13.1 Mediation: Intro

We start with an overview of the concept of mediation, with special consideration to its interpretation for the time being.

13.1.1 Introduction to mediation

Mediation refers to a specific model where we hypothesise that the relationship between a predictor X and an outcome Y is explained by the effect of a third mediating variable. You can imagine a simple linear regression in the following way, with c representing the direct effect (or the regression coefficient) between the predictor and the outcome.

But what happens if we believe that there actually isn’t as direct of a relationship? In other words, we believe that our predictor X actually predicts/affects Y through a mediating variable, M? That might look like the following:

In other words, mediation occurs when the effect of X on Y is explained through the effect of M. When paired with clever and careful study designs, mediations can be used to test causality. The underlying principle of the diagram above is that X causes M, and M causes Y; i.e. we implicitly specify directional relationships between our predictor, mediator and outcome.

13.1.2 In mathematical terms

The basic idea of mediation is that the total direct effect, c, should reduce once the mediator is accounted for. This new direct effect is denoted as c’ (c-prime). If a mediating effect is significant, then c’ should be smaller than c; after all, if the mediator explains what is going on then this should explain the direct effect between the predictor and outcome.

The a and b paths denote the relationship between the predictor and mediator (a), and the mediator and the outcome (b). Together, they denote the indirect effect of the mediator, which we denote as ab - literally, the product of the two coefficients.

What is the relationship between the direct and indirect effect? Well, if the original effect c is the total effect, we can decompose this as:

Total effect = direct effect (c’) + indirect effect (ab)

Without a mediator, the indirect effect ab is equal to zero, and so we only have a direct effect. However, if the indirect effect fully explains the relationship between the predictor and the outcome then we would expect the direct effect (c’) to be close to 0, and the indirect effect to fully explain/comprise the total effect.