Integrating Mediation and Moderation to Advance TheoryDevelopment and Testing

Bryan T. Karazsia,1 PHD, Kristoffer S. Berlin,2 PHD, Bridget Armstrong,3 BA, David M. Janicke,3 PHD,

and Katherine E. Darling,1 BA1Department of Psychology, The College of Wooster, 2Department of Psychology, University of Memphis, and3Department of Psychology, University of Florida

All correspondence concerning this article should be addressed to Bryan T. Karazsia, PHD, Department of

Psychology, The College of Wooster, Wooster, OH 44691, USA. E-mail: bkarazsia@wooster.edu

Received March 1, 2013; revisions received September 19, 2013; accepted September 25, 2013

Objective The concepts and associated analyses of mediation and moderation are important to the field of

psychology. Although pediatric psychologists frequently incorporate mediation and moderation in their theo-

ries and empirical research, on few occasions have we integrated mediation and moderation. In this article,

conceptual reasons for integrating mediation and moderation are offered. Method We illustrate a model

that integrates mediation and moderation. Results In our illustration, the strength of an indirect or a

mediating effect varied as a function of a moderating variable. Conclusions Clinical implications of the

integration of mediation and moderation are discussed, as is the potential of integrated models to advance

research programs in pediatric psychology.

Key words BMI; mediated moderation; mediation; moderated mediation; moderation.

The concepts and associated analyses of mediation and

moderation are important to the field of pediatric psychol-

ogy (Holmbeck, 1997). Delineation of mediators and mod-

erators is a mark of maturity of a discipline (Frazier, Tix, &

Barron, 2004; Judd, McClelland, & Culhane, 1995)

because doing so extends research from bivariate relations

to investigations of ‘‘how’’ (i.e., mediation) and ‘‘when’’ or

‘‘for whom’’ (i.e., moderation). More importantly, accurate

identification of mediators and moderators advances clini-

cal practice (Holmbeck, 1997; Rose, Holmbeck, Coakley,

& Franks, 2004). The popularity of incorporating media-

tors and moderators in psychological research increased

dramatically following the seminal work of Baron and

Kenny (1986). Holmbeck (1997) illustrated the impor-

tance of mediators and moderators within the field of pedi-

atric psychology.

Many previous writings on mediation and moderation

focused on the distinction between moderators and medi-

ators, as the terms are often confused and used inter-

changeably (e.g., Frazier et al., 2004; Holmbeck, 1997,

2002; Kraemer, Kiernan, Essex, & Kupfer, 2008; Muller,

Judd, & Yzerbyt, 2005; Preacher & Hayes, 2004; Preacher,

Rucker, & Hayes, 2007; Rose et al., 2004; Shrout &

Bolger, 2002). This emphasis on distinction may be one

reason why scholars often overlook the fact that the early

seminal writings on mediation and moderation include

discussion of how these processes may be integrated

(e.g., Baron & Kenny, 1986; Holmbeck, 1997; Rose et

al., 2004). In what follows, we discuss why and how

integrating mediation and moderation can offer a more

complete approximation of how real-world phenomena

operate.

Mediation and Moderation

A sound understanding of both mediation and moderation

is essential before considering how they can be integrated.

For a thorough overview of these concepts, we refer the

interested reader to reader-friendly and practical illustra-

tions of mediation and moderation specific to the fields

Journal of Pediatric Psychology 39(2) pp. 163–173, 2014

doi:10.1093/jpepsy/jst080

Advance Access publication October 30, 2013

Journal of Pediatric Psychology vol. 39 no. 2 � The Author 2013. Published by Oxford University Press on behalf of the Society of Pediatric Psychology.All rights reserved. For permissions, please e-mail: journals.permissions@oup.com

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of clinical child and pediatric psychology (Holmbeck,

1997, 2002). Mediators and moderators play some role

in the relation between two other variables or constructs,

namely, an independent variable (IV) or predictor and a

dependent variable or criterion. In this document, we

adopt the terms ‘‘predictor’’ and ‘‘criterion,’’ though our

illustrations also apply to experimental designs in which an

IV is manipulated.

A mediator accounts for or explains (at least partially)

the relation between a predictor and a criterion. Mediators

answer the questions of how or why a predictor influences

a criterion. In the context of clinical research when the

predictor is a treatment condition (treatment vs. control),

mediating mechanisms offer explanations of why a treat-

ment produces a causal effect on the outcome of interest.

