매개된 조절효과, 조절된 매개효과

매개된 조절효과, 조절된 매개효과

University of Colorado at Boulder

Vincent Y. Yzerbyt

Catholic University of Louvain at Louvain-la-Neuve, Belgium

Procedures for examining whether treatment effects on an outcome are mediated and/or moderated have

been well developed and are routinely applied. The mediation question focuses on the intervening

mechanism that produces the treatment effect. The moderation question focuses on factors that affect the

magnitude of the treatment effect. It is important to note that these two processes may be combined in

informative ways, such that moderation is mediated or mediation is moderated. Although some prior

literature has discussed these possibilities, their exact definitions and analytic procedures have not been

completely articulated. The purpose of this article is to define precisely both mediated moderation and

moderated mediation and provide analytic strategies for assessing each.

Keywords: mediation, moderation, mediated moderation, moderated mediation

There is by now a very large literature on the important topics

of mediation and moderation (e.g., Aiken & West, 1991; Baron &

Kenny, 1986; James & Brett, 1984; Judd & Kenny, 1981; Kenny,

Kashy, & Bolger, 1998; Kraemer, Wilson, Fairburn, & Agras,

2002; MacKinnon, Lockwood, Hoffman, West, & Sheets, 2002)

and in general it is fair to say that the analytic strategies underlying

the assessment of each are well understood (even if they are still

developing). Both processes focus on a given treatment effect. The

issue of mediation addresses how that treatment effect is produced.

Mediational analyses attempt to identify the intermediary process

that leads from the manipulated independent variable to the out-

come or dependent variable. The issue of moderation focuses on

factors that influence the strength and/or direction of the relation

between the treatment variable and the dependent variable. Mod-

erational analyses attempt to identify individual difference or

contextual variables that strengthen and/or change the direction of

the relationship between the treatment variable and the dependent

variable.

In this growing literature, there have been occasional discus-

sions of how the two issues of mediation and moderation might

themselves be combined in theoretically interesting ways. Thus, in

some of the early classic papers on mediation and moderation,

James and Brett (1984) discuss moderated mediation, and Baron

and Kenny (1986) devote a page to both moderated mediation and

mediated moderation. More recently Wegener and Fabrigar (2000)

also discuss these two topics. However, all of these treatments are

relatively brief, and our perusal of the literature that has made

reference to one or the other of these topics suggests that they are

not clearly understood. Additionally, there exists no source that

comprehensively articulates the definition of these two processes

and the analytic models that underlie them.

It is our intention in the current article to accomplish this. In the

initial section, we clearly define both mediated moderation and

moderated mediation and provide examples of each. In the second

section, we lay out the analytic models that are used to examine

both mediated moderation and moderated mediation. As we show

there, both of these processes rely on the same underlying models

of the data, but both have different starting points and thus respond

to distinct research questions. There is, however, a fundamental

defining algebraic equality that underlies both processes. Accord-

ingly, while we explicate the analyses for each, our argument is

that these two processes are in some sense the flip sides of the

same coin. In the third section, we use hypothetical data from the

two examples developed in the initial section to illustrate both

processes. We conclude by further discussing how these processes

relate to each other and then by considering a variety of issues

which our discussion has raised.

Defining Terms and Illustrating Processes

Initially we define terms in an abstract, generalized case. Sub-

sequent to this, we provide more detailed substantive examples

that hopefully will make clear why both processes, mediated

moderation and moderated mediation, are theoretically important.

The abstract case initially focuses on four variables. First there

is the manipulated independent variable, X

i

. To keep things simple,

Dominique Muller, Université Paris Descartes, France; Charles M. Judd,

University of Colorado at Boulder; Vincent Y. Yzerbyt, Catholic Univer-

sity of Louvain at Louvain-la-Neuve, Belgium.

This work was supported by a Lavoisier fellowship from the Ministe`re

des Affaires étrange`res, France, awarded to Dominique Muller and by

National Institute of Mental Health Grant R01MH45049 awarded to

Charles M. Judd. We express our gratitude to Olivier Corneille, Olivier

Desrichard, Marcello Galucci, and David MacKinnon for their comments

on a draft of this article.

Correspondence concerning this article should be addressed to Domin-

ique Muller, Laboratoire de Psychologie Sociale, Université Paris-5 René

Descarte, 71, avenue Edouard Vaillant, 92774 Boulogne Billancourt Ce-

dex, France, or to Charles M. Judd, Department of Psychology, University

of Colorado, Boulder, CO 80309-0345. E-mail: dominique.muller@univ-

paris5.fr or charles.judd@colorado.edu

Journal of Personality and Social Psychology

Copyright 2005 by the American Psychological Association

2005, Vol. 89, No. 6, 852–863

0022-3514/05/$12.00 DOI: 10.1037/0022-3514.89.6.852

852

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Page 2

we assume it has only two values, indicating whether a participant

was in the treatment or control condition, and its values are

contrast coded (e.g., 1, 1 or .5, .5). We further assume that

participants have been randomly assigned to one of these two

levels, so that causal inferences can be made about the treatment

effect.

1

The second variable is the outcome variable, Y

i

, which is

some measured response of the participants, presumed to be af-

fected by the treatment. Next there is a mediating variable, Me

i

,

which is another measured response variable, also expected to be

affected by the treatment variable. The mediational hypothesis, to

be examined, is that this mediator is responsible for the causal

effect of X

i

on Y

i

. Finally, there is a potential moderating variable,

Mo

i

, which is either some stable individual difference variable,

assumed not to be affected by the treatment, or else some measure

of the context or situation under which the treatment is delivered.

We presume it is measured prior to the delivery of the treatment,

and therefore, given random assignment to X

i

, it is assumed that

Mo

i

and X

i

are independent of each other.

2

In the general case, we

assume that this moderator is continuously measured, although

what we have to say also applies with a dichotomous, and hence

contrast-coded, moderator. The moderational hypothesis, to be

examined, is that the magnitude of the causal effect of X

i

on Y

i

depends on the moderator.

It is important to note that, throughout our discussion (unless

explicitly stated otherwise), we are presuming that all variables

(with the exception of the outcome) have been centered at their

mean. This assumption is made to increase the interpretability of

various parameters in models that include interaction terms (Aiken

& West, 1991; Judd & McClelland, 1989).

3

Although there is some continuing discussion about the neces-

sary and sufficient conditions to establish mediation (see below),

we have chosen to adopt the original and classic approach as

outlined by Judd and Kenny (1981) and Baron and Kenny (1986).

According to this approach, to demonstrate mediation, one esti-

mates three different models (typically using least squares

estimators)

4

Y

10

11

X

1

(1)

Me

20

21

X

2

(2)

Y

30

31

X

32

Me

3

(3)

and four conditions must be met:

1. In Equation 1, there must be an overall treatment effect

on the outcome variable; that is, b

11

is significant.

5

2. In Equation 2, there must be a treatment effect on the

mediator; that is, b

21

is significant.

