Direct & Indirect Effects

Controlled and natural direct effects, the indirect effect, and the bias from an unmeasured mediator–outcome confounder.

Day 58: Mediation: Direct & Indirect Effects

CDE(m)NDE = CDE at E[M|X=0]total effect

β0: mediator level, untreated1β1: X → M0.5θ1: X → Y direct1θ2: M → Y2θ3: X × M interaction0.5

g: U → M0c: U → Y0

NDE

1.50

estimated 1.50

NIE

1.25

estimated 1.25

2.75

mediated 45%

M = β0 + β1·X + g·U + e_M and Y = θ1·X + θ2·M + θ3·X·M + c·U + e_Y. The controlled direct effect CDE(m) = θ1 + θ3·m varies with the mediator level (line); NDE and NIE come from the mediation formula. With an unmeasured mediator–outcome confounder U (g, c ≠ 0), estimates from the regression of Y on X, M and X·M (dashed) are biased.

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