As a variable that is influenced by a predictor and subse-

quently influences a criterion, the proposed mediator func-

tions as both a criterion and a predictor (see Figure 1a;

Holmbeck, 1997). Although some perspectives espouse

that a significant relation between a predictor and criterion

is a prerequisite for mediation (e.g., Baron & Kenny,

1986), an emerging perspective is that indirect effects

can be identified and relevant even in the absence of a

significant direct relation between a predictor and criterion

(cf. Rucker, Preacher, Tormala, & Petty, 2011; Shrout &

Bolger, 2002).

An example of a mediational model is the Theory of

Planned Behavior (Ajzen, 1991), which posits that future

engagement in some behavior of interest (such as physical

exercise) will depend on one’s perceptions of social norms

(‘‘Do my friends exercise?’’), perceived control of behavior

(‘‘If I wanted to exercise, would I be able to?’’), and atti-

tudes about the target behavior (‘‘Will exercise really ben-

efit me?’’). Ajzen (1991) postulated that these direct effects

are mediated by behavioral intentions. That is, perceptions

of norms, perceived control, and attitudes toward the be-

havior influence one’s behavioral intentions, which in turn

impact likelihood of behavioral engagement.

A moderator is a variable that affects the relation be-

tween a predictor and criterion. As such, figures that depict

moderation often show a path from the moderator to the

arrow that represents the relation from the predictor to the

criterion: The influence is on neither the predictor nor

criterion alone, but rather on the relation between them

(see Figure 1b). A moderator changes the strength or

direction of the relationship between the predictor and

criterion. In interaction terms, the effect of a predictor on

the criterion depends on the level of the moderator. In this

respect, a moderator variable answers the questions of

when or for whom a given relation exists (Holmbeck, 1997).

An example of a moderational model is the work sum-

marized by Schwebel and Barton (2005). A large body of

literature indicates that child temperament interacts with

parenting behaviors to predict pediatric injury risk. One

constellation of a child risk factor is temperament.

Children with approach-oriented tendencies, impulsivity,

inattention, and aggression are at a higher risk of injury

(e.g., Schwebel & Gaines, 2007). Parent supervision has

been shown to moderate the link between child tempera-

ment and injury risk. Children with challenging tempera-

ments are at a high risk of injury generally, but their risk of

injury is attenuated in the context of high parental super-

vision; the presence of adequate parental supervision alters

the link between child temperament and injury risk (e.g.,

Schwebel & Barton, 2005). Stated differently, parental su-

pervision is important for protecting children from injuries,

but it is particularly important for subgroups of children

with very challenging temperaments.

Integrating Mediation and Moderation

There are two notions central to understanding why inte-

grating mediation and moderation can offer a more com-

plete understanding of a phenomenon than focusing solely

on mediation or moderation (Karazsia, van Dulmen, Wong,

& Crowther, 2013). First, mediation is not always a uni-

versal process. Just as bivariate relations may be moderated

by a third variable, so too may the strength of a mediating

relationship change as a function of some other variable.

Second, oftentimes the process(es) through which moder-

ating effects occur may be of considerable interest. Thus,

scholars may wish to identify mediating mechanisms of a

previously identified moderating effect (i.e., through what

mediating processes does moderation occur?).

A review of the use of mediation and moderation in the

Journal of Pediatric Psychology revealed >100 uses of medi-

ation or moderation since the year 2000, but we found only

five examples during this time span that considered the in-

tegration of mediation and moderation (Bearden, Feinstein,

& Cohen, 2012; Guite, Walker, Smith, & Garber, 2000;

Hains et al., 2007; Petty, Davis, Tkacz, Young-Hyman, &

Waller, 2009; Schwebel & Barton, 2005, 2007). Therefore,

the purpose of this article is to advance understanding of

how mediation and moderation can be integrated. We then

offer an illustration of a model in which the strength of a

mediating pathway is moderated by another variable, fol-

lowed by a discussion of ways in which integrating media-

tion and moderation may be useful for advancing research

programs and clinical practice within the field of pediatric

psychology.

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Moderated Mediation

An implicit assumption often made by researchers analyz-

ing basic mediation models is that the mediation process is

universal. That is, it is assumed implicitly that the mediat-

ing mechanisms explain the relation between a predictor

and criterion for the entire population that was sampled.

However, it is plausible that the strength of mediating path-

ways vary as a function of some other individual difference,

such as symptom severity or demographic characteristics.

Importantly, a proposed moderator variable may alter the

direction or strength of the path between the predictor and

criterion, the predictor and mediator (i.e., path ‘‘a’’), or the

mediator and criterion (i.e., path ‘‘b’’) (Hayes, 2013a).

