Causal Analysis in Theory and Practice

Our attention was called to a new attack on graphical models and structural equation models (SEM), this time in the name of “correctness”..

The article in question is: Cloak and DAG: A response to the comments on our comment by Martin A. Lindquist and Michael E. Sobel (L&S) Forthcoming , NeuroImage http://www.sciencedirect.com/science/article/pii/S1053811911013085

The advice that L&S give to NeuroImaging researchers reads as follows:

“For if fMRI researchers continue to use their “familiar approach”, drawing diagrams and fitting SEMs without realizing the assumptions they are making, many of the causal inferences thereby generated will be incorrect, and the development and use of alternative ways of studying effective connectivity will be stifled.”

L&S’s warning of the importance of scrutinizing assumptions is admirable. Yet readers of NeuroImage will have difficulty understanding why they are judged incapable of scrutinizing causal assumptions in the one language that makes these assumptions transparent, i.e., diagrams or SEM, and why they are threatened with “incorrect inferences” for not rushing to translate meaningful assumptions into a language where they can no longer be recognized, let alone justified.

For a simple example, …

Click here for the full post.

The following paradox was brought to our attention by Pablo Lardelli from Granada (Spain).

Pablo writes:

1. Imagine that you design a cohort study to assess the causal effect of X on Y, E[Y|do(X=x)]. Prior knowledge informs you that variable M is a possible confounder of the process X—>Y, which leads you to assume X<---M--->Y.

To adjust for the effect of this confounder, you decide to design a matched cohort study, matching on M non exposed to exposed. You know that matching breaks down the association between X and M in the sample.
[……]
The problem arises when you draw the DAG […] and realize that S is a collider on the path X—>S<---M and, since we are conditioning on S (because the study sample is restricted to S=1) we are in fact opening a non causal path between X and Y (through M) in the sample. But this stands in contradiction to everything we are told by our textbooks. Click here for full discussion of matching in DAGs, persistent-unfiathfulness and unit-to-unit interactions.