Moderated Mediation

Verified

Mediation (legacy hub)

Independently verified. Every statistic this test reports has been re-derived against an independent reference — never the library the pipeline itself calls — the rendered output was read back in a browser, and the result is locked with a committed regression suite.

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Tests whether an indirect (mediation) effect DEPENDS on a moderator — moderated mediation, i.e. conditional indirect effects.

Moderated mediation estimates how the strength of an X→M→Y indirect effect changes across levels of a moderator, via an index of moderated mediation with a bootstrap CI.

Worked example

Is the mediation stronger for one group than another?

The X→M→Y indirect effect was estimated at low and high moderator levels (index of moderated mediation, 5,000 bootstraps).

Result

The indirect effect was significant at high moderator levels (0.20) but near zero at low (0.02); index = 0.09, 95% CI [0.04, 0.15].

How you'd report it (APA)

Moderated mediation was supported (index = 0.09, 95% CI [0.04, 0.15]); the indirect effect held only at high moderator levels.

Try it yourself: Load this ready-made sample and follow the run above.

When to use it

  • You expect the mechanism to be conditional
    The X→M→Y path is stronger for some people than others. e.g. mediation that holds for high-support but not low-support groups.
  • You want the formal test, not two subgroup runs
    The index of moderated mediation tests the difference directly, rather than eyeballing separate CIs.

When NOT to — use instead

  • The moderator acts on a single path, not the indirect effect
    If you only care whether one path (say X→M) is moderated, a simpler conditional-process model may suffice. → Simple mediation
  • No mediator at all
    A plain interaction on the outcome is moderation, not moderated mediation. → Moderation (2-way)

Hypotheses

H₀: the index of moderated mediation is zero — the indirect effect a·b does not change across levels of the moderator.
Hₐ: the index is non-zero — the conditional indirect effect differs by moderator level. Supported when the index's bootstrap 95% CI excludes 0.

Parameter tested: the index of moderated mediation (how much a·b changes per unit of the moderator), plus conditional indirect effects at chosen moderator values

Assumptions (and what to do if they fail)

All the mediation assumptions still holdhigh

Check: Causal order and no-unmeasured-confounding apply here too — moderation adds to them, it does not replace them.

If violated: A conditional indirect effect built on a biased indirect effect is still biased.

The moderator is measured wellmedium

Check: Interaction terms are sensitive to measurement error in the moderator.

If violated: The index is attenuated; a real conditional effect can be missed.

Enough spread and n at each moderator levelmedium

Check: Conditional effects far out on the moderator rest on fewer cases.

If violated: Conditional-effect CIs at extreme moderator values become unstable.

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