In the original formulation of the previously men-

tioned Theory of Planned Behavior (Ajzen, 1991), the

mediating role of intentions was thought to be universal.

However, subsequent research revealed that not everyone

who intends to engage in a behavior actually acts on these

intentions. Rhodes and colleagues (e.g., Rhodes, Corneya,

& Hayduck, 2002; Rhodes, Corneya, & Jones, 2005) dem-

onstrated that personality constructs moderate the link

between intentions and actual behavior engagement.

Specifically, individuals higher in conscientiousness are

more likely to engage in physical exercise after reporting

strong intentions to do so (Rhodes et al., 2002). Thus,

intentions mediated the strength of relationship between

hypothesized predictors and actual exercise behavior, but

the strength of the mediation effect varied as a function of

one’s self-reported conscientiousness. This is an example

of mediation that is moderated (see Figure 1c).

Figure 1. (a) Conceptual model of mediation. Note. The path between predictor and mediator is often referred to as path ‘‘a’’; the path between

mediator and criterion is often referred to as path ‘‘b.’’ (b) Conceptual model of moderation. (c) Example of moderated mediation (i.e., mediation

that is moderated). (d) Example of mediated moderation (i.e., moderation that occurs through a mediating variable). Note. Figure adapted with

permission from Schwebel and Barton (2005).

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Mediated Moderation

The implicit assumption of a basic moderation model is

that the moderating effect on the criterion is direct.

However, just as the path of a predictor on some criterion

of interest may be mediated by one or multiple variables, so

too may moderating paths occur through one or more me-

diating variables. Schwebel and Barton (2005) summarized

existing literature on children’s unintentional injury risk to

propose a conceptual model explaining how parent and

child risk factors interact to predict pediatric injury risk.

Their model is an excellent illustration of how mediation

and moderation can be integrated to develop testable hy-

potheses on the roles of multiple influences on behavior

(see Figure 1d). Schwebel and Barton (2005) hypothesized

that the interaction between child temperament and paren-

tal supervision described earlier is not direct. That is, the

link between the parent–child interaction and pediatric

injury risk may be explained by the way in which children

interact with stimuli in their environment. Children who

are not being supervised and who demonstrate difficult

temperaments are much more likely to overestimate their

physical abilities (i.e., they think they can do more physi-

cally than they actually can), which in turn places them at

risk of incurring an injury. However, when a child with a

challenging temperament is in a context where a caregiver

is offering adequate supervision, the child’s estimations of

physical abilities tend to be more accurate, thereby decreas-

ing injury risk. Importantly, subsequent empirical research

supported this model (Barton & Schwebel, 2007). We

should note that some authors have recently suggested

that models of mediated moderation be reframed as

models of moderated mediation (see Edwards, 2009;

Hayes, 2013a).

Multiple Mediators and Moderators

Importantly, neither mediated moderation nor moderated

mediation applies only to cases with a single mediator and

moderator. In any given model, multiple mediators or

moderators may exist. Revisiting the application of the

Theory of Planned Behavior to physical exercise, Rhodes

and colleagues (2005) have actually demonstrated that dif-

ferent personality traits moderate different pathways in the

model. For example, components of extraversion appear to

moderate the association between perceived behavioral

control and one’s intentions to engage in exercise behav-

iors. Although this research was conducted with adult pop-

ulations, we illustrate it here because of the incorporation

of multiple moderators and because it has been suggested

that this theory be extended to pediatric populations

(Wilson & Lawman, 2009).

Statistical Analysis

The concepts of mediation, moderation, and their integra-

tion enable the development of seemingly infinite plausible

applications to specific areas of research, and they can be

challenging to analyze appropriately. Holmbeck’s (1997,

2002) seminal works on the analysis of mediation and

moderation make this apparent. In a basic moderational

model, regression results are obtained, and then ‘‘post hoc

probing’’ procedures are used to investigate the modera-

tion effect. Post hoc probing involves creation of a regres-

sion equation and then estimating the predicted value of

the criterion at various levels of the moderator (for a com-

plete overview of post hoc probing, see Holmbeck, 2002).

For assessment of the indirect or mediating relations,

Baron and Kenny (1986) advocated for a four-step process

wherein the relation between the predictor and criterion is

established (step 1), followed by the relation between the

predictor and hypothesized mediator (step 2), and the

relation between the mediator and the outcome (step 3).

