OT: Mediation vs Confounding

[Bruce Weaver]

Another current thread that mentions mediation analysis (http://spssx-discussion.1045642.n5.nabble.com/Effect-size-Multiple-Mediation-Macro-Preacher-HAyes-tp5729821.html) has prompted me to jot down some of my (current) thoughts on mediation vs confounding.  Perhaps they will stimulate some discussion.

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I know that nowadays, mediation analyses abound in psychology and related fields.  As far as I can tell, the only difference between a mediator of the relationship between X and Y and a confounder is that the mediator is presumed to be on a causal pathway between X and Y, whereas the confounder is not.  Maybe I'm just suspicious by nature, but I fear that many people using mediation analysis do not know this about mediators and confounders, and that their 'logic' goes something like this:

"If the coefficient for X changes when I include Z in the model, then Z must be a mediator."

There is a major problem with that 'logic', as I see it.  Specifically, I think it is an example of "affirming the consequent" (https://en.wikipedia.org/wiki/Affirming_the_consequent).  In other words, I think the correct premises are as follows:

1. If Z is a mediator, then the coefficient for X will change when Z is included in the model.
2. If Z is a confounder, then the coefficient for X will change when Z is include in the model.

If these are indeed the correct premises, one could validly argue that if the coefficient for X does NOT change when Z is included in the model, then Z is neither a mediator nor a confounder.  If the coefficient DOES change, we still don't know if Z is a mediator or a confounder.  Some other (hopefully fairly convincing) evidence would be needed to support the claim that Z is on a causal pathway between X and Y.  

Another thing I find interesting about this topic is that in the past, the conventional advice from the world of biostatistics has been that one should not perform a statistical test for confounding--it was more a case of eye-balling the change in the coefficient, and deciding whether it was clinically significant.  But I gather that the mediation analysis folks in psychology do perform statistical tests of mediation.  

For anyone who is interested, Mike Babyak has nice article on this topic in EBMH.  

Babyak, M. A. (2009). Understanding confounding and mediation. Evidence Based Mental Health, 12(3), 68-71.
http://ebmh.bmj.com/content/12/3/68.short

Cheers,
Bruce