Moderation and Mediation

• Moderation


  Interactions in the Linear Model
• Moderation


  1. Predictor variable

  2. Moderator variable

  3. Interaction effect

  
• Moderator variable


  A variable that affects the relationship between two others
• A significant interaction effect does not justify making a causal assumption, it merely shows that the two variables have a combined effect on the outcome
• Statistical model for moderation

  Y = a + b1x1 + b2x2 + b3x1x2

  
• Centering variables


  Transforming a variable into deviations around a fixed point (e.g. grand mean)
• Centering has no effect on the b for the highest-order predictor, but will affect the bs for the lower-order predictors
• Centering is important when the model contains an interaction term, as it makes the bs for lower-order effects easier to interpret when the higher-order interaction is significant
• Simple slopes analysis


  Working out the model equations for the predictor and outcome at low, high, and average levels of the moderator
• Moderation is shown by a significant interaction effect
• Simple slopes analysis interprets the nature of the moderation effect
• The Johnson-Neyman method identifies the range of the moderator where the predictor-outcome relationship is significant

  
• Mediation


  The relationship between a predictor variable and an outcome variable can be explained by their relationship to a third variable (a mediator)
• Direct effect


  Effect of X on Y
• Indirect effect


  Effect of X on Y through M
• Total effect


  Direct effect + Indirect effect
• Statistical model for mediation

  1. Linear model predicting outcome from predictor

  2. Linear model predicting mediator from predictor

  3. Linear model predicting outcome from predictor and mediator
• The 4 conditions for mediation are: 1) predictor must predict outcome, 2) predictor must predict mediator, 3) mediator must predict outcome, 4) predictor must predict outcome less strongly when mediator is included
• The Sobel test estimates the significance of the indirect effect
• Index of mediation


  Useful for comparing mediation models with different measures
• Proportion mediated (PM)


  Ratio of indirect effect to total effect
• Reporting mediation analysis should include the indirect effect with confidence interval, and the proportion mediated