In the final step (step 4), the predictor and mediator are

entered simultaneously, and mediation is demonstrated if

the path between the predictor and criterion decreases sub-

stantially. Note that analysis of step 1 may not be necessary

(see Shrout & Bolger, 2002). These steps are often referred

to as an indirect assessment of mediation. An oft-used al-

ternative or supplement to this approach is the widely used

Sobel test (Sobel, 1982), which computes the indirect

effect by multiplying the measured paths from predictor

to mediator (path ‘‘a’’) and from the mediator to criterion

(path ‘‘b’’) (i.e., the indirect or mediating effect is quanti-

fied directly). When this path differs from zero, then it can

be concluded that an indirect or mediation relation exists.

While these analytic procedures are used widely,

methodologists have raised concerns about them (e.g.,

Hayes, 2009). Two of these concerns include statistical

power within the Baron and Kenny (1986) approach and

a nonnormal sampling distribution within the Sobel test.

With respect to statistical power, Preacher and Hayes

(2004, 2008) noted that in large samples, the likelihood

of the path between the predictor and criterion becoming

nonsignificant in Step 4 of the Baron and Kenny approach

is small. Thus, scholars may conclude that there is no

mediation when in fact it exists (Type II error). Regarding

the Sobel test, Preacher and Hayes (2004, 2008) explained

that the sampling distribution of the product of ‘‘a’’ and

‘‘b’’ paths is usually nonnormal, particularly in small sam-

ples, again influencing the accuracy of conclusions based

on this test.

Importantly, tools for overcoming these limitations

exist. One such tool is a nonparametric bootstrapping

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procedure that offers a direct test of mediation (Preacher &

Hayes, 2004, 2008). As an alternative to the Sobel test, this

bootstrapping procedure is accomplished by taking a large

number of samples (n > 1,000) from the original data and

computing the product of paths ‘‘a’’ and ‘‘b.’’ A confidence

interval can then be generated around the point estimate of

the product of ‘‘a’’ and ‘‘b’’ (for specific details of this

bootstrapping procedure and how the confidence interval

and point estimates are calculated, please consult Preacher

& Hayes, 2004, 2008). When this confidence interval does

not contain zero, it can be concluded that there is an in-

direct or mediating effect. As discussed by Hayes (2009)

and colleagues (Preacher & Hayes, 2004, 2008), this

bootstrapping approach overcomes limitations of the

widely used Baron and Kenny (1986) and Sobel (1982)

approaches, thus yielding results that are more accurate

and less influenced by sample size (Hayes, 2009;

Preacher & Hayes, 2004, 2008).

An Illustration

Here, we provide a demonstration of how the integration of

mediation and moderation can be applied in research rel-

evant to pediatric psychologists. The prevalence of pediat-

ric obesity and overweight has increased dramatically in the

past 30 years, with recent estimates suggesting that 33.6

and 18.4% of US youth aged 12–19 years are currently

considered overweight and obese, respectively (Ogden,

Carroll, Kit, & Flegal, 2012). Studies have shown that

having a higher body mass index (BMI), and hence a

body that deviates to a greater extent from what is consid-

ered ideal, is associated with more body image dissatisfac-

tion in children and adolescents (Taylor & Altman, 1997).

Given the substantial health and psychosocial risks associ-

ated with obesity (e.g., Goran, Ball, & Cruz, 2003), there is

significant pressure on obese adolescents to lose weight,

and on their parents to help them lose weight. Although

increased child weight status warrants a degree of parental

concern and may motivate parents to implement strategies

to reduce or regulate child weight, some well-intentioned

parental practices may exacerbate the problem. Several

studies have highlighted the role of maternal encourage-

ment to diet in multiple negative psychosocial outcomes,

such as disordered eating behaviors and body dissatisfac-

tion (van den Berg, Keery, Eisenberg, & Neumark-Sztainer,

2010).

Although it is clear that child BMI, maternal encour-

agement to diet, and child body dissatisfaction are related,

less attention has been paid to elucidating a model that

depicts these relationships. For example, maternal

encouragement to diet may mediate the association be-

tween child BMI and child body dissatisfaction. Further,

it has been proposed that heavier parents may express their

own body dissatisfaction, therefore providing opportunities

for children to emulate these behaviors (Davidson & Birch,

2001). Therefore, the current study hypothesized that the

indirect relation between child BMI and child body dissat-

isfaction will be moderated by parent BMI (i.e., moderated

mediation). See Figure 2 for the graphical illustration of

this hypothesized model.

MethodParticipants

Participants were 117 children/adolescents between the

ages of 8 and 17 years and a parent or legal guardian at-

tending a regularly scheduled acute care or annual checkup

appointment at a pediatric primary care clinic. Table I pre-

sents demographic data and descriptive statistics for all

participants in present analyses.