3. In Equation 3, there must be an effect of the mediator on

the outcome controlling for the treatment; that is, b

32

is

significant.

4. In Equation 3, the residual direct effect of the treatment

variable on the outcome (

31

) should be smaller (in

absolute value) than the overall treatment effect in Equa-

tion 1 (

11

).

The following equality relationship exists among the parameters

of these models (see, e.g., MacKinnon, Warsi, & Dwyer, 1995):

11

31

21

*

32

meaning that the difference between the overall treatment effect

and the residual direct effect is equal to what is called the indirect

effect via the mediator (i.e.,

21

*

32

).

A continuing issue in the literature has focused on how one

establishes Condition 4. Alternatives here, outlined by MacKinnon

et al. (2002), involve testing whether the parameter difference on

the left side of the above equality departs from zero or whether the

product on the right side does so. An additional issue that contin-

ues to be debated concerns the necessity of Condition 1 (again,

MacKinnon et al., 2002; Shrout & Bolger, 2002). We agree here

with Shrout and Bolger (2002) who acknowledge that “experimen-

talists who wish to elaborate the mechanisms of an experimental

effect need to first establish that the effect exists” (p. 430). We do,

however, recognize that there may be grounds for disagreement here.

To demonstrate moderation, one estimates the following model:

Y

40

41

X

42

Mo

43

XMo

4

(4)

where XMo is computed as the product of the treatment variable

and the moderating variable. A test of the effect of that partialled

product (i.e., the significance of b

43

) is a test of the Treatment

Moderator interaction, asking whether the treatment effect varies

in magnitude as a function of the value of the moderator.

In this context, having defined the relevant variables and the

meaning of mediation and moderation, we are now able to define

the two processes of central interest to this article: mediated

moderation and moderated mediation. To clearly differentiate be-

tween them, we will define them in the most prototypic case,

clearly contrasting the two. Subsequently, we will examine their

interrelations and how one bleeds into the other.

The first of these, mediated moderation, can happen only when

moderation occurs: the magnitude of the overall treatment effect

on the outcome depends on the moderator. Given that the magni-

tude of the treatment effect depends on an individual difference or

context variable, then the mediated moderation question is con-

cerned with the mediating process that is responsible for that

moderation. What is the process through which that overall mod-

erated treatment effect is produced? An advantage of seeing me-

1

In this regard we concur with recent arguments of Kraemer et al.

(2002) who have the strong preference to confine discussion of mediation

(and moderation) to experimental situations in which units are randomly

assigned to the manipulated levels of the treatment variable.

2

Again, we are consistent with Kraemer et al., (2002) in making these

assumptions.

3

In fact, the models we explicate do not depend on this centering

assumption. The relevant variables could be deviated from values other

than their means, with appropriate modifications in the interpretation of

parameter estimates associated with lower-order predictor variables in

models involving higher-order interactions. See Aiken and West (1991)

and Judd and McClelland (1989).

4

Throughout we will use ’s to refer to unknown population parameters

and b’s to refer to their sample estimates. In all equations we omit the i

subscript from all variables.

5

Here and everywhere in the text, we use “overall effect” to refer to the

direct plus the indirect effect of the independent variable on the outcome.

Correspondingly, we use “residual direct effect” to refer to the direct effect

of the independent variable on the outcome controlling for the mediator.

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MEDIATED MODERATION AND MODERATED MEDIATION

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diation as a series of analytic steps (as outlined above) is that it

permits one to recognize that there is more than one way by which

an overall moderated treatment effect might be produced. We

discuss these alternatives in the later section where we outline the

analytic approach to mediated moderation.

Moderated mediation happens if the mediating process that is

responsible for producing the effect of the treatment on the out-

come depends on the value of a moderator variable. In other

words, if the moderator is an individual difference variable, then it

would mean that the mediating process that intervenes between the

treatment and the outcome is different for people who differ on

that individual difference. If the moderator is a contextual variable,

then it would mean that the mediating process varies as a function

of context. Note that this definition importantly implies mediation

(at least for some people or in some contexts), as we defined it

previously, but it does not imply any overall moderation of the

treatment effect. And in fact, we will see that it is most convenient

to clearly define moderated mediation in the prototypic case where

there is no moderation of the X to Y effect. What varies as a

function of the moderator is not the magnitude of the overall

treatment effect on the outcome but the mediating process that

produces it. Again, moderated mediation can happen in a number

of different ways. We describe these in the section below where we

discuss analytic models.

We now turn to illustrations of both mediated moderation and

moderated mediation. These examples were chosen from existing

social psychological research but they were constructed in such a

way to illustrate both processes in prototypic cases. As such, they

are reasonable models that might be examined in social psycho-

logical research, but they are deliberate oversimplifications.

To illustrate mediated moderation, consider recent work by

Smeesters, Warlop, Van Avermaet, Corneille and Yzerbyt (2003)

on the role of “morality” versus “might” primes on cooperative

versus competitive behavior in a prisoner’s dilemma choice sce-

nario. They argued that participant’s social value orientation (pro-

self vs. prosocial) would moderate the impact of such primes.

Specifically, they showed that for participants who were more

prosocial, the primes affected the choice of cooperative versus

competitive behaviors (“morality” primes increased cooperation,

compared to “might” primes) whereas for more proself partici-

pants, this difference was not found. Their explanation for the

mediating process underlying this overall moderation was that the

primes produce expectations about how the partner in the prison-

er’s dilemma game would behave. The “morality” prime induced

expectations that the partner would cooperate; the “might” prime

induced expectations that the partner would compete. And the

researchers reasoned that these primed expectations would then be

acted upon differently by prosocial and proself participants. Those

who are more prosocial should attempt to match their behavior to

what they expect from the partner: if they expect competition, their

choice should be competitive; if they expect cooperation, their

choice should be cooperative. But among more proself partici-

pants, competitive choices should predominate regardless of the

expectations: if they expect competition, their choice should be

competition; and if they expect cooperation, they should also

compete in an attempt to exploit their partner’s cooperative choice.

In sum, the researchers anticipated that the effect of the prime on

behavioral choice would depend on whether participants were

prosocial or proself (overall moderation of the treatment effect).

And they further predicted that this moderation would be mediated

by expectations about the partner’s behavior. Primes would induce

expectations about partner’s behavior, that they would either co-

operate or compete, and participants who were prosocial would

match their own behavior to their partner’s whereas those who

were more proself would compete regardless of their expectation.

To illustrate moderated mediation, we draw on research by

Petty, Schumann, Richman, and Strathman (1993) that examined

the role of positive mood in persuasion. They manipulated partic-

ipants’ mood (either positive mood or no mood induction) and

subsequently exposed them to counterattitudinal persuasive infor-

mation. They predicted that those in a positive mood would show

more persuasion than those in the control condition. And overall

they found this treatment effect. But they further were interested in

understanding differences in what mediates this overall treatment

effect as a function of a “need for cognition” individual difference

variable. They argued that for those high in need for cognition, the

mediating process producing more persuasion as a result of a

positive mood would be one where the mood causes people to

generate more positively valenced thoughts in response to the

persuasive communication and then these thoughts in turn produce

greater persuasion. on the other hand, they argued that for those

participants who were low in need for cognition, the mediating

process would not be through positively valenced thoughts. In

other words, positive thoughts would mediate the mood—persua-

sion effect for those high in need for cognition, while for those low

in need for cognition the same mood—persuasion effect would not

be mediated by positive thoughts (or would be mediated by them

less). This illustrates moderated mediation: a treatment effect is

mediated differently as a function of some moderator variable.

