Heterogeneous Agents, Social Interactions, and Causal Inference

  • Guanglei HongEmail author
  • Stephen W. Raudenbush
Part of the Handbooks of Sociology and Social Research book series (HSSR)


Most causal analyses in the social sciences depend on the assumption that each participant possesses a single potential outcome under each possible treatment assignment. Rubin (J Am Stat Assoc 81:961–962, 1986) labeled this the “stable unit treatment value assumption” (SUTVA). Under SUTVA, the individual-specific impact of a treatment depends neither on the mechanism by which the treatment is assigned nor on the treatment assignments of other individuals. However, in the social world, heterogeneous agents enact most interventions of interest: Teachers implement curricula, psychologists enact family therapy, and precinct captains supervise community policing. Moreover, the potential outcomes of one participant will often depend on the treatment assignment of other participants (classmates, family members, neighbors). This chapter presents a model that relaxes the conventional SUTVA by incorporating agents and social interactions. We define a treatment setting for an individual participant as a local environment constituted by a set of agents and participants along with their treatment assignments. Our model assigns a single potential outcome to each participant in each of such treatment settings. In a cluster-randomized trial, if no interference exists between clusters and if cluster composition remains intact, the treatment setting is fixed for all participants in a cluster and SUTVA becomes reasonable. However, when participants are assigned to treatments within clusters, we need a model for within-cluster interference among participants. When clusters are spatially contiguous, social interactions generate interference between clusters. We also incorporate new models for interference as a part of the meditation mechanism. In general, when SUTVA is relaxed, new causal questions come to light. We illustrate these ideas using studies of grade retention in elementary school, community policing in cities, school-wide interventions for behavioral improvement, and system-wide curricular changes for promoting math learning.


