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 (CaUnTs) 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 = (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

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 CaUnTs Aggress. FORMATS CaUnTs (F8.0) . 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 .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 CaUnTs.

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 Error/residual

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.

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.

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, 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 (k2) (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, κ2 = .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 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