Need for cognition moderates the way in which the mood—persua-

sion effect is produced. Note that there is no overall moderation here:

it is not the case that the mood—persuasion effect is larger or smaller

for those who differ in need for cognition. Rather the mediating

process for the same effect was hypothesized to be different.

6

Analytic Models for Moderated Mediation and Mediated

Moderation

There are three fundamental models that underlie both mediated

moderation and moderated mediation.

7

We have already given the

6

Petty et al. (1993) note that had there been an overall moderation of the

mood effect by need for cognition, the assessment of moderated mediation

would have been problematic. Finding a pattern by which, for instance, the

effect of mood was absent for those high in need for cognition simply

“precludes examination of any differential mediation of the positive mood

effect for people high and low in NC because there was no effect of

positive mood to mediate for the high-NC individuals.” (p. 9) Although not

intractable, we would agree that interpretational problems arise in talking

about moderated mediation whenever the magnitude of the treatment effect

on the outcome variable varies as a function of the moderator.

7

The models that we give here appear somewhat different from those

proposed by Baron and Kenny (1986, p. 1179) in their brief treatment of

mediated moderation and moderated mediation. This is because in their

example the moderator was a manipulated independent variable and it was

then subsequently measured (as a manipulation check) to serve as a

mediator. Our approach, utilizing conceptually different moderator and

mediator variables and a single set of equations, is more parsimonious.

854

MULLER, JUDD, AND YZERBYT

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first of these as Equation 4, to assess moderation of the overall

treatment effect:

Y

40

41

X

42

Mo

43

XMo

4

(4)

This model allows the overall treatment effect of Equation 1 to

be moderated by Mo. The second model allows the treatment effect

on the mediator, in Equation 2, to be moderated:

Me

50

51

X

52

Mo

53

XMo

5

(5)

And the third model is a moderated version of Equation 3, in

which both the mediator’s (partial) effect on the outcome and the

residual effect of the treatment on the outcome, controlling for the

mediator, are allowed to be moderated:

Y

60

61

X

62

Mo

63

XMo

64

Me

65

MeMo

6

(6)

In all three models, we are making the same assumptions about

all variables that we did earlier. Namely, there are two levels of X

(contrast coded) to which experimental units have been randomly

assigned, X and Mo are therefore uncorrelated, and both Me and

Mo have been centered.

8

Given these assumptions, the slope

parameters in these three models can be interpreted as defined in

Table 1.

In Figure 1, we present the fundamental model that subsumes

both mediated moderation and moderated mediation. The top panel

in this Figure represents the overall treatment effect on the out-

come, and the extent to which it is moderated. Accordingly, the

overall treatment effect depends on the level of the moderator, to

the extent that

43

departs from zero. The bottom panel presents

the mediated model, allowing the treatment effect on the mediator

to be moderated (to the extent that

53

departs from zero), the

mediator’s partial effect on the outcome to be moderated (to the

extent that

65

departs from zero), and the residual direct effect of

the treatment on the outcome (controlling for the mediator) to be

moderated (to the extent that

63

departs from zero).

From this Figure, the overall (moderated) treatment effect is

41

43

Mo. Using the estimated values for these parameters,

one can use this ｅxpression to estimate “simple” overall treatment

effects at particular levels of Mo. The (moderated) indirect effect,

via the mediator, equals

51

53

Mo

64

65

Mo . And the

residual (moderated) treatment effect equals

61

63

Mo.

Again, the parameter estimates from these ｅxpressions can be used

to estimate “simple” effects at particular levels of Mo.

Parallel to what we saw in the case of simple mediation (Equa-

tions 1–3), there exists a fundamental equality among the param-

eters of these models, focusing on the moderation of the indirect

and residual direct effects. In the Appendix, we prove that at the

level of the population parameters, making the assumptions we

have made, the following equality holds:

43

63

64

53

65

51

(7)

This equality will not exactly hold in terms of parameter esti-

mates, from a sample of data, unless the moderator is dichotomous

and contrast coded (see Appendix). Nevertheless, this equality

provides us with fundamental insights into the definitions of me-

diated moderation and moderated mediation.

We now turn to these definitions and what they imply about the

three models we have just identified. Doing this provides us with

analytic strategies for estimating both mediated moderation and

moderated mediation. And the consideration of these processes, in

the context of these models, will provide insights about the dif-

ferent ways in which each process might be produced.

Mediated Moderation

The above Models 4 through 6 are used to establish mediated

moderation. Equation 7 establishes an equality condition on the

8

When the parameters of these models are estimated in a sample of data,

additional assumptions are necessary, of course, to derive their standard

errors. Namely, residuals must be independent, normally distributed, and

have a common variance.

Table 1

Interpretation of the Slope Parameters in Equations 4, 5, and 6

Slope

parameters

Interpretation of slope parameters

41

Overall treatment effect on Y at the average level of Mo

42

Moderator effect on Y on average across the two treatment

levels

43

Change in overall treatment effect on Y as Mo increases

51

Treatment effect on Me at the average level of Mo

52

Moderator effect on Me on average across the two

treatment levels

53

Change in treatment effect on Me as Mo increases

61

Residual direct treatment effect on Y at the average level

of Mo

62

Moderator effect on Y on average within the two treatment

levels and at the average level of Me

63

Change in residual direct treatment effect on Y as Mo

increases

64

Mediator effect on Y on average within the two treatment

levels and at the average level of Mo

65

Change in mediator effect on Y as Mo increases

Figure 1. Models illustrating moderated mediation and mediated

moderation.

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MEDIATED MODERATION AND MODERATED MEDIATION

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parameters from these models. one could first focus on the two

parameters on the left side of this equality, that is,

43

and

63

.

With mediated moderation, there is overall moderation of the

treatment effect, that is,

43

0, and the question then is whether

the mediating process accounts for this moderation. If it does, then

the moderation of the residual direct effect of the treatment should

be reduced compared to the moderation of the overall treatment

effect, that is,

63

should be smaller in absolute value than

43

. For

this to be the case, we see on the right side of Equation 7 that there

must be mediation and one or both of the indirect paths from the

treatment to the outcome must be moderated. That is, either the

effect of X on Me depends on the moderator (

53

0, and the

average partial effect of Me on Y [

64

] is nonzero) and/or the

partial effect of Me on Y depends on the moderator (

65

0, and

the average effect of X on Me [

51

] is nonzero).

