Advertisement

Prevention Science

, Volume 20, Issue 3, pp 419–430 | Cite as

Testing the Causal Direction of Mediation Effects in Randomized Intervention Studies

  • Wolfgang WiedermannEmail author
  • Xintong Li
  • Alexander von Eye
Article

Abstract

In a recent update of the standards for evidence in research on prevention interventions, the Society of Prevention Research emphasizes the importance of evaluating and testing the causal mechanism through which an intervention is expected to have an effect on an outcome. Mediation analysis is commonly applied to study such causal processes. However, these analytic tools are limited in their potential to fully understand the role of theorized mediators. For example, in a design where the treatment x is randomized and the mediator (m) and the outcome (y) are measured cross-sectionally, the causal direction of the hypothesized mediator-outcome relation is not uniquely identified. That is, both mediation models, x → m → y or x → y → m, may be plausible candidates to describe the underlying intervention theory. As a third explanation, unobserved confounders can still be responsible for the mediator-outcome association. The present study introduces principles of direction dependence which can be used to empirically evaluate these competing explanatory theories. We show that, under certain conditions, third higher moments of variables (i.e., skewness and co-skewness) can be used to uniquely identify the direction of a mediator-outcome relation. Significance procedures compatible with direction dependence are introduced and results of a simulation study are reported that demonstrate the performance of the tests. An empirical example is given for illustrative purposes and a software implementation of the proposed method is provided in SPSS.

Keywords

Mediation analysis Randomized design Direction of effects Direction dependence Non-normality 

Notes

Funding

No funding was received for this work.

Compliance with Ethical Standards

Conflict of Interest

The authors declare that they have no conflict of interest.

Ethical Approval

This article does not contain any studies with human participants or animals performed by any of the authors.

Informed Consent

Informed consent was not required for this study.

Supplementary material

11121_2018_900_MOESM1_ESM.pdf (48 kb)
ESM 1 (PDF 47 kb)
11121_2018_900_MOESM2_ESM.pdf (79 kb)
ESM 2 (PDF 78 kb)
11121_2018_900_MOESM3_ESM.sav (10 kb)
ESM 3 (SAV 9 kb)
11121_2018_900_MOESM4_ESM.sps (5 kb)
ESM 4 (SPS 5 kb)
11121_2018_900_MOESM5_ESM.sps (7 kb)
ESM 5 (SPS 7 kb)

