Abstract
Social and behavioral scientists have long used path analysis and related linear structural equation models (SEMs) to decompose parameters of ordered systems of equations into “direct effects” and “indirect effects” through mediating variables. These decompositions have been used to address substantive questions of fundamental interest, for example, how a person’s social background affects his/her earnings through education. However, in general, the “direct effects” and “indirect effects” defined in and estimated from these models should not be given causal interpretations, even in randomized experiments. To illustrate this, we first define various direct and indirect effects using potential outcomes notation and discuss situations where an investigator might want to consider these. Second, we consider identification of these effects: the required identifying assumptions are more often than not implausible for the kinds of data collected and questions considered in social and behavioral research. Third, we present other identifying assumptions that might be used to identify direct and indirect effects, and then briefly discuss different methods to estimate these effects, including regression, instrumental variables, marginal structural models, and weighting methods.Finally, we introduce an alternative approach to mediation (principal stratification), define several possible effects of interest, and briefly discuss identifying assumptions and estimation.
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References
Angrist, J. D., Imbens, G. W., & Rubin, D. B. (1996). Identification of causal effects using instrumental variables. Journal of the American Statistical Association, 91, 444–472.
Baron, R. M., & Kenny, D. A. (1986). The moderator-mediator variable distinction in social psychological research: Conceptual, strategic and statistical considerations. Journal of Personality and Social Psychology, 51, 1173–1182.
Belsen, W. A. (1956). A technique for studying the effects of a television broadcast. Applied Statistics, 5, 195–202.
Bolger, N., & Amarel, D. (2007). Effects of social support visibility on adjustment to stress: Experimental evidence. Journal of Personality and Social Psychology, 92, 458–475.
Brumback, B. A., Hernán, M. A., Haneuse, S. J., & Robins, J. M. (2004). Sensitivity analyses for unmeasured confounding assuming a marginal structural model for repeated measures. Statistics in Medicine, 23, 749–767.
Dawid, A. P. (2008). Beware of the DAG!. Journal of Machine Learning Research: Workshop and Conference Proceeding, 6, 59–86.
Duncan, O. D. (1966). Path analysis: Sociological examples. American Journal of Sociology, 76, 1–16.
Emsley, R., Dunn, G., & White, I. R. (2010). Mediation and moderation of treatment effects in randomised controlled trials of complex interventions. Statistical Methods in Medical Research, 19, 237–270.
Frangakis, C. E., & Rubin, D. B. (1999). Addressing complications of intentto-treat analysis in the combined presence of all-or-none treatment-noncompliance and subsequent missing outcomes. Biometrika, 86, 365–379.
Frangakis, C. E., & Rubin, D. B. (2002). Principal stratification in causal inference. Biometrics, 58, 21–29.
Gennetian, L. A., Morris, P. A., Bos, J. M., & Bloom, H. S. (2005). Constructing instrumental variables from experimental data to explore how treatments produce effects. In H. S. Bloom (Ed.), Learning more from social experiments: Evolving analytic approaches (1st ed., pp. 75–114). New York: Russell Sage Foundation.
Halaby, C. N. (1979). Job-specific sex differences in organizational reward attainment: Wage discrimination vs. rank segregation. Social Forces, 58, 108–127.
Hauser, R. M., & Featherman, D. L. (1977). The process of stratification: Trends and analyses. New York: Academic Press.
Hernán, M. A., & Robins, J. M. (2009). Estimation of the causal effects of time-varying exposure. In G. Fitzmaurice, M. Davidian, G. Verbeke, & G. Molenberghs (Eds.), Longitudinal data analysis. Boca Raton: Chapman and Hall/CRC.
Hill, J., Waldfogel, J., & Brooks-Gunn, J. (2002). Differential effects of high-quality child care. Journal of Policy Analysis and Management, 21, 601–627.
Hirano, K., Imbens, G. W., Rubin, D. B., & Zhou, X.-H. (2000). Assessing the effect of an influenza vaccine in an encouragement design. Biostatistics, 1, 69–88.
Holland, P. W. (1988). Causal inference, path analysis, and recursive structural equation models (with discussion). Sociological Methodology, 18, 449–493.
Hong, G., & Nomi, T. (2012). Weighting methods for assessing policy effects mediated by peer change. Journal of Educational Effectiveness (special issue on the statistical approaches to studying mediator effects in education research), 5, 261–289.
Horvitz, D. G., & Thompson, D. J. (1952). A generalization of sampling without replacement from a finite universe. Journal of the American Statistical Association, 47, 663–685.
Imai, K., Keele, L., & Yamamoto, T. (2010). Identification, inference and sensitivity analysis for causal mediation effects. Statistical Science, 25, 51–71.
Imai, K., Tingley, D., & Yamamoto, T. (2013). Experimental designs for identifying causal mechanisms. Journal of the Royal Statistical Society, Series A, 176, 5–51.
Jin, H., & Rubin, D. B. (2008). Principal stratification for causal inference with extended partial compliance. Journal of the American Statistical Association, 103, 101–111.
Jin, H., & Rubin, D. B. (2009). Public schools versus private schools: Causal inference with partial compliance. Journal of Educational and Behavioral Statistics, 34, 24–45.
Jo, B. (2002). Estimating intervention effects with noncompliance: Alternative model specifications. Journal of Educational and Behavioral Statistics, 27, 385–430.
Jo, B. (2008). Causal inference in randomized experiments with mediational processes. Psychological Methods, 13, 314–336.