In light of this, to demonstrate mediated moderation in a sample

of data, one estimates Models 4 through 6. In Model 4, we would

expect b

43

to be significant, indicating overall treatment modera-

tion. In Models 5 and 6, either (or both) of two patterns should

exist: both b

53

and b

64

are significant or both b

51

and b

65

are

significant. And, as a result, the moderation of the residual treat-

ment effect, b

63

, should be reduced in magnitude (and may be

nonsignificant in the case of what might be called “full” mediated

moderation) compared to the moderation of the overall treatment

effect.

Moderated Mediation

In the prototypic case of moderated mediation, there is an

overall treatment effect (

41

) and the magnitude of this effect does

not depend on the moderator (

43

0). However, the potency of

the mediating process depends on the moderator. Accordingly,

either the effect of the treatment on the mediator depends on the

moderator (

53

0) or the partial effect of the mediator on the

outcome depends on the moderator (

65

0), or both. Parallel to

this, if the treatment effect on the mediator depends on the mod-

erator (

53

0), then there must be a partial effect of the mediator

on the outcome on average (

64

0), or if the partial effect of the

mediator on the outcome depends on the moderator (

65

0), then

there should be an overall treatment effect on the mediator

(

51

0). In other words, at least one of the products on the

right-hand side of the equality in Equation 7 must depart from

zero.

Accordingly, if the right-hand side of the equality in Equation 7

departs from zero, then too must the left-hand side parameter

difference. We have assumed that the first term in this difference

equals zero (i.e.,

43

0, there is no overall moderation of the

treatment effect). This implies that the second term (

63

) differs

from zero.

In sum, moderated mediation implies that the indirect effect

between the treatment and the outcome depends on the moderator.

That is, either the effect from X to Me depends on the moderator

(

53

0, and the average partial effect of Me on Y [

64

] is

nonzero) and/or the partial effect of Me on Y depends on the

moderator (

65

0, and the average effect of X on Me [

51

] is

nonzero). In either case, given no overall moderation of the treat-

ment effect (i.e.,

43

0), this implies that the residual direct

treatment effect on the outcome, controlling for the mediator, is

moderated (i.e.,

63

0).

9

In light of this, to demonstrate moderated mediation in a sample

of data, one estimates Models 4 through 6. In Model 4, the

prototypic case leads to the expectation that b

41

is significantly

different from zero, while b

43

is not. In Models 5 and 6, either (or

both) of two patterns should exist: both b

53

and b

64

are significant

or both b

51

and b

65

are significant. A consequence is that the

residual treatment effect should now be moderated, that is b

63

may

be significant. Although this is likely, we do not believe that the

significance of b

63

should be seen as a necessary condition for

establishing moderated mediation.

Summary

In sum, for mediated moderation, there is overall moderation,

produced by the mediating process, and when this process is

controlled, the residual moderation of the treatment effect is re-

duced. What we have called prototypic moderated mediation is

found when there is an unmoderated overall treatment effect, but

the indirect effect of the treatment via the mediator is moderated.

As a result, the residual treatment effect is likely to be moderated.

Data-Based Examples

In this section, we return to the two examples we used earlier to

illustrate mediated moderation and moderated mediation, but this

time with hypothetical data

10

and illustrative model estimates from

those data.

Mediated Moderation Example

The example that we used to illustrate the definition of mediated

moderation focused on cooperative behavior in a prisoner’s di-

lemma situation (Smeesters et al., 2003). Participants were primed

with either “might” or “morality” primes and then engaged in a

one-trial prisoner’s dilemma with a fictitious partner. Additionally,

participants’ social value orientation (from proself to prosocial)

was measured. The researchers found an overall moderation of the

effect of the prime by social value orientation: those participants

who were more prosocial indicated they would more likely coop-

erate under the “morality” prime while they were more likely to

compete under the “might” prime. on the other hand, more pro-

self participants tended to choose competition regardless of the

prime. It was then suggested that this moderation was produced by

expectations about the partner. More specifically, the “morality”

prime led to expectations that the partner would cooperate, while

the “might” prime led to expectations of partner competition. And

participants proself versus prosocial status was found to moderate

the impact of these partner expectations on behavior: Prosocial

participants attempted to match the behaviors expected from their

9

In rare cases, it is possible that the effect of the treatment on the

mediator is moderated in one direction while the effect of the mediator on

the outcome is moderated in the opposite direction. In these cases, the

overall moderation of the treatment effect may be the same as the moder-

ation of the residual direct treatment effect.

10

We used simulated data instead of real data to keep things parsimo-

nious. Additionally, they are publicly available, as indicated below, so that

the reader can recreate our analyses.

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MULLER, JUDD, AND YZERBYT

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partner, while proself participants competed regardless of how

they expected their partner to behave.

For this illustration, data were generated for 100 cases on four

variables:

11

(a) A dichotomous treatment variable indicating the type of

prime received (X: referred to as PRIME): “might” priming ( 1)

versus “morality” priming ( 1). Values on this variable were

randomly assigned to the 100 cases.

(b) A continuous moderator variable (MO: referred to as SVO

for social value orientation, with lower numbers for more proself

participants and higher numbers for those who are more prosocial):

randomly generated from a normal distribution with a mean of

zero and a standard deviation of 1.35. This variable was centered

in the sample. Sample values ranged from 3.369 to

3.833.

(c) A continuous mediator variable (ME: referred to as EXP for

expectations about the partner’s behavior, with higher numbers

indicating that the partner was expected to be more cooperative).

It was generated to be a function of prime, adding a random error

component. Again, it was centered in the sample and had a

standard deviation of 7.913.

(d) A continuous outcome variable (Y: referred to as BEH for

behavior, with higher numbers indicating a greater probability of

cooperative behavioral choices). This outcome variable was con-

structed to be affected by the prime, social value orientation,

expectations, and the Mediator

Moderator interaction, plus a

random error component.

As just described, these data were generated to be consistent

with the mediated moderation hypothesis, that is, that the overall

effect of the treatment (PRIME) on the outcome (BEH) would be

moderated by social value orientation (SVO) and that this inter-

action would be due to the effect of the treatment on the mediator

(EXP) and the moderation of the mediator effect on the outcome

(BEH) by social value orientation (SVO).

Table 2 contains the univariate statistics and bivariate correla-

tions for all four variables. Table 3 presents the regression models

that estimate Equations 4 through 6 with these variables. Presented

here are the unstandardized coefficients (b) and their associated t

statistics. In these equations, there are product predictors included

to estimate the interactions (PRIMESVO

PRIME*SVO;

EXPSVO

EXP*SVO).

The results from Equation 4 find evidence for the predicted

interaction between PRIME and SVO on the outcome variable,

BEH. As predicted, “morality” primes are associated with a higher

probability of cooperative behaviors than “might” primes, and this

difference increases as participants are more prosocial and less

proself. The treatment variable’s (PRIME) effect on the outcome

(BEH) is moderated by social orientation (SVO).