References

  1. Aiken, L. S., & West, S. G. (1991). Multiple regression: Testing and interpreting interactions. Thousand Oaks, CA: Sage.Google Scholar
  2. 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.  https://doi.org/10.1037/0022-3514.51.6.1173.CrossRefGoogle Scholar
  3. Bullock, J. G., Green, D. P., & Ha, S. E. (2010). Yes, but what’s the mechanism? (Don’t expect an easy answer). Journal of Personality and Social Psychology, 98, 550–558.  https://doi.org/10.1037/a0018933.CrossRefGoogle Scholar
  4. Cain, M. K., Zhang, Z., & Yuan, K. H. (2017). Univariate and multivariate skewness and kurtosis for measuring nonnormality: Prevalence, influence and estimation. Behavior Research Methods, 49, 1716–1735.  https://doi.org/10.3758/s13428-016-0814-1.CrossRefGoogle Scholar
  5. Chen, H. T. (1990). Theory-driven evaluations. Newbury Park: Sage.Google Scholar
  6. Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Hillsdale, NJ: Erlbaum.Google Scholar
  7. Davison, A. C., & Hinkley, D. V. (1997). Bootstrap methods and their application. Cambridge, UK: Cambridge University Press.CrossRefGoogle Scholar
  8. de Wit, M., & Hajos, T. (2013). Health-related quality of life. In M. D. Gellman & J. Rick Tuner (Eds.), Encyclopedia of behavioral medicine (pp. 929–931). New York, NY: Springer.Google Scholar
  9. Dodge, Y., & Rousson, V. (2000). Direction dependence in a regression line. Communications in Statistics: Theory and Methods, 29, 1957–1972.  https://doi.org/10.1080/03610920008832589.CrossRefGoogle Scholar
  10. Farahani, M. A., & Assari, S. (2010). Relationship between pain and quality of life. In V. R. Preedy & R. R. Watson (Eds.), Handbook of disease burdens and quality of life measures (pp. 3933–3953). New York, NY: Springer.CrossRefGoogle Scholar
  11. Fox, J. (2008). Applied regression analysis and generalized linear models (2nd ed.). Thousand Oaks, CA: Sage.Google Scholar
  12. Gelfand, L. A., Mensinger, J. L., & Tenhave, T. (2009). Mediation analysis: A retrospective snapshot of practice and more recent directions. Journal of General Psychology, 136, 153–178.  https://doi.org/10.3200/GENP.136.2.153-178.CrossRefGoogle Scholar
  13. Gottfredson, D. C., Cook, T. D., Gardner, F. E., Gorman-Smith, D., Howe, G. W., Sandler, I. N., & Zafft, K. M. (2015). Standards of evidence for efficacy, effectiveness, and scale-up research in prevention science: Next generation. Prevention Science, 16, 893–926.  https://doi.org/10.1007/s11121-015-0555-x.CrossRefGoogle Scholar
  14. Gretton, A., Fukumizu, K., Teo, C. H., Song, L., Schölkopf, B., & Smola, A. J. (2008). A kernel statistical test of independence. Advances in Neural Information Processing Systems, 20, 585–592.Google Scholar
  15. Hayes, A. F. (2013). Introduction to mediation, moderation, and conditional process analysis: A regression-based approach. New York, NY: Guilford.Google Scholar
  16. Huang, F. L. (2016). Alternatives to multilevel modeling for the analysis of clustered data. Journal of Experimental Education, 84, 175–196.  https://doi.org/10.1080/00220973.2014.952397.CrossRefGoogle Scholar
  17. Hyvärinen, A., Karhunen, J., & Oja, E. (2001). Independent components analysis. New York, NY: Wiley & Sons.CrossRefGoogle Scholar
  18. Iacobucci, D., Saldanha, N., & Deng, X. (2007). A meditation on mediation: Evidence that structural equations models perform better than regressions. Journal of Consumer Psychology, 17, 139–153.  https://doi.org/10.1016/S1057-7408(07)70020-7.CrossRefGoogle Scholar
  19. Imai, K., Keele, L., & Yamamoto, T. (2010). Identification, inference and sensitivity analysis for causal mediation effects. Statistical Science, 5, 1–71.  https://doi.org/10.1214/10-sts321.Google Scholar
  20. Imai, K., Keele, L., Tingley, D., & Yamamoto, T. (2011). Unpacking the black box of causality: Learning about causal mechanisms from experimental and observational studies. American Political Science Review, 105, 765–789.  https://doi.org/10.1017/S0003055411000414.CrossRefGoogle Scholar
  21. MacKinnon, D. P. (2008). Introduction to statistical mediation analysis. New York, NY: Erlbaum.Google Scholar
  22. Micceri, T. (1989). The unicorn, the normal curve, and other improbable creatures. Psychological Bulletin, 105, 156–166.  https://doi.org/10.1037/0033-2909.105.1.156.CrossRefGoogle Scholar
  23. Pearl, J. (2001). Direct and indirect effects. In Proceedings of the 17th conference in uncertainly in artificial intelligence (pp. 411–420). San Francisco, CA: Morgan Kaufmann Publishers Inc..Google Scholar
  24. Shimizu, S., Inazumi, T., Sogawa, Y., Hyvärinen, A., Kawahara, Y., Washio, T., Hoyer, P. O., & Bollen, K. (2011). DirectLiNGAM: A direct method for learning a linear non-Gaussian structural equation model. Journal of Machine Learning Research, 12, 1225–1248.Google Scholar
  25. Shrout, P. E., & Bolger, N. (2002). Mediation in experimental and nonexperimental studies: New procedures and recommendations. Psychological Methods, 7, 422–445.  https://doi.org/10.1037//1082-989x.7.4.422.CrossRefGoogle Scholar
  26. Stelzl, I. (1986). Changing the causal hypothesis without changing the fit: Some rules for generating equivalent path models. Multivariate Behavioral Research, 21, 309–331.  https://doi.org/10.1207/s15327906mbr2103_3.CrossRefGoogle Scholar
  27. Stewart, A. L., & Ware Jr., J. E. (Eds.). (1992). Measuring functioning and well-being: The medical outcomes study approach. Durham, NC: Duke University Press.Google Scholar
  28. Székely, G. J., Rizzo, M. L., & Bakirov, N. K. (2007). Measuring and testing dependence by correlation of distances. Annals of Statistics, 35, 2769–2794.  https://doi.org/10.1214/009053607000000505.CrossRefGoogle Scholar
  29. Vickers, A. J. (2006). Whose data set is it anyway? Sharing raw data from randomized trials. Trials, 7.  https://doi.org/10.1186/1745-6215-7-15.
  30. Vickers, A. J., Rees, R. W., Zollman, C. E., McCarney, R., Smith, C. M., Ellis, N., ... & Van Haselen, R. (2004). Acupuncture for chronic headache in primary care: Large, pragmatic, randomised trial. BMJ, 328. doi:bmj.38029.421863.EB.Google Scholar
  31. von Eye, A., & DeShon, R. P. (2012). Directional dependence in developmental research. International Journal of Behavioral Development, 36, 303–312.  https://doi.org/10.1177/0165025412439968.CrossRefGoogle Scholar
  32. Wiedermann, W., & Li, X. (2018). Direction dependence analysis: A framework to test the direction of effects in linear models with an implementation in SPSS. Behavior Research Methods.  https://doi.org/10.3758/s13428-018-1031-x.
  33. Wiedermann, W., & von Eye, A. (2015a). Direction of effects in mediation analysis. Psychological Methods, 20, 221–244.  https://doi.org/10.1037/met0000027.CrossRefGoogle Scholar
  34. Wiedermann, W., & von Eye, A. (2015b). Direction-dependence analysis: A confirmatory approach for testing directional theories. International Journal of Behavioral Development, 39, 570–580.  https://doi.org/10.1177/0165025415582056.CrossRefGoogle Scholar
  35. Wiedermann, W., & von Eye, A. (2016). Directionality of effects in causal mediation analysis. In W. Wiedermann & A. von Eye (Eds.), Statistics and causality: Methods for applied empirical research (pp. 63–106). Hoboken, NJ: Wiley and Sons.CrossRefGoogle Scholar
  36. Wiedermann, W., Arntner, R., & von Eye, A. (2017). Heteroscedasticity as a basis of direction dependence in reversible linear regression models. Multivariate Behavioral Research.  https://doi.org/10.1080/00273171.2016.1275498.

Copyright information

© Society for Prevention Research 2018

Authors and Affiliations

  • Wolfgang Wiedermann
    • 1
    Email author
  • Xintong Li
    • 1
  • Alexander von Eye
    • 2
  1. 1.Statistics, Measurement, and Evaluation in Education, Department of Educational, School, and Counseling Psychology, College of EducationUniversity of MissouriColumbiaUSA
  2. 2.Michigan State UniversityEast LansingUSA

Personalised recommendations