Hostname: page-component-8448b6f56d-wq2xx Total loading time: 0 Render date: 2024-04-16T11:02:55.260Z Has data issue: false hasContentIssue false

Identification and Sensitivity Analysis for Multiple Causal Mechanisms: Revisiting Evidence from Framing Experiments

Published online by Cambridge University Press:  04 January 2017

Kosuke Imai*
Affiliation:
Department of Politics, Princeton University, Princeton NJ 08544
Teppei Yamamoto
Affiliation:
Department of Political Science, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139 e-mail: teppei@mit.edu
*
e-mail: kimai@princeton.edu (corresponding author)

Abstract

Social scientists are often interested in testing multiple causal mechanisms through which a treatment affects outcomes. A predominant approach has been to use linear structural equation models and examine the statistical significance of the corresponding path coefficients. However, this approach implicitly assumes that the multiple mechanisms are causally independent of one another. In this article, we consider a set of alternative assumptions that are sufficient to identify the average causal mediation effects when multiple, causally related mediators exist. We develop a new sensitivity analysis for examining the robustness of empirical findings to the potential violation of a key identification assumption. We apply the proposed methods to three political psychology experiments, which examine alternative causal pathways between media framing and public opinion. Our analysis reveals that the validity of original conclusions is highly reliant on the assumed independence of alternative causal mechanisms, highlighting the importance of proposed sensitivity analysis. All of the proposed methods can be implemented via an open source R package, mediation.

Type
Research Article
Copyright
Copyright © The Author 2013. Published by Oxford University Press on behalf of the Society for Political Methodology 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

Authors' note: The proposed methods can be implemented via open-source software mediation that is freely available as an R package at the Comprehensive R Archive Network (CRAN, http://cran.r-project.org/package=mediation). The replication archive for this article is available online as Imai and Yamamoto (2012). We are grateful to Ted Brader, Jamie Druckman, and Rune Slothuus for sharing their data with us. We thank Dustin Tingley and Mike Tomz for useful discussions that motivated this article. John Bullock, Adam Glynn, and Tyler VanderWeele provided helpful suggestions. We also thank the Associate Editor and two anonymous referees for their comments that significantly improved the paper. An earlier version of this article was circulated under the title “Sensitivity Analysis for Causal Mediation Effects under Alternative Exogeneity Conditions.”

