1. Moderation: Introduction
David A. Kenny

2. What Is Moderation
The causal relationship from a causal variable or X to an outcome or Y changes as a function of a moderator or M.
X and M interact to cause Y.
Effect of stress on mood is moderated by gender.

4. Causation and Correlation
Need to know causal direction of the X to Y relationship.
If X is a manipulated variable, there should be no relationship between X and M.
Unlike mediation, there is no reason why necessarily X and M should be correlated.

5. Timing of Measurement
Typically M is measured before or at the same time as X.
Will discuss whether a moderator can be caused by X when we discuss Assumptions.

6. Statistical Estimation
Typically estimated as the interaction between X and M
Y = aX + bM + cXM + E
a = “main effect” of X
b = “main effect” of M
c = interaction between X and M
Important to include both X and M in the model.
Will discuss the Interpretation in another webinar.

7. Linearity
Using an product term implies a linear relationship between M and X to Y relationship.
The effect of X on Y changes by a constant amount as M increases or decreases
For example: the effect of Stress on Marital Satisfaction changes by the same amount for every year married.

8. Statistical Estimation
What was described has been called moderated regression analysis.
One equation
Moderation as an interaction
Problematic alternatives
Separate slopes
Difference in correlations
Median split

9. Separate Slopes? M is categorical.
Slope computed for each group in separate analyses.
Difficult to test for moderation and less power.
Is the correct analysis when there are heterogeneous errors.

10. Separate Correlations?
Categorical moderator.
Compute the correlation between X and Y to determine moderation within each category.
Problem: Differences in X variance.
If men have more variance on X than women, then women would likely have a weaker correlation (restriction in range).

11. Median Split? M is measured at the interval level of measurement.
A questionable way to measure and test for moderation is to split M at the mediation and compute slopes for X to Y above and below the split value.
Big loss in power (see Aiken & West).

12. Flipping X and M
Because XM is an interaction, it can be interpreted as the effect of X depends on M or the that the effect of M depends on X.
Either a different discipline or a rethinking might lead to treating X as the moderator instead of M.
Sometimes this is a useful exercise.

13. Diagrams of Moderation

14. .5 .7

15. Key Resource
Aiken, L. S., & West, S. G. (1991). Multiple regression: Testing and interpreting interactions. Newbury Park, CA: Sage.

16. Additional Webinars Interpretation Assumptions Effect Size and Power
ModText