Commentary: Causal Effects in Mediation Modeling: An Introduction with Applications to Latent Variables

Causal mediation1 is an increasingly popular analysis, as recently described by Muthén and Asparouhov (2015, M&A)2. We suggest a simplified notation for causal mediation effects, iT/iP=BK and dT/dP, provide a graphical view of potential outcomes (PO) and expand the M&A approach by using VanderWeele’s (2014) mediation decomposition. An intuitive way to label and see causal in/direct effects is to directly display POs, as in Figure 1 below. POs are values that could be observed, but have not been realized (yet). They reveal themselves partially once nature or researchers assign people to specific experimental conditions, or when people make choices. POs are useful in defining causal total effects (TE), as differences between the same individual’s (i) two POs, Yi1 – Yi0, had the person been treated (subscript 1), and alternatively (but simultaneously) not treated (0); evidently, in our reality one of these has to be “contrary-to-fact” (CF). The indirect effect of X on Y through a mediator M is the part of the total effect that “flows through” M, or the contribution of the path X->M->Y to the observed association between X and Y, which is an open path because causal association flows through it (Elwert, 2013). The key problem in intuitively grasping causal in/direct effects is the “nesting” of the POs due to the double role of the mediator as a cause and an effect3: the PO “Y if X was set to x,” or Yx, can be combined with “Y if M was set to m,” or Ym (we suggest using a superscript for scenarios involving M). So ∗YM0 1 , for example, labeled Y(1, M(0)) in M&A, is the PO of the outcome Y if a person was treated (1), but his/her mediator took on the value had s/he would belonged to the opposite (control) condition (M0). This PO is clearly contrary-to-fact (CF), never observable, a “cross-worlds” quantity (Lok, 2016), hence our ∗ sign. Y0 and Y 1 1 are in principle realizable, only one of them at a time for the same person, however.