The results from Equation 5 show an effect of the prime on the

mediator, that is expectations about the partner’s behavior (EXP).

Moreover, this effect is not moderated by social orientation (the

PRIMESVO coefficient is not significant). In order to help with

the interpretation of the indirect effect in these data it is informa-

tive to calculate the simple effects of the prime (PRIME) on the

mediator (EXP) at different levels of the moderator (SVO), as

discussed earlier. Because the moderator varies continuously, we

have calculated these simple effects at values of one standard

deviation (1.398) above and below the mean SVO score:

For High SVO ( 1 SD): b

51

b

53

Mo

2.692

0.089 1.398

2.816

For Low SVO ( 1 SD): b

51

b

53

Mo

2.692

0.089( 1.398)

2.568

The estimation of Equation 6 reveals a significant effect of the

mediator (EXP) by moderator (SVO) interaction on the outcome

(the EXPSVO coefficient is significant). We can again calculate

the simple effect of EXP on BEH at values of SVO one standard

deviation above and below the mean SVO score:

For High SVO ( 1 SD): b

64

b

65

Mo

0.840

0.765 1.398

1.909

For Low SVO

1 SD : b

64

b

65

Mo

0.840

0.765

1.398

0.229

Taking the product of the two simple effects for each of the two

values of SVO, we get the total indirect effects through the

mediator (EXP) for each of these two values:

For High SVO ( 1 SD): 2.816*1.909

5.377

For Low SVO ( 1 SD): 2.568*

0.229

0.589

Accordingly, for all participants, regardless of social orientation,

the cooperative prime increases expectations that the partner will

cooperate. And such expectations lead to cooperative behavior on

the part of the participants but only in the case of those who are

high (prosocial) on social value orientation. It would seem that the

moderation of the overall effect of the prime (by social value

orientation) can be understood from the fact that the cooperative

prime induces cooperative expectations among all participants, but

those expectations translate into cooperative behavior only for

those who have a cooperative social value orientation.

Consistent with this, Equation 6 also reveals that the residual

direct effect of the prime on the outcome (BEH) is less (and

actually not at all in this example) moderated by social value

orientation, once the mediator (EXP) and its interaction with SVO

11

The raw data are available at http://www.psp.ucl.ac.be/mediation/

Table 2

Univariate and Bivariate Statistics for Mediated Moderation

Example

Variable

PRIME

(Treatment)

SVO

(Moderator)

EXP

(Mediator)

BEH

(Outcome)

M

.000

.000

.000

58.171

SD

1.005

1.398

7.913

14.691

Correlations

PRIME

—

.004

.342**

.314**

SVO

—

.016

.165

EXP

—

.385

BEH

—

Note. SVO

social value orientation; EXP

expectations about part-

ner’s behavior; BEH

behavior.

** p

.01.

857

MEDIATED MODERATION AND MODERATED MEDIATION

---

Page 7

are controlled. Indeed, the coefficient associated with the PRIME

* SVO interaction has been reduced from 2.508 (in Equation 4) to

0.041 (in Equation 6). once we control for the mediator and allow

the indirect effect via the mediator to be moderated, the residual

direct effect of the prime on the outcome no longer depends on this

moderator.

As we made clear earlier, mediated moderation may be pro-

duced in either (or both) of two ways. In the first way, the

moderator affects the magnitude of the treatment effect on the

mediator (and this is found in conjunction with a mediator effect in

Equation 6). Alternatively, and this is the situation illustrated in

our example, the moderator affects the magnitude of the media-

tor’s partial effect on the outcome (and this is found in conjunction

with a treatment effect on the mediator in Equation 5).

Moderated Mediation Example

We illustrate this analysis with data based loosely on the mod-

erated mediation example we highlighted in the introduction (Petty

et al., 1993). Recall that in this example the effect of positive mood

(vs. control) on persuasion was thought to be more mediated by

positive valenced thoughts in the case of individuals who are high

in “need for cognition” than in the case of individuals low in “need

for cognition.” For this illustration data were generated for 100

cases on four variables:

12

(a) A dichotomous treatment variable (X: referred to as MOOD):

positive mood induction ( 1) versus no mood induction ( 1).

Values on this variable were randomly assigned to the 100 cases.

(b) A continuous moderator variable (MO: referred to as NFC

for need for cognition scores with higher numbers for higher need

for cognition): randomly generated from a normal distribution with

a mean of zero and a standard deviation of 1.35. This variable was

centered in the sample. Sample values ranged from 4.82 to

3.07.

(c) A continuous mediator variable (ME: referred to as POS for

positive valenced thoughts, with higher numbers indicating more

positive valenced thoughts). This is the mediator. It was generated

to be a function of the treatment variable and its interaction with

NFC, adding in a random error component. Again it was centered

in the sample and ranged from 18.05 to

21.74.

(d) A continuous outcome variable (Y: referred to as ATT for

attitude change, with higher numbers indicating more attitude

change). This outcome variable was constructed to be affected by

the treatment variable and the mediator, plus a random error

component.

As just described, these data were constructed following the

theoretical model of Petty et al. (1993), so that there was an overall

treatment effect on attitude change, unmoderated by need for

cognition. For those high in need for cognition, the treatment

variable affected the mediator (positive valenced thoughts) more

than for those low in need for cognition, while this mediator

affected the outcome equally for all participants. Unlike Petty et al.

(1993), we assumed that need for cognition scores were continuously

measured rather than dichotomizing the variable at its median.

Table 4 contains univariate statistics and bivariate correlations

for all four variables. Table 5 presents the regression models that

estimate Equations 4 through 6 with these variables. Presented

here are the unstandardized coefficients (b) and their associated t

statistics. In these equations, product predictors are included to

estimate the interactions (MOODNFC

MOOD*NFC; POSNFC

POS*NFC).

The results from Equation 4 indicate an overall effect of the

treatment, MOOD, on the outcome variable, ATT. This effect is

not moderated by need for cognition, NFC.

In Equation 5, the mediator, POS, is the criterion. Here, there is

a significant effect of MOOD and a significant MOOD

NFC

interaction. This significant interaction is indicative of moderated

mediation, in that it means that the magnitude of the indirect effect

of MOOD, via the mediator, varies in magnitude as a function of

NFC. As in the previous example, it is useful to again calculate the

simple effects of MOOD on POS at one standard deviation (1.405)

above and below the NFC mean:

For High NFC ( 1 SD): b

51

b

53

Mo

4.336

1.256 1.405

6.101

12

The raw data are available at http://www.psp.ucl.ac.be/mediation/

Table 3

Least Squares Regression Results for Mediated Moderation Example

Equation 4

(criterion BEH)

Equation 5

(criterion EXP)

Equation 6

(criterion BEH)

Predictors

b

t

b

t

b

t

X: PRIME

4.580

3.40**

2.692

3.57**

2.169

2.03*

(b

41

)

(b

51

)

(b

61

)

MO: SVO

2.042

2.09*

0.085

0.16

2.569

3.54

(b

42

)

(b

52

)

(b

62

)

XMO: PRIMESVO

2.574

2.64**

0.089

0.16

0.041

0.05

(b

43

)

(b

53

)

(b

63

)

ME: EXP

0.840

6.05**

(b

64

)

MEMO: EXPSVO

0.765

7.91**

(b

65

)

BEH

behavior; EXP

expectations about partner’s behavior; MO

moderator variable; SVO

social value

orientation; ME

mediator variable.

