RCCP states that if X and Y are statistically dependent, then there exists Z causally influencing both. I've heard a variation of RCCP that states that if X and Y are statistically dependent, one of the following scenarios is possible
- Z = X
- Z = Y
- Z is a confounder that is different from X and Y (Z ≠ Y, Z ≠ X), but causes both X and Y
I think that even Bernhard Schölkopf presented RCCP in this manner.
My question is
Given that X and Y are statistically dependent and Z influences both, Z ≠ Y, Z ≠ X, can we say that Z is a confounder? In other words, are the 2 RCCP formulations written above equivalent?
If A->B->X and A->Y, is A a confounder? (note that A doesn't directly cause X because of mediator B)
In the case above, what can allow us to define the combination of A and B with Z and state that Z is, indeed, the confounder?