Among the three variables of executive function (EF), language (L), and hemodynamic response (HDR), what are their causal relationships? Suppose the underlying structure is
L \rightarrow HDR, EF \rightarrow HDR, EF \rightarrow L
Under this assumption, I suggest the following strategy:
- When examining the association between L and HDR, include EF as a covariate, since EF is a common cause of both.
- When examining the association between EF and HDR, do not include L as a covariate, because L lies on the causal pathway from EF to HDR and adjusting for it would block part of the effect of interest.
A more general discussion of covariate selection and its causal implications is provided in this blog post.
Gang Chen