Statistical mediation analysis is used to study indirect effects between variables, typically by using path analysis, structural equation modeling, or a series of regression models. Mediation analysis is important in areas of the social sciences where variables cause variation in other variables that then in turn cause variation in yet other variables:
X --> M --> Y
where X is called an exogenous variable, M is a mediator variable, and Y is the final outcome variable. For example, in Whitelaw and Liang's (1991) theoretical model, physical health (X; the absence of diseases) causes functional health (M; e.g., the ability to exercise or climb stairs) which in turn causes subjective health (Y; e.g., self-rated health and well-being).
Mediation analysis allows researchers to study the importance and statistical significance of both direct and indirect (mediated) causal path ways. For example, there may be a direct link between the physical health status and subjective health as well as an indirect path via functional health. Mediation analysis allows us to estimate and test both the direct and indirect effects.
See also my Youtube playlist on statistical mediation analysis:
https://www.youtube.com/playlist?list=PL-kVjeOVYChqDbmDCLn4DFNEyPu6y_BID
For more details, see:
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.
Cole, D. A., & Maxwell, S. E. (2003). Testing mediational models with longitudinal data: Questions and tips in the use of structural equation modeling. Journal of Abnormal Psychology, 112, 558–577.
Hayes, A. F. (2018). Introduction to mediation, moderation, and conditional process analysis (2nded.). New York: Guilford Press.
MacKinnon, D. P. (2008). Introduction to statistical mediation analysis. Routledge.
Preacher, K. J., & Kelley, K. (2011). Effect size measures for mediation models: Quantitative strategies for communicating indirect effects. Psychological Methods, 16, 93-115.
Shrout, P. E., & Bolger, N. (2002). Mediation in experimental and nonexperimental studies: New procedures and recommendations. Psychological Methods, 7, 422-445.
Whitelaw, N. A., & Liang, J. (1991). The structure of the OARS physical health measures. Medical Care, 29(4), 332-347.
Disclaimer: I do not have Christian Geiser's level of expertise concerning mediation analysis. Nevertheless, I would add these two articles to the good reading list he gave you.
MacKinnon, D. P., Krull, J. L., & Lockwood, C. M. (2000). Equivalence of the mediation, confounding and suppression effect. Prevention science, 1, 173-181.
Fiedler, K., Harris, C., & Schott, M. (2018). Unwarranted inferences from statistical mediation tests–An analysis of articles published in 2015. Journal of Experimental Social Psychology, 75, 95-102.
I consider these to be essential reading for (aspiring) mediation analysts. ;-)
Hi sir, please help me Bruce Weaver does mediation analysis need classic assumption check like heterokendasity n multicolinearity?? I really confuse about that course I think mediation doesn't need that, ASAP. thankyou sir
Anindya Ayu my question would be: why do you believe that basic assumptions are not required anymore? Furthermore, if heteroscedasticity, multicollinearity, non-normality or whatever pose a problem is not a dichotomous either/or decision, but a gradual one and you have to decide a) if the violation is large enough to be problematic and b) which part of your analysis may be affected by it (e.g. the inferential part, the parameter estimation...). Additionally, there may be strategies, i.e. robust analyses, which may remedy these problems. Therefore, I don't think that there is a simple answer to your question without seeing the data and knowing more about your research questions. Others, like Bruce Weaver may disagree and I dont want to speak for him. Just my two cents to this question.
Thank you sir Rainer Duesing actually I confuse with that cause several people say if the data is not normal we haven't checked another basic assumption like multicolinearity n heterocendasticity. But, at the same time, several people say that the data must need basic assumptions. So, confuse n need more information,and knowledge about mediation analysis. That's why i asked here. If you have another knowledge i really happy to study it. Thank you for ur responses.
Anindya Ayu can you please provide any sources saying:"[...] if the data is not normal we haven't checked another basic assumption like multicolinearity n heterocendasticity"?
As stated above, this is not a dichotomous decision. You have to explore the data and judge, if your data are sufficiently ok, to assume that basic assumptions will hold. In reality, data will NEVER be perfectly normal, homoscedastic or not multicollinear (where that latter is a basic tenet for mediation. Your predictor and your mediator need to be correlated, therefore, in your model where both predict your dependent variable, they will be necessarily multicollinear to some degree).
Just to give an example: How do you "test" for normality? It is not very wise to exculusively rely on statistical tests, like KS-test or SW-test. Both (and others) are dependend on power, i.e. sample size. In large samples they will detect deviations from normality even if they are small and will not matter much, if you invoke the CLT. Additionally, they dont tell you why your data is not normal. It may be due to not-perfect, but acceptable normality, due to some outliers or because your residual distribution it totally off the limits and then maybe your statistical model is not suitable (e.g. if you use OLS regression for a dichotomous dependent variable).
The statement about the normality is strange on another level, since the normality assumption is often considered as less problematic, especially in large samples. Therefore, please provide your sources, to get a better undertanding of your point.
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