Hoorcollege Moderation and Mediation

# Summary and study notes

## Welke onderwerpen worden behandeld in het hoorcollege?

Moderation = the effect of predictor X1 on outcome Y is different for different level of a second predictor X2. This is the same as an interaction effect. There are two ways you can plot a moderation. The theoretical relation, where a second predictor influence the relationship between X and Y. And a statistical model, where three variables influence Y: the first predictor, the second predictor and the interaction effect.

Mediation = the effect of the independent variable on a dependent variable is explained by a third intermediate variable. There are two types of mediation: complete or partial mediation. When there is still a relationship between the two current variables (X and Y), there is partial mediation. When all the effect is through the intermediate variable (M), there is complete mediation.

## Welke onderwerpen worden besproken die niet worden behandeld in de literatuur?

In dit college worden geen andere onderwerpen besproken dit niet worden behandeld in de literatuur.

## Welke recente ontwikkelingen in het vakgebied worden besproken?

Er worden geen recente ontwikkelingen besproken.

## Welke opmerkingen worden er tijdens het college gedaan door de docent met betrekking tot het tentamen?

Er worden geen opmerkingen gedaan die betrekking hebben tot het tentamen.

## Welke vragen worden behandeld die gesteld kunnen worden op het tentamen?

Er worden geen tentamenvragen behandeld.

# Hoorcollege aantekeningen

Moderation and mediation

Multiple predictors in a regression model can have different types of relations with the outcome. Linear additive model = two predictors for each of them they have a linear relationship with the outcome variable and these effects add up.

Moderation = the effect of predictor X1 on outcome Y is different for different level of a second predictor X2. This is the same as an interaction effect. There are two ways you can plot a moderation. The theoretical relation, where a second predictor influence the relationship between X and Y. And a statistical model, where three variables influence Y: the first predictor, the second predictor and the interaction effect. From the statistical model it is not sure which variable is the moderator, you can see this clearly in the theoretical model. In the equation is there the intercept, the two main effects and the interaction effect (which is the product of the two variables).

In the analysis you do a hierarchical regression, whereby you have a model with just the main effects and a model where you include the interaction effect. When the interaction model is significant, there is a moderation effect. But further investigation of interaction is needed and called. You can do this with simple slope analysis = where you can look at the slope of the two different groups of the moderator. The scores are -1 SD and + 1 SD of the average. The steeper the slope, the larger the effect.

Inflated type I error = there is no effect in the population, but your analysis will say there is an effect. This error will be more likely when you do many tests and have many models.

How can you test for interaction?

• You can do it in SPSS: analyze – regression – linear – add 3 predictors (X1, X2, X1X2). Important: center the predictors before computing the product; this avoids multicollinearity = relation between variables. Center means subtract the average score for all the scores of the variables (X1 and X2). After that you create the interaction term.
• The second option is with PROCESS. Choose model 1 for moderation. Use options for centering and for getting syntax that gives you the ‘mean +/- 1 SD plots’.

Mediation = the effect of the independent variable on a dependent variable is explained by a third intermediate variable. There are two types of mediation: complete or partial mediation. When there is still a relationship between the two current variables (X and Y), there is partial mediation. When all the effect is through the intermediate variable (M), there is complete mediation. There is a special notation by mediation:

• c = total effect of X on Y.
• c’ = direct effect of X on Y.
• a*b = indirect effect of X through M on Y.

Baron and Kenny

A four-step method involving 3 regression models:

1. Is there a significant effect of X on Y? (c). Criticism on this step because a significant effect of X on Y (c) is not a requirement for mediation.
2. Is there a significant effect of X on M? (a)
3. Is there a significant effect of M on Y, controlled for X? (c’)
4. Is the effect of X on Y smaller when controlling for M?

Criticism on this theory is that the mediated effect (a*b) is not tested on significance. Instead they use ‘eyeballing’ to decide if c’ is smaller than c.

Sobel’s solution

Sobel defined a test for the indirect effect a*b. He tested the hypothesis a*b = 0 (no direct effect). A significant test results (p<.05) rejects this H0 and we conclude that the indirect effect is significant. However, it is based on the assumption that a*b is normally distributed but this is not correct and therefore not valid.

Current best practice

If you don’t know the shape of your sampling distribution, you can create it yourself by bootstrapping. Bootstrapping will be explained in the next seminar.

Output

In the output you get information about the total, direct and indirect effect. The total effect shows if there is a relation between X and Y. When the direct effect is significant, then there is partial mediation, because there is still an effect of c’. When the bootstrap interval for the indirect effect doesn’t include 0, then the effect is significant and there is a mediation effect.

multiple mediator model is a model with more mediators. Then you can have a total indirect effect a1*b1 + a2*b2 + a3 * b3 and you have an unique indirect effect of each mediator within the model a*b.

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