Mediation analysis

A Causal inference with observational data method. But it can be used in combination with experiments. See also Instrumental variables estimation.

The basic idea is following (Baron1986moderator). When $X \rightarrow M \rightarrow Y$ , running a regression without $M$ will show $X$ is predictive of $Y$. However, if $M$ is the mediator and there is no direct connection from $X$ to $Y$, adding M to the model will remove the effect of $X$.

Imai2010general addresses the problem of the traditional approach and proposes an alternative. mediation is an R implementation.