# Fundamental query on mediation and indirect effect

Am trying to understand the basics of mediation and am confused between an actual indirect effect and mediation effect.

My query is what if A causes B and B causes C, but there is no direct effect between A and C? It is obviously not mediation given that there is no direct effect of A on C (I would like to call this an indirect effect). I have seen people representing mediation in the same manner as this indirect effect. My query is, isnt this wrong given how A to C need not be true in an indirect effect but has to be true in a mediation?

Secondly, I read on another thread that if A affects B and B affects C, then mediation need not be tested, its assumed. My point is shouldn't it be necessary for A to affect C? Given that direct effect is the first step in the process?

• Welcome to the site. which book or thteads you are you reading ? – Subhash C. Davar Jun 18 '17 at 9:50
• When you say "No direct effect between A and C" do you mean that there is no relationship, or no effect when you control for B? – Jeremy Miles Jun 19 '17 at 17:50
• Hi Subhash, am reading Kenny's guide on moderation/mediation. – Rohit Jun 27 '17 at 12:20
• Hi Jeremy, Yes, I mean there is no significance for the total effect of A and C when I just test the two of them in the equation. – Rohit Jun 27 '17 at 12:21

## 1 Answer

Barron and Kenny assumptions are the following

• a change in levels of the exposure variable significantly affects the changes in the mediator (i.e., Path from $A$ to $B$);
• there is a significant relationship between the mediator and the outcome (i.e., Path from $B$ to $C$);
• a change in levels of the exposure variable significantly affects the changes in the outcome (i.e., total effect of $A$ on $C$ is significant);
• when the previously defined paths are controlled, a previously significant relation between the exposure and outcome is no longer significant, with the strongest demonstration of mediation occurring when the path from the independent variable to the outcome variable is zero.

Here $A$ is your treatment, $B$ is your mediator, and $C$ is the outcome.

what if A causes B and B causes C, but there is no direct effect between A and C?

Since there is no significance for the total effect of $A$ on $C$, assumption 3 fails.However, recent developments in science suggest that assumption 3 is not needed.

Consensus is that the relationship between $A$ and $C$ need not be statistically significant for $B$ to be a mediator. The reason is that the effect of $A$ on $C$ may not be significant when direct and mediated effects have opposite sign.

It is obviously not mediation given that there is no direct effect of A on C (I would like to call this an indirect effect).

It is unclear why would you deviate from the traditional definition. Different definitions exist for different approaches, but all of them agree that indirect effect is associated with mediator.

Secondly, I read on another thread that if A affects B and B affects C, then mediation need not be tested, its assumed.

Again, this approach contradicts the assumptions 3 and 4. The scientific consensus is that those assumptions are too harsh and points have been made on how to relax those. I suggest reading the following for more up to date information about mediation(the last article contains an excellent summary of Barron and Kenny vs new approaches):

MacKinnon, D. P. (2008). Introduction to statistical mediation analysis. New York, NY: Erlbaum.

Pearl, J. (2001). Direct and indirect effects. In J. Breese & D. Koller (Eds.), Proceedings of the seventeenth conference on uncertainty in artificial intelligence (pp. 411–420). San Francisco, CA: Morgan Kaufmann.

Valeri, L., & VanderWeele, T. J. (2013). Mediation analysis allowing for exposure–mediator interactions and causal interpretation: Theoretical assumptions and implementation with SAS and SPSS macros. Psychological Methods, 18(2), 137-150.

Also, here is a good discussion on whether Barron and Kenny's method is outdated.