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ARE THOSE mediation modelS?
ARE THOSE mediation modelS?
A mediating variable...
A mediating variable...
Tells how or why a relationship occurs.
Tells a generative mechanism through which IV(s) influence DV(s).
Specifies how a given effect occurs (Baron & Kenney, 1986).
Mediation is best done in the case of a strong relation between the predictor & criterion variable (Baron & Kenny, 1986).
How did it work?
How did it work?
Why did it work?
Why did it work?
Baron and Kenny Approach
Baron and Kenny Approach
Mediation generally presents when...
Mediation generally presents when...
IV significantly affects the mediator,
IV significantly affects the DV in the absence of the mediator,
Mediator has a significant unique effect on the DV, and
The effect of IV on DV shrinks upon the addition of the mediator to the model.
Four steps approach of assessing mediating effect
Four steps approach of assessing mediating effect
Regressing Y on X (path c).
Regressing M on X (path a).
Regressing Y on both X and M.
To establish that M completely mediates the X-Y relationship, the effect of X on Y controlling for M (path c') should be zero.
Baron and Kenny recommended Sobel Test to confirm the existence of indirect effect.
Critics on Baron & Kenny
Critics on Baron & Kenny
Zhao et al. (2010)
Zhao et al. (2010)
The strength of mediation should be measured by the size of indirect effect (a x b), not by the existence of indirect effect and no direct effect.
There should be only one requirement to establish mediation (i.e., the indirect effect (a x b) is significant). No need for significant “effect to be mediated” (path c).
Sobel test is low in power compared to a bootstrap test.
Andrew F. Hayes
Andrew F. Hayes
Student: My advisor tells me I should use the Baron and Kenny strategy for assessing mediation. But my reading of the literature tells me this isn’t recommended these days. What should I do?”
Hayes: You have counted on your advisor for guidance and support. Now return the favor. All but the most stubborn of advisors are open to new ideas, and many are too busy or just don’t care enough to stay informed on recent developments. Give him or her a copy of the relevant literature or a copy of my book and make your case. Try my Beyond Baron and Kenny paper for a start (Communication Monographs, 2009, Vol 76, p. 408-420).
In my mediation analysis examining the direct and indirect effects of X on Y through M, the path from X to Y is not statistically significant. Does this mean there is no way that M could mediate the relationship between X and Y? According to Baron and Kenny (1986), it cannot. Should I bother estimating the indirect effect in this case?“
These days, we don't rely on statistical significance criteria for the individual paths in a mediation model in order to assess whether M functions as a mediator. The pattern of significance or non significance for individual paths in a mediation model is not pertinent to whether the indirect effect is significant. You absolutely should estimate the indirect effect. See Hayes (2009) for a brief discussion [PDF], or Chapter 6 of Hayes (2013).
"How can I tell whether I can claim full or partial mediation from the output of one of your mediation macros?“
These are based on the relative size and significance of the total and direct effect. "Full" or "Complete" and "Partial" mediation are outdated, 20th century concepts that have no place in 21st century mediation analysis. I recommend you avoid the use of these terms, and don't attempt to interpret your analysis based on the relative size and significance of the total and direct effects. For a discussion, see section 6.1 in Hayes (2013).
Suggested Test for Mediation Model: Bootstrapping
Suggested Test for Mediation Model: Bootstrapping
Bootstrapping is a computerized-based statistical re-sampling technique by taking repeated samples with replacement from an original data set.
Objective: To generate estimates and standard error for hypothesis testing.
Bootstrapping, a nonparametric resampling procedure, has been recognized as one of the more rigorous and powerful methods for testing the mediating effect (Hayes, 2009; Shroud & Bolger, 2002; Zhao et al., 2010).
The application of bootstrapping for mediation analysis has recently been advocated by Hair et al. (2014) whom noted that “when testing mediating effects, researchers should rather follow Preacher and Hayes (2004, 2008) and bootstrap the sampling distribution of the indirect effect, which works for simple and multiple mediator models” (p. 223).
Furthermore, this method is said to be perfectly suited for PLS-SEM because it makes no assumption about the shape of the variables’ distribution or the sampling distribution of the statistic and therefore can be applied to small sample sizes (Hair et al., 2014; Preacher & Hayes, 2008).
Reporting
Reporting
The bootstrapping analysis showed that the indirect effect β = 0.159 (0.546*0.291) was significant with a t-value of 3.682.