Jo, B., & Stuart, E. A. (2009). On the use of propensity scores in principal causal effect estimation. Statistics in Medicine, 28, 2857–2875.
Joffe, M. M., Small, D., & Hsu, C.-Y. (2007). Defining and estimating intervention effects for groups that will develop an auxiliary outcome. Statistical Science, 22, 74–97.
Jöreskog, K. (1977). Structural equation models in the social sciences: Specification, estimation and testing. In P. R. Krishnaiah (Ed.), Application of Statistics (pp. 265–287). Amsterdam: North-Holland.
Lindquist, M. A. (2012). Functional causal mediation analysis with an application to brain connectivity. Journal of the American Statistical Association, 107, 1297–1309.
Lindquist, M. A., & Sobel, M. E. (2011a). Graphical models, potential outcomes and causal inference: Comment on Ramsey, Spirtes and Glymour. Neuroimage, 57, 334–336.
Lindquist, M. A., & Sobel, M. E. (2011b). Cloak and DAG: A response to the comments on our comment. Neuroimage, doi:10.1016/j.neuroimage.2011.11.027.
Little, R. J., & Yau, L. H. Y. (1998). Statistical techniques for analyzing data from prevention trials: Treatment of no-shows using Rubin’s causal model. Psychological Methods, 2, 147–159.
MacKinnon, D. P. (2008). Introduction to statistical mediation analysis. New York: Lawrence Erlbaum Associates.
Molm, L. D., Takahashi, N., & Peterson, G. (2003). In the eye of the beholder: Procedural justice in social exchange. American Sociological Review, 68, 128–152.
Pearl, J. (2001). Direct and indirect effects. In Proceedings of the seventeenth conference on uncertainty and artificial intelligence (pp. 411–420). San Francisco, CA: Morgan Kaufmann.
Pearl, J. (2009). Causality: Models, reasoning, and inference. Cambridge: Cambridge University Press.
Peterson, M. L., Sinisi, S. E., & van der Laan, M. J. (2006). Estimation of direct causal effects. Epidemiology, 17, 276–284.
Riach, P. A., & Rich, J. (2006). An experimental investigation of sexual discrimination and hiring in the English labor market. The B. E. Journal of Economic Analysis and Policy, 6(2), 1.
Robins, J. M. (1986). A new approach to causal inference in mortality studies with sustained exposure periods – Application to control of the healthy worker survivor effect. Mathematical Modeling, 7, 1393–1512.
Robins, J. M. (1999). Association, causation and marginal structural models. Synthese, 121, 51–179.
Robins, J. M. (2003). Semantics of causal DAG models and the identification of direct and indirect effects. In P. Green, N. L. Hjort, & S. Richardson (Eds.), Highly structured stochastic systems (pp. 70–81). New York: Oxford University Press.
Robins, J. M., & Greenland, S. (1992). Identifiability and exchangeability of direct and indirect effects. Epidemiology, 3, 143–155.
Rosenbaum, P. R. (1984). The consequences of adjustment for a concomitant variable that has been affected by the treatment. Journal of the Royal Statistical Society, Series A, 147, 656–666 (General).
Rosenbaum, P. R. (2010). Design of observational studies. New York: Springer.
Rubin, D. B. (1977). Assignment to treatment group on the basis of a covariate. Journal of Educational Statistics, 2, 1–26.
Rubin, D. B. (1980). Discussion of ‘randomization analysis of experimental data: The Fisher randomization test’ by D. Basu. Journal of the American Statistical Association, 75, 591–593.
Small, D., Ten Have, T., Joe, M., & Cheng, J. (2006). Random effects logistic models for analysing efficacy of a longitudinal randomized treatment with non-adherence. Statistics in Medicine, 25, 1981–2007.
Sobel, M. E. (1990). Effect analysis and causation in linear structural equation models. Psychometrika, 55, 495–515.
Sobel, M. E. (2008). Identification of causal parameters in randomized studies with mediating variables. Journal of Educational and Behavioral Statistics, 33, 230–251.
Sobel, M. E. (2012). Does marriage boost men’s wages?: Identification of treatment effects in fixed and random effects regression models for panel data. Journal of the American Statistical Association, 107, 521–529.
Sobel, M. E., & Muthén, B. O. (2012). Compliance mixture modeling with a zero effect complier class and missing data. Biometrics, 68, 1037–1045.
VanderWeele, T. J. (2009). Marginal structural models for the estimation of direct and indirect effects. Epidemiology, 20, 18–26.
VanderWeele, T. J. (2010). Bias formulas for sensitivity analysis for direct and indirect effects. Epidemiology, 21, 540–551.
VanderWeele, T. J., & Vansteelandt, S. (2009). Conceptual issues concerning mediation, interventions and composition. Statistics and Its Interface, 2, 457–468.
Yau, L. H. Y., & Little, R. J. (2001). Inference for the complier-average causal effect from longitudinal data subject to noncompliance and missing data, with application to a job training assessment for the unemployed. Journal of the American Statistical Association, 96, 1232–1244.
Acknowledgements
We thank Felix Elwert, Stephen Morgan, Geoffrey Wodtke, Kenneth Bollen and Judea Pearl for helpful comments. Any remaining errors are the authors’ alone.
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Wang, X., Sobel, M.E. (2013). New Perspectives on Causal Mediation Analysis. 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_12
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DOI: https://doi.org/10.1007/978-94-007-6094-3_12
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