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I have a question regarding mediation analysis. I'm wondering why oftentime the fraction of the total effect which corresponds to the indirect effect, i.e. 1 - NDE/TE, is different from the natural indirect effect, i.e. NIE/TE. In Pearl's "Primer" book (p121), NIE/TE is considered as the "portion of the effect that can be explained by mediation alone". But isn't it also what 1 - NDE/TE is meant to capture ?

In the Training/Homework/Success example ("Primer" p123-124), NIE/TE=7% whereas 1-NDE/TE=30.4%. According to the formulas, I would have considered NIE as the intrinsic effect of the mediator M on the oputcome Y independently of treatment T (Y0M1 - Y0M0), whereas 1 - NDE/TE would be the effect of treatment T transmitted to Y through M fixed ((1 - (Y1M0 - Y0M0))?

Another way to phrase it would be : is the effect of M on Y only originates from T (M acts as an intermediate transmitter of T to Y) or is M allowed to have its own intrincic effect on Y ? I'm stille confused about it.

Thank you for your response.

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    $\begingroup$ Please spell out the acronyms, thank you. $\endgroup$ Commented Apr 29, 2023 at 15:24
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    $\begingroup$ Sorry ! TE=total effect, NDE=natural direct effect, NIE=natural indirect effect $\endgroup$ Commented Apr 29, 2023 at 20:17

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