References

Albert, J. M., and Nelson, S. 2011. Generalized causal mediation analysis. Biometrics 67(3): 1028–38.CrossRefGoogle ScholarPubMed
Angrist, J. D., Imbens, G. W., and Rubin, D. B. 1996. Identification of causal effects using instrumental variables (with discussion). Journal of the American Statistical Association 91: 434, 444–55.Google Scholar
Avin, C., Shpitser, I., and Pearl, J. 2005. Identifiability of path-specific effects. In Proceedings of the nineteenth international joint conference on artificial intelligence, 357–63. Edinburgh: Morgan Kaufmann.Google Scholar
Baron, R. M., and 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(6): 1173–82.CrossRefGoogle ScholarPubMed
Brader, T., Valentino, N., and Suhay, E. 2008. What triggers public opposition to immigration? Anxiety, group cues, and immigration threat. American Journal of Political Science 52(4): 959–78.CrossRefGoogle Scholar
Bullock, J., Green, D., and Ha, S. 2010. Yes, but what's the mechanism? (Don't expect an easy answer). Journal of Personality and Social Psychology 98(4): 550–8.CrossRefGoogle ScholarPubMed
Callaghan, K., and Schnell, F., eds. 2005. Framing American politics. Pittsburgh, PA: University of Pittsburgh Press.CrossRefGoogle Scholar
Chong, D., and Druckman, J. N. 2007. A theory of framing and opinion formation in competitive elite environments. Journal of Communication 57: 99118.Google Scholar
Druckman, J. N., and Nelson, K. R. 2003. Framing and deliberation: How citizens' conversations limit elite influence. American Journal of Political Science 47(4): 729–45.CrossRefGoogle Scholar
Glynn, A. N. 2012. The product and difference fallacies for indirect effects. American Journal of Political Science 56(1): 257–69.CrossRefGoogle Scholar
Hafeman, D. 2008. Opening the black box: A reassessment of mediation from a counterfactual perspective. PhD thesis, Columbia University.Google Scholar
Holland, P. W. 1986. Statistics and causal inference (with discussion). Journal of the American Statistical Association 81: 945–60.Google Scholar
Imai, K., and Yamamoto, T. 2012. Replication data for: Identification and sensitivity analysis for multiple causal mechanisms: Revisiting evidence from framing experiments. Dataverse Network, hdl:1902.1/19036.Google Scholar
Imai, K., Keele, L., and Tingley, D. 2010a. A general approach to causal mediation analysis. Psychological Methods 15(4): 309–34.CrossRefGoogle ScholarPubMed
Imai, K., Keele, L., Tingley, D., and Yamamoto, T. 2010b. Advances in social science research using R. In Causal mediation analysis using R, ed. Vinod, H. D., 129–54. Lecture Notes in Statistics. New York: Springer-Verlag.CrossRefGoogle Scholar
Imai, K., Keele, L., Tingley, D., and Yamamoto, T. 2011. Unpacking the black box of causality: Learning about causal mechanisms from experimental and observational studies. American Political Science Review 105(4): 765–89.CrossRefGoogle Scholar
Imai, K., Keele, L., and Yamamoto, T. 2010c. Identification, inference, and sensitivity analysis for causal mediation effects. Statistical Science 25(1): 5171.CrossRefGoogle Scholar
Imai, K., Tingley, D., and Yamamoto, T. 2013. Experimental designs for identifying causal mechanisms. Journal of the Royal Statistical Society, Series A (Statistics in Society) 176(1): 551.CrossRefGoogle Scholar
Imbens, G. W., and Manski, C. F. 2004. Confidence intervals for partially identified parameters. Econometrica 72(6): 1845–57.CrossRefGoogle Scholar
Isbell, L., and Ottati, V. 2002. The emotional voter: Effects of episodic affective reactions on candidate evaluation. In The social psychology of politics: Social psychological application to social issues, eds. Ottati, V., Tindale, R., Edwards, J., Bryant, F., Heath, L., O'Connell, D., Suarez-Balcazar, Y., and Posavac, E., Vol. 5, 5574. New York: Kluwer.CrossRefGoogle Scholar
Iyengar, S. 1991. Is anyone responsible? Chicago: University of Chicago Press.CrossRefGoogle Scholar
Kaufman, S., Kaufman, J. S., and MacLehose, R. F. 2009. Analytic bounds on causal risk differences in directed acyclic graphs involving three observed binary variables. Journal of Statistical Planning and Inference 139: 3473–87.CrossRefGoogle ScholarPubMed
Kinder, D. R., and Sanders, L. M. 1990. Mimicking political debate with survey questions: The case of white opinion on affirmative action for blacks. Social Cognition 8(1): 73103.CrossRefGoogle Scholar
Kraemer, H. C., Kiernan, M., Essex, M., and Kupfer, D. J. 2008. How and why criteria defining moderators and mediators differ between the Baron & Kenny and MacArthur approaches. Health Psychology 27(2): S1018.CrossRefGoogle ScholarPubMed
Miller, J. M. 2007. Examining the mediators of agenda setting: A new experimental paradigm reveals the role of emotions. Political Psychology 28(6): 689717.CrossRefGoogle Scholar
Nelson, T. E., and Kinder, D. R. 1996. Issue framing and group-centrism in american public opinion. Journal of Politics 58: 1055–78.CrossRefGoogle Scholar
Nelson, T. E., Clawson, R. A., and Oxley, Z. M. 1997. Media framing of a civil liberties conflict and its effect on tolerance. American Political Science Review 91(3): 567–83.CrossRefGoogle Scholar
Neyman, J. 1923. On the application of probability theory to agricultural experiments: Essay on principles, section 9 (translated in 1990). Statistical Science 5: 465–80.Google Scholar
Pearl, J. 2001. Direct and indirect effects. In Proceedings of the seventeenth conference on uncertainty in artificial intelligence, 411–20. San Francisco: Morgan Kaufmann.Google Scholar
Petersen, M. L., Sinisi, S. E., and van der Laan, M. J. 2006. Estimation of direct causal effects. Epidemiology 17(3): 276–84.CrossRefGoogle ScholarPubMed
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: 1393–512.CrossRefGoogle Scholar
Robins, J. M. 2003. Semantics of causal DAG models and the identification of direct and indirect effects. In Highly structured stochastic systems, eds. Green, P. J., Hjort, N. L., and Richardson, S., 7081. Oxford, UK: Oxford University Press.CrossRefGoogle Scholar
Robins, J. M., and Greenland, S. 1992. Identifiability and exchangeability for direct and indirect effects. Epidemiology 3(2): 143–55.CrossRefGoogle ScholarPubMed
Robins, J. M., and Richardson, T. 2010. Alternative graphical causal models and the identification of direct effects. In Causality and psychopathology: Finding the determinants of disorders and their cures, eds. Shrout, P., Keyes, K., and Omstein, K., 103–59. Oxford, UK: Oxford University Press.Google Scholar
Rubin, D. B. 1974. Estimating causal effects of treatments in randomized and non-randomized studies. Journal of Educational Psychology 66: 688701.CrossRefGoogle Scholar
Rubin, D. B. 2004. Direct and indirect causal effects via potential outcomes (with discussions). Scandinavian Journal of Statistics 31(2): 161–70.CrossRefGoogle Scholar
Sjölander, A. 2009. Bounds on natural direct effects in the presence of confounded intermediate variables. Statistics in Medicine 28(4): 558–71.CrossRefGoogle ScholarPubMed
Slothuus, R. 2008. More than weighting cognitive importance: A dual-process model of issue framing effects. Political Psychology 29(1): 128.CrossRefGoogle Scholar
Taylor, A. B., MacKinnon, D. P., and Tein, J.-Y. 2008. Tests of the three-path mediated effect. Organizational Research Methods 11(2): 241–69.CrossRefGoogle Scholar
Tchetgen Tchetgen, E. J., and Shpitser, I. 2011. Semiparametric theory for causal mediation analysis: Efficiency bounds, multiple robustness, and sensitivity analysis. Technical report. Cambridge, MA: Harvard University School of Public Health.Google Scholar
Tingley, D., Yamamoto, T., Keele, L., and Imai, K. 2012. Mediation: R package for causal mediation analysis. Available at the Comprehensive R Archive Network (CRAN), http://CRAN.R-project.org/package=mediation.Google Scholar
Tversky, A., and Kahneman, D. 1981. The framing of decisions and the psychology of choice. Science 211: 453–8.CrossRefGoogle ScholarPubMed
VanderWeele, T. J. 2009. Marginal structural models for the estimation of direct and indirect effects. Epidemiology 20(1): 1826.CrossRefGoogle ScholarPubMed
VanderWeele, T. J. 2010. Bias formulas for sensitivity analysis for direct and indirect effects. Epidemiology 21(4): 540–51.CrossRefGoogle ScholarPubMed
Zaller, J. 1992. The nature and origins of mass opinion. New York: Cambridge University Press.CrossRefGoogle Scholar