* p

.05. ** p

.01.

858

MULLER, JUDD, AND YZERBYT

---

Page 8

For Low NFC ( 1 SD): b

51

b

53

Mo

4.336

1.256( 1.405)

2.571

For someone well above the mean on need for cognition, pos-

itive mood, compared to control, leads to a considerably higher

POS score. on the other hand, for someone well below the mean

on the moderator, there is less of an effect of MOOD on POS.

From the Equation 6 results, importantly we see that there is a

significant effect of the mediator (POS) on the outcome. More-

over, this is not moderated by need for cognition (the POSNFC

coefficient is not significant). In order to help interpretations we

can however, again calculate the simple effects of the mediator on

the outcome at values of NFC one standard deviation above and

below the mean:

For High NFC ( 1 SD): b

64

b

65

Mo

1.248

.036 1.405

1.197

For Low NFC ( 1 SD): b

64

b

65

Mo

1.248

.036( 1.405)

1.299

Taking the product of the two simple effects, once at one

standard deviation above the mean NFC and once at one standard

deviation below the mean, we get the total indirect effects at the

two values:

For High NFC ( 1 SD): 6.101*1.197

7.303

For Low NFC ( 1 SD): 2.571*1.299

3.340

Equation 6 also reveals, as might be expected, that the residual

direct effect of the treatment (MOOD) on the outcome is moder-

ated, once the mediator is controlled. That is, there is a significant

effect of the MOOD

NFC interaction. Since the overall effect of

the treatment on the outcome does not vary as a function of NFC

(from Equation 4), and since the indirect effect via the mediator

does vary as a function of NFC, then it is the case that the residual

direct effect, controlling for the mediator, is moderated by NFC.

Again, we can calculate the two simple residual treatment effects

at the two levels of NFC (plus and minus one standard deviation

from the mean):

For High NFC ( 1 SD): 1.480

2.169 1.405

1.567

For Low NFC ( 1 SD): 1.480

2.169( 1.405)

4.527

These results as a whole make very clear that the indirect effect,

via the mediator, is much higher when NFC is high rather than

low, while the residual direct effect is much higher when NFC is

low rather than high. This pattern is what is expected under

prototypical moderated mediation.

This example illustrates a case where there is moderated medi-

ation because the effect of the treatment on the mediator depends

on the moderator. As a result, the overall magnitude of the indirect

effect via the mediator depends on the moderator. Alternatively, as

we made clear previously, moderated mediation could also happen

when the effect of the mediator on the outcome depends on the

moderator, producing a moderated indirect effect in a different

manner.

Table 4

Univariate and Bivariate Statistics for Moderated Mediation

Example

Variable

MOOD

(Treatment)

NFC

(Moderator)

POS

(Mediator)

ATT

(Outcome)

M

.000

.000

.000

1.98

SD

1.005

1.405

8.322

16.79

Correlations

MOOD

—

.023

.521**

.405**

NFC

—

.068

.110

POS

—

.629**

ATT

Note. NFC

need for cognition; POS

positive valenced thoughts;

ATT

attitude change.

* p

.05. ** p

.01.

Table 5

Least Squares Regression Results for Moderated Mediation Example

Equation 4

(Criterion ATT)

Equation 5

(Criterion POS)

Equation 6

(Criterion ATT)

Predictors

b

t

b

t

b

t

X: MOOD

6.813

4.415**

4.336

6.219**

1.480

.957

(b

41

)

(b

51

)

(b

61

)

MO: NFC

1.268

1.117

.767

1.496

.356

.366

(b

42

)

(b

52

)

(b

62

)

XMO: MOODNFC

.691

.609

1.256

2.450*

2.169

2.112*

(b

43

)

(b

53

)

(b

63

)

ME: POS

1.248

6.613**

(b

64

)

MEMO: POSNFC

.036

.279

(b

65

)

Note. ATT

attitude change; POS

positive valenced thoughts; MO

moderator variable; NFC

need for

cognition; ME

mediator variable.

* p

.05. ** p

.01.

859

MEDIATED MODERATION AND MODERATED MEDIATION

---

Page 9

Integrating the Two Processes

Although our purpose in this article has been to clearly define

both mediated moderation and moderated mediation, it should by

now be apparent that ultimately they both rest on the same analytic

models and the same fundamental equality, given in Equation 7:

43

63

64

53

65

51

(7)

We can conceptualize a continuum of analytic cases, varying in

the relative magnitude of the difference on the left side of this

equality (and thereby varying as well as a function of the terms on

its right side). The continuum is defined by the relative magnitude

of the difference between the absolute values of both

43

and

63

:

|

43

|

|

63

|.

13

In the middle of this continuum lies the situation in

which this difference equals zero. In this case, neither mediated

moderation nor moderated mediation can be said to occur. Below

this point lies the range of cases in which |

43

|

|

63

|

0 and

above it lies the range of cases in which |

43

|

|

63

|

0.

Our consistent definition of mediated moderation rests on this

difference being greater than zero: There is moderation of the

overall treatment effect in Equation 4 (

43

), and this is reduced in

magnitude once the moderation of the indirect effect is controlled

(

63

).

One might then be tempted to say that the other process,

moderated mediation, occurs whenever the difference is smaller

than zero, that is, whenever it is the case that the moderation of the

residual treatment effect (

63

) is greater than the moderation of the

overall treatment effect (

43

). But we have been very careful

throughout our discussion to always talk about moderated media-

tion in the “prototypic” case when there is no overall moderation,

that is, when

43

0. Our reasons for this insistence on defining

the “prototypic” case of moderated mediation can now be made

clear. If one defines moderated mediation without the assumption

that

43

0, then we would suggest that any point along the

continuum we have just defined (other than zero), including points

where |

43

|

|

63

|

0, can be seen as moderated mediation, de-

pending on the theoretical intentions of the researcher. That is, if

moderated mediation consists solely in identifying whether a me-

diating process between the treatment and the outcome is moder-

ated, then any time the terms on the right or left side of Equation

7 depart from zero, this can be said to occur.

This continuum of values for |

43

|

|

63

| thus provides concep-

tual insights about the processes we are examining. When this

difference equals zero, then neither mediated moderation nor mod-

erated mediation can be said to occur. When mediated moderation

is hypothesized this difference must be positive. on the other hand,

when moderated mediation is hypothesized this difference will be

negative if

43

0, which is the case for what we have called

prototypic moderated mediation. If one defines moderated medi-

ation as occurring whenever the mediating indirect effect is mod-

erated, relaxing the restriction of the prototypic case that

43

0, then moderated mediation can be said to occur regardless of

the sign of |

43

|

|

63

|, so long as it is not zero. Accordingly,

under this more relaxed definition, every case of mediated mod-

eration could be called moderated mediation, but the reverse is not

true.

