Identification of Causal Parameters in Randomized Studies With Mediating Variables

Treatments in randomized studies are often targeted to key mediating variables. Researchers want to know if the treatment is effective and how the mediators affect the outcome. The data are often analyzed using structural equation models (SEMs), and model coefficients are interpreted as effects. However, only assignment to treatment groups is randomized, so mediators are self-selected treatments. Thus, the so-called direct effects of mediators on later outcomes do not usually warrant a causal interpretation. Holland (1988) studied the case of a single continuous mediator, criticizing the use of SEMs. He uses treatment assignment as an instrument for the effect of the mediator on the outcome. However, the assumptions he made to justify this approach are overly strong and substantively implausible. This article (a) makes explicit the assumptions needed to justify equating the parameters of SEMs with the effects of mediators, (b) provides weaker and more plausible conditions under which the instrumental variable estimand may be interpreted as an effect, and (c) extends the analysis to include the case of noncompliance.

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