Can a Variable be both a Mediator and a Moderator?

Dominique Muller(University of Grenoble/University Institute of France)

Charles M. Judd(University of Colorado)

Vincent Yzerbyt (Catholic University of Louvain)

2

Y i3 c ' X bMe e

3

Y i1 cX e

1

Me i2 aX e

2

Mediation (Baron & Kenny, 1986; Judd & Kenny, 1981)

X is a treatment and units are randomly assigned to conditions

Me is a mediator measured after X (and before Y)

Y is the dependent variable

3

X Y

Me

c '

a b

Mediation

X Y c

Y i3 c ' X bMe e

3

Y i1 cX e

1

Me i2 aX e

2

4

X Y

Me

c '

a b

Mediation

Y i3 c ' X bMe e

3

Y i1 cX e

1

Me i2 aX e

2

Without a causal argument, these are nothing else than regression equations, not a strong case for mediation

Social psychologists have been very concerned with causality in mediation models (e.g., Spencer, Zanna, & Fong, 2005)

5

Mediation in the MacArthur approach

dXMe e3

Y i1 cX e

1

Me i2 aX e

2

The MacArthur approach (see Kraemer, Kiernan, Essex, & Kupfer, 2008) takes its root in clinical interventions and randomized clinical trials (RCT)

Y i3 c ' X bMe

c, a, and b conjointly significantorc, a, and d conjointly significant

Mediation

6

Moderation in social psychology

Y i4 c

21S

1 c

22P

2 c

23SP e

4

Y (i4 c

22P

2) (c

21 c

23P)S e

4

S Y

P

7

Y i4 c

21S c

22P c

23SP e

4

Y (i4 c

21S) (c

22 c

23S)P e

4

P Y

S

Moderation in social psychology

8

Y i4 c

21S c

22P c

23SP e

4

S Y

P

P Y

S

Social psychologists are fine with both models

Only preferences dictate which one will be used

Moderation in social psychology

Moderation is equated with simply a statistical interaction

9

Y i4 c

21X c

22Mo c

23XMo e

4

X is a treatment and units are randomly assigned to conditions

Mo, the moderator, is measured PRIOR to the treatment

And therefore, the Treatment and the moderator are uncorrelated

Moderation in the Mac Arthur approach

Moderation is not the same as simply a statistical interaction

Y (i4 c

22Mo) (c

21 c

23Mo)X e

4

10

In social psychology:

Definition of moderation

In Mac Arthur Approach:

A moderator P is a variable that affects a S – Y relationship or a moderator S is a variable that affects a P – Y relationship

A moderator is a variable that affects a causal effect of X on Y

11

Can a variable be both a mediator and a moderator?

Y i3 c ' X bMe dXMe e

3

Y i1 cX e

1

Me i2 aX e

2

From a social psychology perspective:

-> Me is a mediator (c, a, and b are conjointly significant)

-> Me is a moderator (the d interaction is significant)

For the MacArthur approach:

-> Me is only a mediator (c, a, and d are conjointly significant)

12

Y i3 c ' X bMe dXMe e

3

X Y

Me

Y i3 bMe (c ' dMe)X e

3

For social psychologists

13

Y i3 c ' X bMe dXMe e

3

Y i3 c ' X (b dX )Me e

3

X Y

Me

This explains why it has been argued that this is a case of moderated mediation (Preacher, Rucker, & Hayes, 2007)

For social psychologists

14

Y i3 c ' X bMe dXMe e

3

X Y

Me

XMe

For the MacArthur approach

15

X Y

Me

X Y

Me

X Y

Me

XMe

Can a variable be both a mediator and a moderator?

Social psychology perspective MacArthur Approach

16

Conclusion

Can a variable be both a mediator and a moderator?

Yes, it can be both if moderation and statistical interactions are equated

No, if moderation and statistical interactions are not equated

How should we define moderation?