Mediation analysis with intermediate confounding: structural equation modeling viewed through the causal inference lens.
Bottom Line: By giving model-free definitions of direct and indirect effects and clear assumptions for their identification, the latter school has formalized notions intuitively developed in the former and has greatly increased the flexibility of the models involved.However, through its predominant focus on nonparametric identification, the causal inference approach to effect decomposition via natural effects is limited to settings that exclude intermediate confounders.Such confounders are naturally dealt with (albeit with the caveats of informality and modeling inflexibility) in the SEM framework.
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Mentions: As we stated above, there is an interesting difference with regard to the identifying assumptions invoked by the 2 approaches when the model involves intermediate confounders. Under the SEM, all of the error terms are assumed to be uncorrelated with each other, a scenario which would not be satisfied were the L-Y relationship affected by unmeasured confounding, given C and X (represented by U in Figure 3). This is not a restriction invoked by the causal inference framework (as it concerns only confounding of X-Y, X-M, and M-Y).Figure 3.