1. Moderation and Mediation
Prof. Andy Field

2. Aims
Conceptual and statistical basis of moderation and mediation analysis
PROCESS
Interpretation of analysis results

3. Moderation
The combined effect of two variables on another is known conceptually as moderation, and in statistical terms as an interaction effect.
When/under which conditions does a particular effect occur?

4. Example Do violent video games make people antisocial? Participants
442 youths
Outcome
Aggression,
Callous unemotional traits (CaUnTs)
Number of hours spent playing video games per week

5. Conceptual moderation model
If callous-unemotional traits were a moderator then we’re saying that the strength or direction of the relationship between game playing and aggression is affected by callous-unemotional traits.

8. The Statistical Moderation Model
Error/residual
Yi = (b0 + b1Ai + b2Bi + b3ABi) + i
𝒀 𝒊 = 𝒃 𝟎 + 𝒃 𝟐 𝑩 𝒊 + 𝒃 𝟏 + 𝒃 𝟑 𝑩 𝒊 𝑨 𝒊 +  𝒊
Yi = (b0 + b1Gamingi + b2Callousi + b3Interactioni) + i

9. Centering predictor and moderator variables
Centering: the process of transforming a variable into deviations around a fixed point.
The interaction term makes the bs for the main predictors uninterpretable in many situations. E.g. better interpretation of b-value if predictor value of 0 in not meaningful
For this reason, it is common to transform the predictors using mean-centering.
‘Truths and myths about mean-centering’ (Hayes, 2013)

10. PROCESS (Hayes, 2013) SPSS custom dialog Moderation analysis
Mediation analysis
Conditional-process analysis
Download
Install

11. Output from moderation analysis

12. Output from moderation analysis II

13. Output from moderation analysis III

14. Following up Moderation with Simple Slopes analysis I

15. Following up Moderation with Simple Slopes analysis II
DATA LIST FREE/Vid_Game CaUnTs Aggress.
FORMATS CaUnTs (F8.0) .
BEGIN DATA.
END DATA.
GRAPH/SCATTERPLOT=Vid_Game WITH Aggress BY CaUnTs.

16. different slopes for different folks

17. different slopes for different folks

18. Reporting moderation analysis

19. Mediation
Refers to a situation when the relationship between a predictor variable and outcome variable can be explained by their relationship to a third variable (the mediator).
How/why does a particular effect occur?

20. The Statistical Model
Error/residual
Error/residual

21. Baron and Kenny (1986)
Mediation is tested through three regression models:
Predicting the outcome from the predictor variable.
Predicting the mediator from the predictor variable.
Predicting the outcome from both the predictor variable and the mediator.

22. Baron and Kenny (1986) Four conditions of mediation:
The predictor must significantly predict the outcome variable (Model 1).
The predictor must significantly predict the mediator (Model 2).
The mediator must significantly predict the outcome variable (Model 3).
The predictor variable must predict the outcome variable less strongly in Model 3 than in Model 1.

23. Limitations of Baron and Kenny’s (1986) Approach
How much of a reduction in the relationship between the predictor and outcome is necessary to infer mediation?
People tend to look for a change in significance, which can lead to the ‘all or nothing’ thinking that p-values encourage.
Zhao, X., Lynch, J.G. & Chen, O. (2010). Reconsidering Baron and Kenny: myths and truths about mediation analysis. Journal Of Consumer Research, 37,

24. Sobel Test (Sobel, 1982)
An alternative is to estimate the indirect effect and its significance using the Sobel test (Sobel, 1982)
If the Sobel test is significant, there is significant mediation
Sobel test assumes normality of indirect effect
Assumption is deemed unrealistic
“Sobel’s not noble” (Zhao et al., 2010, p. 202)
Use bootstrapped confidence intervals instead

25. Effect Sizes of Mediation

26. Effect Sizes of Mediation II

27. Effect Sizes of Mediation III Kappa-squared (k2) (Preacher & Kelley, 2011)

28. Example of a Mediation Model
Error/residual

29. Running the Analysis

30. Output from Mediation Analysis

31. Output from Mediation Analysis II

32. Output from Mediation Analysis III

33. Output from Mediation Analysis IV

34. Output from Mediation Analysis – Results of Sobel test

35. Reporting Mediation Analysis
There was a significant indirect effect of pornography consumption on infidelity through relationship commitment, b = 0.127, 95% BCa CI [0.023, 0.335]. This represents a relatively small effect, κ2 = .041, 95% BCa CI [.008, .104].

36. Reporting Mediation Analysis

37. Conclusion
Moderation analysis: under which conditions does a particular effect occur? Causal condition
Mediation analysis: how/why does a particular effect occur? Causal process
PROCESS: conditional-process analysis

38. Conclusion (2) Moderation analysis Mediation analysis
Conceptual model versus statistical model
Effects: predictor, moderator, moderated effect of predictor
Follow-up: simple slopes, regression of significance
Mediation analysis
Statistical model = conceptual model
Effects: predictor -> mediator; mediator -> outcome; predictor -> outcome: direct and indirect/mediated
Effect sizes (mediation): unstandardized, standardized, other