In light of this conclusion, it is important to emphasize that the

relative magnitude of the |

43

|

|

63

| difference does not by itself

determine whether one is examining a case of mediated modera-

tion or moderated mediation. Other issues are involved. For in-

stance, as we have made clear, an overall treatment moderation is

assumed in the case of mediated moderation (i.e.,

43

0).

Ultimately, we would suggest that whether reference is made to

mediated moderation or moderated mediation depends on the

theoretical goals of the researcher, having examined the relevant

models. If there is overall moderation of the treatment effect and

if the models are examined in order to determine what is the

process responsible for this overall moderation, then the analysis is

in the service of mediated moderation goals. If, on the other hand,

one suspects that the process mediating a treatment effect depends

on a particular moderator, then the analysis is in the service of

moderated mediation goals. And this may be the case regardless of

whether there is or is not moderation of the overall treatment

effect. In other words, while we have defined the prototypic

moderated mediation case as occurring when the overall treatment

effect is unmoderated, ultimately moderated mediation is the goal

whenever the analysis is undertaken to understand how a mediat-

ing process is moderated, regardless of whether the overall treat-

ment effect is itself moderated.

Remaining Issues and Conclusion

Overall Significance Testing

Our focus throughout has been on specifying the conditions

necessary to establish mediated moderation and moderated medi-

ation. To do this, we have tended to focus on the values of

population parameters and only occasionally have we discussed

their estimates, their standard errors, and traditional significance

testing. Following the advice we have given on these matters, our

approach to testing for mediated moderation and moderated me-

diation may seem rather piecemeal. For instance, in the case of

both processes, we argue that at least one of the two indirect effects

(from the treatment through the mediator to the outcome) should

be significantly moderated, while the other indirect effect should

be significant on average. Additionally, in demonstrating mediated

moderation, we argued that overall moderation should be signifi-

cant. In outlining what we have called prototypic moderated me-

diation, we suggested that the overall treatment effect (i.e., b

41

)

should be significant, overall moderation should not be found (i.e.,

b

43

, ns), but the residual effect of the treatment on the outcome may

be significant (i.e., b

63

).

One might be tempted to argue that some overall test of both

processes might be more appropriate. If so, then the obvious

candidate here is to provide tests of whether the estimated terms on

either side of the equality of Equation 7 differ significantly from

zero. Thus one might be tempted to develop tests of either of the

following null hypotheses and call these overall tests of mediated

moderation or moderated mediation:

Ho:

43

63

0.

Ho:

64

53

65

51

0.

This would provide overall tests analogous to those provided by

MacKinnon et al. (2002) in the case of simple mediation. It would

13

We are assuming here that both of these parameters have the same

sign.

860

MULLER, JUDD, AND YZERBYT

---

Page 10

certainly seem that some of the tests examined by MacKinnon et

al. could be extended to testing at least the first of the above null

hypotheses.

Although such a test might be a desirable addition to our

piecemeal approach, we think that such an overall test would not

be sufficient in and of itself to demonstrate either mediated mod-

eration or moderated mediation. Just as we believe that establish-

ing simple mediation requires that the researcher examine a series

of models and plausible inferences, so too uncovering the more

complex processes we are dealing with involves a bit of detective

work, examining whether the overall pattern of results, including

confidence intervals for a number of different parameters in the

models, support the notions of mediated moderation and moder-

ated mediation. We also believe that it is of theoretical interest for

researchers to differentiate the alternative ways in which mediated

moderation and moderated mediation may be produced, and this

would not occur if a single overall test was the only thing

examined.

Tests of Simple Mediation

In the section where we presented analyses of hypothetical data,

we calculated simple effects to help interpretation. one may want

to actually test these simple effects and, by doing so, to test simple

mediation at various levels of a moderator. In order to do so, one

would need to deviate the moderator not from its mean (as in

centering), but from whatever values are of interest. So for in-

stance, with a dichotomous moderator, one may want to test simple

mediation at each level of the moderator. Here, instead of using a

contrast-coded moderator, one would use codes that give a value of

zero to first one, and then the other, of the two levels of the

moderator (see Judd & McClelland, 1989, for tests of simple

effects in the context of multiple regressions). This would be

equivalent to the use of dummy coding conventions. Consider first

Equations 5 and 6 when we use Mo

a

to code the moderator, with

values of 0 for level A and

1 for level B. (The superscript

indicates the level of the moderator receiving the 0 value). The

resulting equations are:

Me

50

a

51

a

X

52

a

Mo

a

53

a

XMo

a

5

(5a)

Y

60

a

61

a

X

62

a

Mo

a

63

a

XMo

a

64

a

Me

65

a

MeMo

a

6

(6a)

In these equations,

51

a

now equals the simple effect of the

treatment on the mediator for individuals in level A of the Mod-

erator. Likewise,

64

a

equals the simple effect of the mediator on

the outcome for level A. And

61

a

equals the simple residual effect

of the treatment on the outcome, over and above mediation, again

for level A of the moderator. The significance tests associated with

the estimates of these coefficients can be used to test whether those

simple effects differ reliably from zero.

Alternatively we can redefine the moderator as Mo

b

(i.e., Level

B

0; Level A

1):

Me

50

b

51

b

X

52

b

Mo

b

53

b

XMo

b

5

(5b)

Y

60

b

61

b

X

62

b

Mo

b

63

b

XMo

b

64

b

Me

65

b

MeMo

b

6

(6b)

And now

51

b

,

64

b

, and

61

b

represent the simple effects for level

B of the moderator and one can test whether their estimates differ

from zero reliably. In the more general case of a continuous

moderator, one would use the same strategy but would deviate the

moderator from values of interest, for instance one standard devi-

ation above and below its mean.

Although these alternative specifications of the moderator allow

one to estimate and test the simple mediation effects at different

levels of the moderator, it has to be remembered that to demon-

strate moderated mediation it is necessary to show that these

simple mediation effects significantly depend on the moderator. In

other words, it is not sufficient simply to show significant simple

mediation at one level of the moderator but not at another. one

must show that the process of mediation is significantly different

at different levels of the moderator and this is done by testing the

various interaction terms in Equations 5 and 6, as previously

described.

Extensions to Purely Correlational Data

Throughout our presentation we have made the strong assump-

tion that the treatment is an experimentally manipulated one,

permitting causal inference about the overall treatment effect and

its effect on the mediator. This has also permitted us to assume that

the treatment is independent of the moderator, an important con-

dition necessary for the derivation we gave in the Appendix for the

equality underlying both mediated moderation and moderated me-

diation (Equation 7).

