Mediation (statistics) - Regression Equations For Moderated Mediation and Mediated Moderation

Regression Equations For Moderated Mediation and Mediated Moderation

Muller, Judd, and Yzerbyt (2005) outline three fundamental models that underlie both moderated mediation and mediated moderation. Mo represents the moderator variable(s), Me represents the mediator variable(s), and ε_i represents the measurement error of each regression equation.

Step 1: Moderation of the relationship between the independent variable (X) and the dependent variable (Y), also called the overall treatment effect (path C in the diagram).

• To establish overall moderation, the β₄₃ regression weight must be significant (first step for establishing mediated moderation).
• Establishing moderated mediation requires that there be no moderation effect, so the β₄₃ regression weight must not be significant.

Step 2: Moderation of the relationship between the independent variable and the mediator (path A).

• If the β₅₃ regression weight is significant, the moderator affects the relationship between the IV and the mediator.

Step 3: Moderation of both the relationship between the independent and dependent variables (path A) and the relationship between the mediator and the dependent variable (path B).

• If both β₅₃ in step 2 and β₆₄ in step 3 are significant, the moderator affects the relationship between the independent variable and the mediator (path A).
• If both β₅₁ in step 2 and β₆₅ in step 3 are significant, the moderator affects the relationship between the mediator and the dependent variable (path B).
• Either or both of the conditions above may be true.