What is the difference between mediation and moderation?

Mediation explains how X affects Y, through an intervening mediator on the path. Moderation explains when the X to Y effect is stronger or weaker, depending on a third variable. Mediation is about mechanism; moderation is about conditions.

What is full versus partial mediation?

Full (indirect-only) mediation means the indirect effect is significant and the direct effect is not, so the effect runs entirely through the mediator. Partial mediation means both are significant, so the effect is split between the direct route and the mediator.

Do I need to bootstrap the indirect effect?

Yes. The indirect effect is a product of two coefficients and its distribution is not symmetric, so you judge it with a bootstrap confidence interval rather than the significance of the two paths separately.

PLS-SEM METHOD

Mediation in PLS-SEM: how an effect works through a third variable

Mediation analysis asks whether a predictor affects an outcome indirectly, through an intervening mediator, rather than only directly. This page explains direct, indirect and total effects, how to classify mediation, a worked example, and the common pitfalls.

What a mediation analysis tests

Mediation splits the effect of a predictor X on an outcome Y into two routes. The direct effect is the path straight from X to Y. The indirect effect runs through a mediator M: X affects M, and M affects Y. The indirect effect is the product of those two paths (a times b), and the total effect is the direct plus the indirect effect.

Mediation answers how an effect comes about. If training improves performance partly because it raises motivation, then motivation is the mediator and the training-to-performance effect is partly indirect.

A worked example

Say X is training, M is motivation and Y is performance. The model estimates a = 0.50 (training to motivation) and b = 0.60 (motivation to performance), so the indirect effect is 0.50 times 0.60 = 0.30. The direct effect c’ is 0.10 and not significant, so the total effect is 0.30 plus 0.10 = 0.40.

Because the indirect effect is significant and the direct effect is not, this is full (indirect-only) mediation: training lifts performance almost entirely by raising motivation.

The indirect path a times b = 0.30 runs through the mediator; the direct path c’ = 0.10 is not significant. Total effect 0.40.

How to classify the result

First test the indirect effect (a times b) with bootstrapping. Then look at the direct effect to classify the type of mediation.

Indirect sig., direct n.s.: Full mediation (indirect-only). The effect of X on Y runs entirely through the mediator.
Indirect sig., direct sig.: Partial mediation (complementary or competitive). Part of the effect goes through M, part is direct.
Indirect n.s., direct sig.: No mediation (direct-only). X affects Y directly, not through M.
Indirect n.s., direct n.s.: No effect to explain. Neither route is significant.

Judge the indirect effect by a bootstrap confidence interval, not by the significance of a and b separately. The older Baron and Kenny causal steps are no longer recommended.

Key quantities

Direct effect

The path from X to Y that does not pass through the mediator (c prime).

Indirect effect

The effect routed through the mediator, the product a times b. With several mediators, each chain has its own specific indirect effect.

Total effect

The direct effect plus all indirect effects of X on Y.

VAF

Variance accounted for: the indirect effect divided by the total effect. It expresses how much of the total effect the mediator carries.

Running a mediation step by step

Specify the predictor, the mediator and the outcome, with paths X to M, M to Y and the direct X to Y.
Estimate the model to get the direct effect and the specific indirect effect (a times b).
Bootstrap to get a confidence interval for the indirect effect; it is significant if the interval excludes zero.
Classify the mediation from the significance of the indirect and direct effects.
Report the direct, indirect and total effects, and optionally the VAF.

Common pitfalls

Using the old Baron and Kenny causal-steps procedure or the Sobel test instead of bootstrapping the indirect effect. Bootstrapping is the current standard.
Calling partial mediation a weaker version of full mediation. They are different findings, not a ranking.
Testing a and b separately instead of the product a times b. Significance of both does not guarantee a significant indirect effect.
Claiming mediation from cross-sectional data as if it were causal. Mediation is a causal claim that the design has to support.

Mediation in OpenPLS

OpenPLS reports the direct effect, the specific indirect effect of every mediation chain, and the total effect for each relationship, right in the results. Add bootstrapping to get confidence intervals for the indirect effects and classify the mediation. Free and runs in the browser.

Test a mediation on your own model

Build X, M and Y in the visual editor, compute, and read the direct, indirect and total effects in one place. Free, no install.

Open OpenPLS What is PLS-SEM?

Frequently asked questions

What is the difference between mediation and moderation?: Mediation explains how X affects Y, through an intervening mediator on the path. Moderation explains when the X to Y effect is stronger or weaker, depending on a third variable. Mediation is about mechanism; moderation is about conditions.
What is full versus partial mediation?: Full (indirect-only) mediation means the indirect effect is significant and the direct effect is not, so the effect runs entirely through the mediator. Partial mediation means both are significant, so the effect is split between the direct route and the mediator.
Do I need to bootstrap the indirect effect?: Yes. The indirect effect is a product of two coefficients and its distribution is not symmetric, so you judge it with a bootstrap confidence interval rather than the significance of the two paths separately.