In the literature on mediation, we have seen (all too often for our

tastes) researchers take three measured variables, claim a media-

tional model, and believe, because a “test of mediation” (e.g., one

of those recommended by MacKinnon et al., 2002) comes out, that

they have established mediation. But in this case, there is no way

to decide which variable is the treatment whose effect is mediated,

which is the mediator, and which is the outcome. It is not our goal

to encourage these kinds of practices, even though we recognize

that some will use the models that we develop in this article to

claim either mediated moderation or moderated mediation in the

presence of a purely correlational research design. If the research-

ers’ causal model is the correct one, then it stands to reason that the

models we have outlined in this article can in fact be used to

examine issues of mediated moderation and moderated mediation

with purely correlational data. Although the fundamental relation-

ship of Equation 7 would not be expected to hold, the resulting

parameter estimates would be interpretable in a manner consistent

with what we have presented.

Practical Issues

A potentially important issue that we have not previously dis-

cussed concerns the biasing effects of measurement error in the

moderator, mediator, and outcome variables. Unfortunately the

direction of bias due to measurement error is difficult to know,

given the complexities of the models we are dealing with. The

obvious solution is to use multiple indicators of these variables,

weighting them appropriately, as in a structural equation latent

variable approach (SEM). With a dichotomous moderator, this

approach can be implemented by a multiple Group SEM estima-

tion (but this assumes that the moderator is measured perfectly).

861

MEDIATED MODERATION AND MODERATED MEDIATION

---

Page 11

With a continuously measured moderator, there exists no straight-

forward solution for estimating SEM models with latent variable

interactions (see Jaccard & Wan, 1995; Kenny & Judd, 1984; Li et

al., 1998).

One obvious alternative solution is to measure all three variables

(mediator, moderator, and outcome) with multiple indicators

which are then combined or aggregated into index scores, assum-

ing they manifest high internal consistency. Ultimately, for the

sorts of interactive models that underlie the analyses we have

outlined, we suspect that this is the most efficient way to deal with

the measurement error issue. Of course, this approach deals only

with random, rather than systematic, measurement error.

Another practical issue to discuss in estimating these processes

is that of sufficient statistical power. The literature on simple

mediation suggests that some tests of mediation may be relatively

unpowerful (MacKinnon et al., 2002). This may also be true in the

cases we have been considering. The obvious advice is that the

researcher who is interested in examining moderated mediation

and mediated moderation should do whatever he or she can to

maximize statistical power.

We have confined our discussion to cases with a single mediator

and a single moderator. In the case of moderated mediation, it

seems likely that there may exist multiple indirect paths from the

treatment to the outcome, with one mediated pathway being more

potent for some individuals and another being more important for

others. In this case, with potentially collinear mediators (and

moderators), power issues obviously would become particularly

important.

Conclusion

When we first set out to write this article, our goals were to

clearly define both mediated moderation and moderated mediation

and to elaborate in greater detail than had been done previously the

analytic models underlying both. Earlier discussions of these pro-

cesses (Baron & Kenny, 1986; James & Brett, 1984; Wegener &

Fabrigar, 2000) are certainly informative, but it seemed to us that

both processes deserved a more detailed treatment. Thus, we

envisioned ourselves writing a largely didactic piece, laying out

the analytic roadmaps for these alternative analyses.

Although we hope that we have accomplished this, it became

apparent to us, as our ideas (and this article) evolved, that we had

much more to say at a theoretical level about the inherent simi-

larities between the two processes. They both rely on the same

analytic models, they both imply moderated indirect effects of the

treatment variable on the outcome, and they both imply that the

overall moderation of the treatment effect is altered once the

(moderated) mediating process is controlled. At the same time, we

would not want to claim that moderated mediation and mediated

moderation are one and the same. By defining the prototypic

moderated mediation case, we can clearly differentiate between

them. Additionally, mediated moderation clearly does imply that

the overall moderation of a treatment effect is reduced once the

(moderated) mediating process is controlled.

That said, however, we also have argued that if one allows for

the possibility of moderated mediation in cases where there is

overall moderation of the treatment effect, then the distinction

between the two processes can become more a matter of theoret-

ical preference than anything else. Is the emphasis on the reduction

of the moderation of the treatment effect once the (moderated)

mediating process is controlled? Or is the emphasis more on the

fact that there is a moderated mediating process?

The analytic models are clear cut and the two processes can be

defined in the prototypic cases. But these, as we have already said,

represent probably two sides of the same coin. In talking about that

coin, we can either concentrate on describing each side in turn, or

we can recognize that they both define the common coin.

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862

MULLER, JUDD, AND YZERBYT

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Page 12

Appendix

In the case of both mediated moderation and moderated mediation, the

analysis proceeds by estimating three models:

Y

40

41

X

42

Mo

43

XMo

4

(4)

Me

50

51

X

52

Mo

53

XMo

5

(5)

Y

60

61

X

62

Mo

63

XMo

64

Me

65

MeMo

6

(6)

Let us assume that Equations 5 and 6 represent the theoretical models

that are responsible for generating the variance in both the mediator and the

outcome. Accordingly, the model of Equation 4 is a misspecified model. It

then becomes possible to derive the values of the parameters in this

misspecified model in terms of the parameters of Equations 5 and 6.

First, we combine Equations 5 and 6 by substituting for Me in Equation

6 according to Equation 5. This leads to the following result:

Y

60

61

X

62

Mo

63

XMo

64

50

51

X

52

Mo

53

XMo

5

65

50

51

X

52

Mo

53

XMo

5

Mo

6

(6 )

which is given equivalently as:

Y

60

64

50

61

64

51

X

62

64

52

65

50

65 5

Mo

63

64

53

65

51

XMo

65

52

Mo

2

65

53

XMo

2

65 5

6

(6 )

Assuming that X is contrast coded, with an expected value of zero, and

that Mo is normally distributed with a mean of zero and is independent of

X, then it can be shown (Aiken & West, 1991; pp. 177–182; Kenny & Judd,

1984) that the expected covariances of XMo with both Mo

2

and XMo

2

equal

zero. Accordingly, the parameter associated with XMo in the respecified

Equation 6 (

63

64

53

65

51

) must equal its parameter in the

misspecified Equation 4. Accordingly, in the population:

43

63

64

53

65

51

equivalently:

43

63

64

53

65

51

Of course, in any sample of data, the estimated covariances of XMo with

both Mo

2

and XMo

2

will not exactly equal zero and, accordingly, the above

equality will only be approximate.

When Mo is a contrast coded dichotomous variable, then Mo

2

is constant

for all cases (i.e., its variance equals zero). In this case, Equation 6 reduces

to:

Y

60

64

50

65

52

61

64

51

65

53

X

62

64

52

65

50

65 5

Mo

63

64

53

65

51

XMo

64 5

6

(6 )

Accordingly, in this case, the equality holds both in terms of expected

values and in terms of estimated coefficients. In other words, with a

contrast-coded moderator, the following is true of sample estimates:

b

43

b

63

b

64

b

53

b

65

b

51

Received October 11, 2004

Revision received June 20, 2005

Accepted June 20, 2005

863

MEDIATED MODERATION AND MODERATED MEDIATION