Causal Effect Treatment Setting Potential Outcome Treatment Assignment Class Quality 
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  1. Brown, J. L., Jones, S. M., LaRusso, M. D., & Aber, J. L. (2010). Improving classroom quality: Teacher influences and experimental impacts of the 4Rs program. Journal of Educational Psychology, 102, 153–167.CrossRefGoogle Scholar
  2. Gordon, R., Kane, T., & Staiger, D. O. (2006). Identifying effective teachers using performance on the job. In J. Furman & J. Bordoff (Eds.), Path to prosperity: Hamilton project ideas on income security, education, and taxes (pp. 189–226). Washington, DC: The Brookings Institution.Google Scholar
  3. Haavelmo, T. (1943). The statistical implications of a system of simultaneous equations. Econometrika, 11, 1–12.CrossRefGoogle Scholar
  4. Harris, D. (2010). How do school peers influence student educational outcomes? Theory and evidence from economics and other social sciences. Teachers College Record, 112, 1163–1197.Google Scholar
  5. Heckman, J. (1979). Sample selection bias as a specification error. Econometrika, 47, 153–161.CrossRefGoogle Scholar
  6. Heckman, J., Lochner, L., & Taber, C. (1998). General equilibrium treatment effects: A study of tuition policy. American Economic Review (Papers and Proceedings), 88, 381–386.Google Scholar
  7. Holland, P. W. (1986). Statistics and causal inference. Journal of the American Statistical Association, 81, 945–960.CrossRefGoogle Scholar
  8. Holland, P. W. (1988). Causal inference, path analysis, and recursive structural equation models (with discussion). In C. C. Clogg (Ed.), Sociological methodology (pp. 449–493). Washington, DC: American Sociological Association.Google Scholar
  9. Hong, G. (2004). Causal inference for multi-level observational data with application to kindergarten retention. PhD dissertation, Department of Educational Studies, University of Michigan, Ann Arbor.Google Scholar
  10. Hong, G. (2010). Ratio of mediator probability weighting for estimating natural direct and indirect effects. Proceedings of the American Statistical Association, Biometrics Section, 2010, 2401–2415.Google Scholar
  11. Hong, G., & Nomi, T. (2012). Weighting methods for assessing policy effects mediated by peer change. Journal of Research on Educational Effectiveness special issue on the statistical approaches to studying mediator effects in education research, 5, 261–289.Google Scholar
  12. Hong, G., & Raudenbush, S. W. (2005). Effects of kindergarten retention policy on children’s cognitive growth in reading and mathematics. Educational Evaluation and Policy Analysis, 27(3), 205–224.CrossRefGoogle Scholar
  13. Hong, G., & Raudenbush, S. W. (2006). Evaluating kindergarten retention policy: A case study of causal inference for multi-level observational data. Journal of the American Statistical Association, 101, 901–910.CrossRefGoogle Scholar
  14. Hong, G., Deutsch, J., & Hill, H. D. (2011). Parametric and non-parametric weighting methods for estimating mediation effects: An application to the national evaluation of welfare-to-work strategies. Proceedings of the American Statistical Association, Social Statistics Section, 2011, 3215–3229.Google Scholar
  15. Hudgens, M. G., & Halloran, M. E. (2008). Toward causal inference with interference. Journal of the American Statistical Association, 103, 832–842.CrossRefGoogle Scholar
  16. Jones, S. M., Brown, J. L., & Aber, J. L. (2011). Two-year impacts of a universal school-based social-emotional and literacy intervention: An experiment in translational developmental research. Child Development, 82, 533–554.CrossRefGoogle Scholar
  17. Kasim, R., & Raudenbush, S. W. (1998). Application of Gibbs sampling to nested variance components models with heterogeneous within group variance. Journal of Educational and Behavioral Statistics, 23, 93–116.Google Scholar
  18. Manski, C. F. (forthcoming). Identification of treatment response with social interactions. The Econometrics Journal. doi:10.1111/j.1368-423X.2012.00368.x.Google Scholar
  19. National Reading Panel. (2000). Report of the national reading panel – Teaching children to read: An evidence-based assessment of the scientific research literature on reading and its implications for reading instruction. Washington, DC: National Institute of Child Health and Human Development.Google Scholar
  20. Neyman, J., with cooperation of Iwaskiewicz, K., & St. Kolodziejczyk. (1935). Statistical problems in agricultural experimentation (with discussion). Supplement to Journal of the Royal Statistical Society, Series B, 2, 107–180.Google Scholar
  21. Nomi, T. (2010). The unintended consequences of an algebra-for-all policy on high-skill students: The effects on instructional organization and students’ academic outcomes. Paper presented at the Society for Research on Educational Effectiveness, Washington, DC.Google Scholar
  22. Nye, B., Hedges, L. V., & Konstantopouloss, S. (2004). How large are teacher effects? Educational Evaluation and Policy Analysis, 26, 237–257.CrossRefGoogle Scholar
  23. Pearl, J. (2001). Direct and indirect effects. Proceedings of the 17th conference on uncertainty in artificial intelligence (pp. 1572–1581). San Francisco: Morgan Kaufmann.Google Scholar
  24. Peterson, M. L., Sinisi, S. E., & van der Laan, M. J. (2006). Estimation of direct causal effects. Epidemiology, 17, 276–284.CrossRefGoogle Scholar
  25. Raudenbush, S. W., Fotiu, R. P., & Cheong, Y. F. (1998). Inequality of access to educational resources: A national report card for eighth grade math. Educational Evaluation and Policy Analysis, 20, 253–268.Google Scholar
  26. Robins, J. M. (2003). Semantics of causal DAG models and the identification of direct and indirect effects. In P. J. Green, N. L. Hjort, & S. Richardson (Eds.), Highly structured stochastic systems (pp. 70–81). New York: Oxford University Press.Google Scholar
  27. Robins, J. M., & Greenland, S. (1992). Identifiability and exchangeability for direct and indirect effects. Epidemiology, 3, 143–155.CrossRefGoogle Scholar
  28. Rosenbaum, P. R. (2007). Interference between units in randomized experiments. Journal of the American Statistical Association, 102, 191–200.CrossRefGoogle Scholar
  29. Roy, A. D. (1951). Some thoughts on the distribution of earnings. Oxford Economic Papers (New Series), 3, 135–146.Google Scholar
  30. Rubin, D. B. (1974). Estimating causal effects of treatments in randomized and nonrandomized studies. Journal of Educational Psychology, 66, 688–701.CrossRefGoogle Scholar
  31. Rubin, D. B. (1978). Bayesian inference for causal effects: The role of randomization. The Annals of Statistics, 6, 34–58.CrossRefGoogle Scholar
  32. Rubin, D. B. (1986). Comment: Which ifs have causal answers. Journal of the American Statistical Association, 81, 961–962.Google Scholar
  33. Sobel, M. E. (2006). What do randomized studies of housing mobility demonstrate? Causal inference in the face of interference. Journal of the American Statistical Association, 101, 1398–1407.CrossRefGoogle Scholar
  34. Sobel, M. E. (2008). Identification of causal parameters in randomized studies with mediating variables. Journal of Educational and Behavioral Statistics, 33, 230–251.CrossRefGoogle Scholar
  35. Tchetgen Tchetgen, E. J., & VanderWeele, T. J. (2012). On causal inference in the presence of interference. Statistical Methods in Medical Research, 21, 55–75.CrossRefGoogle Scholar
  36. VanderWeele, T. J. (2009). Marginal structural models for the estimation of direct and indirect effects. Epidemiology, 20, 18–26.CrossRefGoogle Scholar
  37. VanderWeele, T. J., Hong, G., Jones, S. M., & Brown, J. L. (forthcoming). Mediation and spillover effects in group-randomized trials: A case study of the 4R’s educational intervention. Journal of the American Statistical Association.Google Scholar
  38. VanderWeele, T. J., & Tchetgen Tchetgen, E. J. (2011). Effect partitioning under interference for two-stage randomized vaccine trials. Statistics and Probability Letters – Special Issue on Statistics in Biological and Medical Sciences, 81, 861–869.Google Scholar
  39. VanderWeele, T. J., & Vansteelandt, S. (2009). Conceptual issues concerning mediation, interventions and composition. Statistics and Its Interface, 2, 457–468.Google Scholar
  40. Verbitsky-Savitz, N., & Raudenbush, S. W. (2004). Causal inference in spatial settings. Proceedings of the American Statistical Association, Social Statistics Section, 2004, 2369–2374.Google Scholar
  41. Verbitsky-Savitz, N., & Raudenbush, S. W. (2012). Causal inference under interference in spatial settings: A case study evaluating community policing program in Chicago. Epidemiologic Methods, 1(1), 107–130. (Online) 2161-962X, doi:10.1515/2161-962X.1020.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Comparative Human Development and EducationUniversity of ChicagoChicagoUSA
  2. 2.Department of SociologyUniversity of ChicagoChicagoUSA

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