Also as indicated by Preacher and Hayes (2008) the indirect effect 0.159, 95% Boot CI: [LL = 0.074, UL = 0.243] does not straddle a 0 in between indicating there is mediation. Thus we can conclude that the mediation effect is statistically significant.
Types of Mediation & Non-Mediation (Zhao et al., 2010)
Types of Mediation & Non-Mediation (Zhao et al., 2010)
Decision Tree for Establishing & Understanding Types of Mediation & Non-Mediation
Decision Tree for Establishing & Understanding Types of Mediation & Non-Mediation
Source: Zhao et al. (2010)
SUMMARY OF MEDIATION ANALYSIS
SUMMARY OF MEDIATION ANALYSIS
No Mediation
No Mediation
No-effect non-mediation: Neither direct nor indirect effect significant →Theoretical framework is flawed!
Direct-only non-mediation: Direct effect (p_{3}) significant but not the indirect effect → Omitted mediator?!
Mediation
Mediation
Complementary mediation: Indirect effect (p_{1}*p_{2}) and direct effect (p_{3}) both significant and point in the same direction → Omitted mediator with an indirect path whose sign is equivalent to the direct effect?!
Competitive mediation: Indirect effect (p_{1}*p_{2}) and direct effect (p_{3}) both significant and point in opposite directions → Omitted mediator with an indirect path whose sign is opposite to the direct effect?!
Indirect-only mediation: Indirect effect (p_{1}*p_{2}) significant but not the direct effect. →Full mediation
emerging issues in mediation
emerging issues in mediation
Points to consider:
Points to consider:
Requiring a significant relation between the IV and the DV
Disregarding the magnitude of the indirect effect
Testing the direct effect as a condition for mediation
Including a direct effect without conceptual justification
Testing mediation with cross-sectional data
Lack of attention to measurement error
How to handle the criticism in the future?
How to handle the criticism in the future?
The criticism of cross-sectional mediation has been there for a long time now, unfortunately many are not aware or are basically ignorant.
To justify the cross-sectional data in mediation, we may use...
Use suitable theory/theories, such as System Theory, Stimulus-Organization-Response Theory, etc.
Use paper by Spector about optimizing the use of cross-sectional designs.
Use paper from Salthouse (2011) saying that all methods have limitations.
Further Readings
Further Readings
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(6), 1173-1182.
Hayes, A. F. (2009). Beyond Baron and Kenny: Statistical mediation analysis in the new millennium. Communication Monographs, 76(4), 408-420. doi: 10.1080/03637750903310360.
Hayes, A. F. (2013). Introduction to mediation, moderation, and conditional process analysis: A regression-based approach. New York: The Guilford Press.
Preacher, K. J., & Hayes, A. F. (2008). Asymptotic and resampling strategies for assessing and comparing indirect effects in multiple mediator models. Behavior Research Methods, 40(3), 879-891. doi: 10.3758/BRM.40.3.879.
MacKinnon, D. P., Coxe, S., & Baraldi, A. N. (2012). Guidelines for the investigation of mediating variables in business research. Journal of Business and Psychology, 27(1), 1-14.
Zhao, X., Lynch Jr., J. G., & Chen, Q. (2010). Reconsidering Baron and Kenny: Myths and truths about mediation analysis. Journal of Consumer Research, 37(2), 197-206. doi: 10.1086/651257.
Nawanir, G., Kong Teong, L., & Norezam Othman, S. (2013). Impact of lean practices on operations performance and business performance: some evidence from Indonesian manufacturing companies. Journal of Manufacturing Technology Management, 24(7), 1019-1050.
Nawanir, G., Lim, K. T., Ramayah, T., Mahmud, F., Lee, K. L., & Maarof, M. G. (2020). Synergistic effect of lean practices on lead time reduction: mediating role of manufacturing flexibility. Benchmarking: An International Journal, 27(5), 1815-1842. doi:10.1108/BIJ-05-2019-0205.
Rungtusanatham, M., Miller, J. W., & Boyer, K. K. (2014). Theorizing, testing, and concluding for mediation in SCM research: tutorial and procedural recommendations. Journal of Operations Management, 32(3), 99-113.
Memon, M. A., Cheah, J., Ramayah, T., Ting, H., & Chuah, F. (2018). Mediation analysis issues and recommendations. Journal of Applied Structural Equation Modeling, 2(1), 1–9.
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