Lecture 2: Moderation & Mediation (ARMS, Utrecht University)

Moderation analysis

Moderation: the effect of predictor X₁ on outcome Y is different for different levels of a second predictor X₂. For example when X₂ is gender: the effect of X₁ on Y is different for males and females. 

The conceptual model for this example is:

The statistical model for this example is:

If you use 10 models in your analysis, you have an inflated type 1 error. This is because the error ‘kind of’ adds up (not literally) with every model you use.

When you’ve established a significant interaction effect, further investigation is needed. This can be done through a simple slope analysis: are the slopes of the relation of one predictor with the outcome different for different levels of the other predictor?

Reading a plot of a simple slope: high means one SD above the average, low means one SD below the average.

How to test for interactions?

1. Through SPSS: analyse > regression > linear. Add 3 predictors:

- X₁, X₂ and X₁X₂

--> Important! Center the predictors before computing the products. This avoids multicollinearity.

2. Use PROCESS. Choose model number 1 for moderation. Use options for centering and for getting syntax that gives you the ‘mean 1 SD plots’.

Mediation analysis

Mediation: the effect of the independent variable on a dependent variable is explained by a third intermediate variable.

Complete mediation: the effect is fully explained by a third intermediate variable.

Partial mediation: the effect is partly explained by a third intermediate variable

This is the model for mediation:

• c is the total effect (of x on y)
• c’ is the direct effect (of x on y)
• a*b is the indirect effect (of x through m on y)

Old methods for mediation (statistical methods):

• Baron and Kenny: used a four step method involving 3 regression models:

1. Is there a significant effect of X on Y?

2. is there a significant effect of X on M?

3. is there a significant effect of M on Y, controlled for X?

Then you see if 1 and 2&3 differ. If yes, M has an effect. Criticism: it is just eyeballing to see if c has become smaller.

• Sobel: assumes H₀: a*b=0 (no indirect effect). A significant test result rejects this and we can conclude that the indirect effect is significant. Criticism: it is based on the assumption that a*b is normally distributed, but this is not correct.

Current best practice: bootstrapping. This method you can use when you don’t know the sampling distribution. We use the output to understand how we interpret the bootstrap values:

The null hypothesis is still a*b=0, because we want to test whether it is significantly non-zero. To see if the effect is significant, you look at the bootstrap interval: BootLLCI (the lower) and the BootULCI (the upper). If 0 does not lay in the entire interval, the effect is significant.

In a multiple mediator model, multiple mediators have an effect on Y.

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