Testing mediation
A mediator M sits between a predictor X and an outcome Y: X affects M, and M affects Y. The indirect effect is the product of the two path coefficients, a × b. The direct effect c′ is the path from X to Y that remains, and the total effect is their sum.
Because the product of two coefficients is rarely normally distributed, the Sobel test is no longer recommended. Instead, bootstrap the indirect effect and check whether its confidence interval excludes zero (Preacher and Hayes, 2008). The older Baron and Kenny steps are also unnecessary: an indirect effect can be significant even when the total effect is not.
In PLS-SEM Studio you only draw the paths. With X → M, M → Y and X → Y in the model, the app reports the specific indirect effect, the total indirect effect, the direct and total effects, and bootstrap intervals for each.
Classifying the type of mediation
Zhao, Lynch and Chen (2010) classify the result by the significance and sign of the indirect and direct effects:
| Indirect a × b | Direct c′ | Type |
|---|---|---|
| Significant | Not significant | Indirect-only (full) mediation |
| Significant | Significant, same sign | Complementary (partial) mediation |
| Significant | Significant, opposite sign | Competitive (partial) mediation |
| Not significant | Significant | Direct-only (no mediation) |
| Not significant | Not significant | No effect (no mediation) |
The app applies this classification automatically in the Mediation summary table. It also reports the variance accounted for (VAF = indirect ÷ total effect), which some reviewers still request. VAF is only meaningful when the indirect and direct effects share a sign.
Parallel and serial mediators
With several mediators, report each specific indirect effect separately. Parallel mediators each sit on their own route (X → M1 → Y and X → M2 → Y). Serial mediators sit on one chain (X → M1 → M2 → Y), and the specific indirect effect is the product of all three coefficients. PLS-SEM Studio enumerates every route, so complex chains need no extra setup.
Testing moderation
A moderator W changes the strength or direction of the relationship between X and Y. In PLS-SEM it enters the model as an interaction term X × W, alongside the main effects of X and W on Y.
Three ways to build the interaction term exist: the product-indicator, orthogonalising and two-stage approaches. The two-stage approach is the recommended default when the goal is to test whether the moderation is significant, and it is the only one that works with formative constructs (Becker, Ringle and Sarstedt, 2018). In stage one the model is estimated without the interaction to obtain the latent variable scores; in stage two the standardised product of the X and W scores is added as a single-item construct.
In the app, open the Moderation box in the model builder, pick the moderator, pick the path it changes, and click Add. The direct path from the moderator to the outcome is added for you, as theory requires.
Interpret the interaction coefficient as the change in the X → Y slope for a one standard deviation increase in W. Its f² is usually small; Kenny (2018) suggests 0.005, 0.01 and 0.025 as small, medium and large interaction effects.
Simple slope analysis
A simple slope plot makes the interaction concrete. It shows the X → Y relationship at low (−1 SD), average and high (+1 SD) levels of the moderator. Lines that fan out show that the effect grows with the moderator; crossing lines show that its direction changes. PLS-SEM Studio reports each slope with a bootstrap confidence interval and draws the plot, which you can save as SVG or PNG.
Moderated mediation
When a moderated path is part of an indirect route, the indirect effect itself depends on the moderator. Report the conditional indirect effects at −1 SD, the mean and +1 SD of the moderator, and the index of moderated mediation, which is the interaction coefficient multiplied by the other path or paths on the route (Hayes, 2015). If the index's confidence interval excludes zero, the mediation is moderated. The app computes all of these whenever your model contains such a route.
Reporting checklist
- Indirect, direct and total effects with bootstrap confidence intervals and the mediation type.
- The interaction term's coefficient, p value, confidence interval and f².
- Simple slopes at ±1 SD, with a slope plot.
- For moderated mediation, conditional indirect effects and the index of moderated mediation.
- The bootstrap settings: number of subsamples, interval type and test type.
References
- Becker, J.-M., Ringle, C. M., & Sarstedt, M. (2018). Estimating moderating effects in PLS-SEM and PLSc-SEM: Interaction term generation × data treatment. Journal of Applied Structural Equation Modeling, 2(2), 1–21.
- Hayes, A. F. (2015). An index and test of linear moderated mediation. Multivariate Behavioral Research, 50(1), 1–22.
- Kenny, D. A. (2018). Moderation. Retrieved from davidakenny.net.
- 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.
- Zhao, X., Lynch, J. G., & Chen, Q. (2010). Reconsidering Baron and Kenny: Myths and truths about mediation analysis. Journal of Consumer Research, 37(2), 197–206.