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Heterogeneous Agents, Social Interactions, and Causal Inference

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Handbook of Causal Analysis for Social Research

Abstract

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.

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References

  • 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.

    Article  Google Scholar 

  • 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 

  • Haavelmo, T. (1943). The statistical implications of a system of simultaneous equations. Econometrika, 11, 1–12.

    Article  Google Scholar 

  • 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 

  • Heckman, J. (1979). Sample selection bias as a specification error. Econometrika, 47, 153–161.

    Article  Google Scholar 

  • 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 

  • Holland, P. W. (1986). Statistics and causal inference. Journal of the American Statistical Association, 81, 945–960.

    Article  Google Scholar 

  • 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 

  • 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 

  • 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 

  • 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 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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 

  • Hudgens, M. G., & Halloran, M. E. (2008). Toward causal inference with interference. Journal of the American Statistical Association, 103, 832–842.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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 

  • 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 

  • 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 

  • 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 

  • 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 

  • Nye, B., Hedges, L. V., & Konstantopouloss, S. (2004). How large are teacher effects? Educational Evaluation and Policy Analysis, 26, 237–257.

    Article  Google Scholar 

  • 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 

  • Peterson, M. L., Sinisi, S. E., & van der Laan, M. J. (2006). Estimation of direct causal effects. Epidemiology, 17, 276–284.

    Article  Google Scholar 

  • 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 

  • 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 

  • Robins, J. M., & Greenland, S. (1992). Identifiability and exchangeability for direct and indirect effects. Epidemiology, 3, 143–155.

    Article  Google Scholar 

  • Rosenbaum, P. R. (2007). Interference between units in randomized experiments. Journal of the American Statistical Association, 102, 191–200.

    Article  Google Scholar 

  • Roy, A. D. (1951). Some thoughts on the distribution of earnings. Oxford Economic Papers (New Series), 3, 135–146.

    Google Scholar 

  • Rubin, D. B. (1974). Estimating causal effects of treatments in randomized and nonrandomized studies. Journal of Educational Psychology, 66, 688–701.

    Article  Google Scholar 

  • Rubin, D. B. (1978). Bayesian inference for causal effects: The role of randomization. The Annals of Statistics, 6, 34–58.

    Article  Google Scholar 

  • Rubin, D. B. (1986). Comment: Which ifs have causal answers. Journal of the American Statistical Association, 81, 961–962.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • Sobel, M. E. (2008). Identification of causal parameters in randomized studies with mediating variables. Journal of Educational and Behavioral Statistics, 33, 230–251.

    Article  Google Scholar 

  • Tchetgen Tchetgen, E. J., & VanderWeele, T. J. (2012). On causal inference in the presence of interference. Statistical Methods in Medical Research, 21, 55–75.

    Article  Google Scholar 

  • VanderWeele, T. J. (2009). Marginal structural models for the estimation of direct and indirect effects. Epidemiology, 20, 18–26.

    Article  Google Scholar 

  • 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 

  • 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 

  • VanderWeele, T. J., & Vansteelandt, S. (2009). Conceptual issues concerning mediation, interventions and composition. Statistics and Its Interface, 2, 457–468.

    Google Scholar 

  • 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 

  • 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 

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Correspondence to Guanglei Hong .

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Hong, G., Raudenbush, S.W. (2013). Heterogeneous Agents, Social Interactions, and Causal Inference. In: Morgan, S. (eds) Handbook of Causal Analysis for Social Research. Handbooks of Sociology and Social Research. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-6094-3_16

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