- Slides: 38
Moderation and Mediation Prof. Andy Field
Aims • Conceptual and statistical basis of moderation and mediation analysis • PROCESS • Interpretation of analysis results
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?
Example • Do violent video games make people antisocial? • Participants – 442 youths • Outcome – Aggression, – Callous unemotional traits (Ca. Un. Ts) – Number of hours spent playing video games per week
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.
The Statistical Moderation Model Error/residual Yi = (b 0 + b 1 Ai + b 2 Bi + b 3 ABi) + i Yi = (b 0 + b 1 Gamingi + b 2 Callousi + b 3 Interactioni) + i
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)
PROCESS (Hayes, 2013) • • • SPSS custom dialog Moderation analysis Mediation analysis Conditional-process analysis Download Install
Output from moderation analysis
Output from moderation analysis II
Output from moderation analysis III
Following up Moderation with Simple Slopes analysis I
Following up Moderation with Simple Slopes analysis II DATA LIST FREE/Vid_Game Ca. Un. Ts Aggress. FORMATS Ca. Un. Ts (F 8. 0). BEGIN DATA. -6. 9622 -9. 6177 33. 2879. 0000 -9. 6177 32. 6568 6. 9622 -9. 6177 32. 0256 -6. 9622. 0000 38. 7861. 0000 39. 9671 6. 9622. 0000 41. 1481 -6. 9622 9. 6177 44. 2844. 0000 9. 6177 47. 2774 6. 9622 9. 6177 50. 2705 END DATA. GRAPH/SCATTERPLOT=Vid_Game WITH Aggress BY Ca. Un. Ts.
different slopes for different folks
different slopes for different folks
Reporting moderation analysis
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?
The Statistical Model Error/residual
Baron and Kenny (1986) • Mediation is tested through three regression models: 1. Predicting the outcome from the predictor variable. 2. Predicting the mediator from the predictor variable. 3. Predicting the outcome from both the predictor variable and the mediator.
Baron and Kenny (1986) • Four conditions of mediation: 1. The predictor must significantly predict the outcome variable (Model 1). 2. The predictor must significantly predict the mediator (Model 2). 3. The mediator must significantly predict the outcome variable (Model 3). 4. The predictor variable must predict the outcome variable less strongly in Model 3 than in Model 1.
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 pvalues encourage. • Zhao, X. , Lynch, J. G. & Chen, O. (2010). Reconsidering Baron and Kenny: myths and truths about mediation analysis. Journal Of Consumer Research, 37, 197 -206.
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
Effect Sizes of Mediation
Effect Sizes of Mediation II
Effect Sizes of Mediation III Kappa-squared (k 2) (Preacher & Kelley, 2011)
Example of a Mediation Model Error/residual
Running the Analysis
Output from Mediation Analysis
Output from Mediation Analysis II
Output from Mediation Analysis III
Output from Mediation Analysis IV
Output from Mediation Analysis – Results of Sobel test
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, κ 2 =. 041, 95% BCa CI [. 008, . 104].
Reporting Mediation Analysis
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
Conclusion (2) • Moderation analysis – Conceptual model versus statistical model – Effects: predictor, 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, other