholar
Keele, L., McConnaughy, C., and White, I. 2012. Strengthening the experimenter's toolbox: Statistical estimation of internal validity. American Journal of Political Science 56(2): 484–99.Google Scholar
Miguel, E., and Kremer, M. 2004. Worms: identifying impacts on education and health in the presence of treatment externalities. Econometrica 72(1): 159–217.CrossRefGoogle Scholar
Neyman, J. 1923. [1990]. On the application of probability theory to agricultural experiments: Essay on principles. Section 9 (1923). Statistical Science 5: 463–480 (Reprint, transl. by Dabrowska and Speed).Google Scholar
Nickerson, D. W. 2008. Is voting contagious? Evidence from two field experiments. American Political Science Review 102 (l): 49–57.Google Scholar
Nickerson, D. W. 2011. Social networks and political context. In Cambridge handbook of experimental political science, eds. Druckman, J. N., Green, D. P., Kuklinski, J. H., and Lupia, A., 273–86. Cambridge, UK: Cambridge University Press.Google Scholar
Nolen, T. L., and Hudgens, M. 2011. Randomization-based inference within principal strata. Journal of the American Statistical Association 106(494): 581–93.Google Scholar
Panagopoulos, Costas. 2006. The impact of newspaper advertising on voter turnout: Evidence from a field experiment. Paper presented at the MPSA 2006.Google Scholar
Panagopoulos, Costas, and Bowers, Jake. 2012. Do newspaper ads raise voter turnout? Evidence from a randomized field experiment. Unpublished manuscript, Chicago, IL.Google Scholar
Rosenbaum, Paul R. 2002. Observational studies. 2nd ed. New York: Springer.Google Scholar
Rosenbaum, Paul R. 2007. Interference between units in randomized experiments. Journal of the American Statistical Association 102(477): 191–200.CrossRefGoogle Scholar
Rosenbaum, Paul R. 2010. Design of Observational studies. New York: Springer. http://www.springer.com/statistics/statistical+theory+and+methods/book/978-1-4419-1212-1.CrossRefGoogle ScholarPubMed
Rosenblum, M., and Van Der Laan, M. J. 2009. Using regression models to analyze randomized trials: Asymptotically valid hypothesis tests despite incorrectly specified models. Biometrics 65(3): 937–45.CrossRefGoogle ScholarPubMed
Rubin, D. B. 1980. Randomization analysis of experimental data: The Fisher randomization test comment. Journal of the American Statistical Association 75(371): 591–93.Google Scholar
Rubin, D. B. 1986. Which ifs have causal answers? Comments on “statistics and causal inference.” Journal of the American Statistical Association 81: 961–62.Google Scholar
Rubin, D. B. 2005. Causal inference using potential outcomes: Design, modeling, decisions. Journal of the American Statistical Association 100: 322–31.Google Scholar
Rubin, D. B. 2010. Reflections stimulated by the comments of Shadish (2010) and West and Thoemmes (2010). Psychological Methods 15(1): 38–46.Google Scholar
Samii, C., and Aronow, P. M. 2012. On equivalencies between design-based and regression-based variance estimators for randomized experiments. Statistics & Probability Letters 82(2): 365–70.Google Scholar
Sekhon, Jasjeet S. 2008. The Neyman-Rubin model of causal inference and estimation via matching methods. In Oxford handbook of political methodology, eds. Box-Steffensmeier, J. M., Brady, H. E., and Collier, D., 271–99. Oxford, UK: Oxford University Press.Google Scholar
Siegel, D. A. 2009. Social networks and collective action. American Journal of Political Science 53(1): 122–38.Google Scholar
Silvapulle, M. J. 1996. A test in the presence of nuisance parameters. Journal of the American Statistical Association 91(436): 1690–1693.Google Scholar
Sinclair, B. 2011. Design and analysis of experiments in multilevel populations. In Cambridge handbook of experimental political science, eds. Druckman, J. N., Green, D. P., Kuklinski, J. H., and Lupia, A., 481–93. Cambridge, UK: Cambridge University Press.Google Scholar
Sinclair, B., McConnell, M., and Green, D. P. 2012. Detecting spillover effects: Design and analysis of multilevel experiments. American Journal of Political Science 56(4): 1055–69.Google Scholar
Sobel, M. E. 2006. What do randomized studies of housing mobility demonstrate? Journal of the American Statistical Association 101(476): 1398–407.Google Scholar
Tchetgen, E. J. T., and VanderWeele, T. J. 2012. On causal inference in the presence of interference. Statistical Methods in Medical Research 21(1): 55–75.CrossRefGoogle Scholar
VanderWeele, T. J. 2008. Ignorability and stability assumptions in neighborhood effects research. Statistics in Medicine 27(11): 1934–43.CrossRefGoogle Scholar
VanderWeele, T. J. 2010. Direct and indirect effects for neighborhood-based clustered and longitudinal data. Sociological Methods & Research 38(4): 515.Google Scholar
VanderWeele, T. J., and Tchetgen, E. J. T. 2011a. Effect partitioning under interference in two-stage randomized vaccine trials. Statistics & probability letters 81(7): 861–69.Google Scholar
VanderWeele, T. J., and Tchetgen, E. J. T. 2011b. Bounding the infectiousness effect in vaccine trials. Epidemiology 22(5): 686–93.Google Scholar
VanderWeele, T. J., Tchetgen, E. J. T., and Halloran, M. E. 2012. Components of the indirect effect in vaccine trials: Identification of contagion and infectiousness effects. Epidemiology 23(5): 751–61.Google Scholar
VanderWeele, T. J., Vandenbroucke, J. P., Tchetgen, E. J. T., and Robins, J. M. 2012. A mapping between interactions and interference: Implications for vaccine trials. Epidemiology 23(2): 285–92.Google Scholar