Mediation & Moderation

Question 1

Mediation & moderation

Answer 1

Mediation; Predictor, mediator, outcome
Moderation; predictor, moderator, outcome

Both one step beyond regression
All assumptions of regressions & correlations are the same for mediation & moderation (normality, heteroscedicity & large sample)

But these assumption are weakened; linearity & additivity if effects, independence (from a measurement standpoint)

Question 2

Mediation

Answer 2

When the relationship between a predictor & an outcome can be better predicted or explained by a third, intervening variable

Mediations (& moderations) specify the nature of the relationship between predictor variables
Normal regressions don’t do this

Question 3

Going from regression to mediation

Answer 3

In a regression we want to see if any of our predictors (X) significantly predict our outcome variable (Y)
Our predictors May or may not be correlated but in regression as long as they’re not too highly correlated (violating assumptions of independence & additivity) we don’t care about relationship between predictors

Analysising as a mediation changes the emphasis we put on predictors & how we interpret our findings

Question 4

Mediation terminology

Answer 4

Total effect; effect of x on y, ignoring everything else (like a simple regression)

Split up into;
Indirect effect= effect of x on y that goes via the mediator
Direct effect= any remaining effect of x on y (that doesn’t go through the mediator)

Effect is not cause & effect, means same as path

Question 5

Paths

Answer 5

c path= total effect

c’ (d) path= direct effect

b path= path from M to Y

a path= path from X to M

a*b= indirect effect

Question 6

Paths & confidence intervals

Answer 6

Each path in mediation analysis is like a mini regression & will be significant or not

We check this using confidence intervals rather than p values

Question 7

For each path we have;

Answer 7

B value (coefficient)= shows strength & direction of relationship between 2 variables

SE= shows the error/fluctuation around this value

Question 8

How do we know if the mediation is significant?

Answer 8

Mediation occurs when the c-path (total effect) gets smaller with the addition of a mediator

We want to know if the difference between the c path & the c’ path (direct effect) is statistically significant

When X & M are continuous= (a path* b path)=c path-c’ path

(Indirect effect= total effect - direct effect )

If a path & b path are both significant, a*b path will also be significant, means the indirect effect will be significant
Same as saying difference between c path & c’ path is significant
Regardless of what’s happening with direct effect, we’ll have a significant mediation

Question 9

Full, partial or no mediation

Answer 9

No mediation= when indirect effect is non-significant

Full mediation= indirect effect significant, direct path non-significant

Partial mediation= indirect effect significant, direct path significant (but smaller than it was)

Question 10

B(italic), B & Beta

Answer 10

Can only report unstandardised B(italic) values in mediation models

Don’t put 0 before reporting Beta as can only very between -1 & 1

B(italic) values can be any score so put 0 before

Question 11

Determining significance with confidence intervals

Answer 11

Upper & lower confidence intervals need to be on same side of 0 to be significant

Question 12

Reporting mediation analysis

Answer 12

A mediation analysis was conducted to examine whether the relationship between [X] & [Y] is mediated by [M]
We employed ____
Results revealed a [S/NS] indirect effect, B(italic)=_X.XX, SE=.XX, 95%CI [X.XX, X.XX]
Specifically, the total effect of X on Y [___] was [reduced/unaffected] [and/but reminded significant/no longer reached significance] when accounting for social support [____]

Question 13

When to run a mediation

Answer 13

If number of predictor variables would all be significantly correlated with the outcome variable
But after entering them into same regression model, only some emerged as significant predictors in the regression
Could be an indicator that mediation is happening

Or can hypothesise a mediation ahead of time
In this case there are set of assumptions/criteria you supposedly need to meet before running a mediation

Question 14

Baron & Kenny (1986)

Answer 14

Mediation tested through 3 regression models

1) predicting outcome (Y) from the predictor variable (X) [original regression model, direct effect]
2) predicting the mediator (M) from the predictor variable (X)
3) predicting the outcome (Y) from both the predictor variable & the mediator

Question 15

Baron & Kenny (1986); conditions of mediation

Answer 15

1) the predictor (X) must significantly predict the outcome variable (Y)
2) the predictor (X) must significantly predict the mediator (M)
3) the mediator (M) must significantly predict the outcome variable (Y)
4) the predictor variable must predict the outcome variable less strongly in model 3 than model 1

Question 16

Limitations of Baron & Kenny’s (1986) approach

Answer 16

How much of a reduction in the relationship between the predictor & 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

More recent stats have shown that you don’t need to have a significant correlation between X & Y for there to be indirect effects (e.g. mediation) between them

Question 17

Moderation

Answer 17

When the relationship between a predictor & an outcome varies (e.g. in strength or significance) dependent on the level of a 3rd, moderating variable

Interaction between predictors (in a regression)

The combined effect of 2 variables on another is known conceptually as moderation, & in stats terms as an interaction effect

Question 18

Moderator variable types

Answer 18

Moderators can be continuous or binary categorical variables

Ideally predictor & outcome variables should still be continuous/interval variables

Question 19

Reporting moderation

Answer 19

Report B(italic) values

Tend to see people use p values, partly because separation multiple regression scores are often reported from main effects so this helps consistency of reporting