Mediation

Trying to understand mediation, and mediation vs. confounding

1 Mediation

The basic idea is that if we are regressing \(y\) on variable of interest \(x\), and (not shown) control variable(s) \(z\), if we introduce mediator \(m\), the \(\beta_{xy}\) coefficient should change. Additionally, \(\beta_{xm} \times \beta_{my}\) should be statistically significant.¹

mediation

2 Mediation vs. Correlated Predictors

As far as I know, all of the relationships detailed below would result in similar patterns of correlations. As far as I know there would be no empirical way to distinguish between these relationships. Only theory, or knowledge of prior relationships could be used to distinguish between these possible explanations for correlated \(x\), \(m\) and \(y\).

mediation and correlation

Footnotes

1. The statistical significance of this quantity may need to be calculated with bootstrapping.