6.5 Moderators

The effect of \(X\) on \(Y\) is moderated by \(Z\) if the effect is different depending on the value of \(Z\).

\[X \rightarrow Y \leftarrow Z\]

A causal diagram may be consistent with many different DGPs

\[Y = 0.2X + 0.3Z\]

• multiple linear regression

\[Y = 1.5X + 5Z + 3XZ\]

• linear regression with an interaction term

\[Y = 2X + 3XZ\]

• \(Z\) has no direct effect on \(Y\), but does moderate the effect of \(X\).