Serial Mediation (M1→M2)

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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 a CHAIN of mediators — X → M1 → M2 → Y — where the mediators influence each other in sequence.

Serial mediation estimates the sequential indirect path through ordered mediators, distinguishing it from parallel mediators that don't affect one another.

Worked example

Does training raise performance via knowledge and then confidence?

Training → knowledge → confidence → performance was tested as a serial mediation (5,000 bootstraps).

Result

The serial indirect path was significant (0.10, 95% CI [0.06, 0.14]) — training built knowledge, which built confidence, which raised performance.

How you'd report it (APA)

A serial mediation showed a significant chain training→knowledge→confidence→performance (0.10, 95% CI [0.06, 0.14]).

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

When to use it

  • The mediators are ordered in time or logic
    M1 plausibly causes M2. e.g. training → knowledge → confidence → performance.
  • You want the specific chained path
    The question is about the whole sequence, not each mediator on its own.

When NOT to — use instead

Hypotheses

H₀: the serial indirect effect a·d·b (X→M1→M2→Y) is zero — the ordered chain carries none of X's effect.
Hₐ: the serial indirect effect is non-zero. Supported when its bootstrap 95% CI excludes 0; the specific-chain estimate is what distinguishes serial from parallel mediation.

Parameter tested: the product of the chained paths (e.g. a·d·b for a two-mediator chain), with a percentile bootstrap CI

Assumptions (and what to do if they fail)

Defensible ordering of the mediatorshigh

Check: The M1 → M2 direction must come from design or theory, not from which fits better.

If violated: Swapping M1 and M2 gives a different, equally-fitting chain; the finding is then arbitrary.

No unmeasured confounding along the chainhigh

Check: Each link (X→M1, M1→M2, M2→Y) needs no common cause left out.

If violated: Any confounded link biases the whole product a·d·b.

Adequate sample for a long pathmedium

Check: Chained products have wide sampling variation; small n gives a very wide CI.

If violated: The chain may be real but undetectable. Increase n or reduce the number of links.

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