Anthropometrics

A medical team assessed child height (cm) and weight (kg)

during the primary care visit. BMI z-scores were calculated

using this information (Kuczmarski et al., 2002). Parent

BMI was calculated using parent self-reports of height

and weight.

Maternal Encouragement to Diet

Youth perception of maternal encouragement to diet was

measured using the question ‘‘[Over the past year] My

mother encouraged me to diet to control my weight.’’

Responses were made using a 4-point Likert scale ranging

from ‘‘strongly disagree’’ to ‘‘strongly agree,’’ with higher

scores indicating more encouragement to diet. Similar one-

item questions have been used to assess encouragement to

diet in previous studies (Bauer, Laska, Fulkerson, &

Neumark-Sztainer, 2011) and have been shown to be as-

sociated with weight loss strategies (McCabe & Ricciardelli,

2005) and to distinguish between women with and with-

out bulimia (Moreno & Thelen, 1993).

Body Dissatisfaction

The Children’s Body Image Scale (Truby & Paxton, 2002)

consists of pictorial scales for boys and girls, containing

seven pictures of varying body size. Children were asked to

identify the body figure most like their own (perceived fig-

ures) and the body figure they would most like to have

(ideal figure). Following scoring instructions described by

Truby and Paxton (2002), the difference between perceived

and ideal figures was used as an index of body

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dissatisfaction. Positive values result when the perceived

figure is larger than the ideal figure and thus corresponds

with a desire for a smaller body size. Negative values result

when the ideal figure is larger than the perceived figure and

corresponds with a desire for a larger body size. Previous

research demonstrated good construct validity and test–

retest reliability of this scale in samples of youth aged �7

years (Truby & Paxton, 2008).

Results

Preliminary screening revealed that all variables were suffi-

ciently normally distributed. To evaluate the model in

Figure 2, we used a PROCESS macro developed by Hayes

(2013a) for SPSS (please note that the same package of

statistics is also available for SAS). A description and

visual depiction of each model that can be tested with

PROCESS is available from Hayes (2013b). Basically, the

macro is based on Ordinary Least Squares (OLS) regres-

sion, and it incorporates aforementioned bootstrapping

procedures for investigating mediation. The current analy-

sis was conducted using 5,000 bootstrapped samples. One

benefit of PROCESS for the present analyses is that the

macro automatically computes post hoc probing for mod-

erating effects. The output will be straightforward to re-

searchers familiar with OLS regression (see Appendix),

with a summary of the model offered first, then the overall

regression results, followed by post hoc probing.

In our analyses, the model was significant,

F(2, 116)¼ 15.62, p < .001, accounting for 21.2% of var-

iance in body dissatisfaction. With regard to predicting

the outcome variable, maternal encouragement to diet

(unstandardized coefficient¼ .29, p¼ .04) as well as child

BMI z-score (unstandardized coefficient¼ .47, p < .001)

emerged as a significant predictors of child body dissatis-

faction. Evidence of moderation of the indirect effect by

parent BMI was found in the significant interaction between

child BMI z-score and parent BMI predicting maternal en-

couragement to diet (unstandardized coefficient¼ .03,

p < .01), indicating that parent BMI moderated the relation-

ship between youth BMI z-score and maternal encourage-

ment to diet. Given that the ‘‘a’’ path of the mediation

model is moderated, this means that the indirect effect

will also be moderated. Results were then evaluated at five

levels of parent BMI (corresponding to the 10th, 25th, 50th,

75th, and 90th percentiles in our sample), and a confidence

interval was generated at each level of the proposed mod-

erator. Where the confidence interval does not contain zero,

it can be concluded that the indirect or mediating effect is

significant. See Table II for the post hoc probing results at

the different parent BMI levels.

In our model, maternal encouragement to diet emerged

as a significant mediator between BMI z-score and body

dissatisfaction. However, as can be seen in Table II, this

mediating effect varied as a function of the proposed mod-

erator. In other words, the mediating effect was not a uni-

versal process. Specifically, the indirect effect of BMI z-score

on body dissatisfaction through maternal encouragement to

diet was significant for youth who had parents who were

overweight or obese (i.e., parent BMI > 25). However, ma-

ternal encouragement to diet was not a significant mediator

of the relationship between BMI z-score and child body

Figure 2. Hypothesized model depicting maternal encouragement to diet as mediator between child body mass index (BMI) z-score and child

body dissatisfaction; it is hypothesized that parent BMI moderates this relationship.

Table I. Demographics and Descriptive Statistics of the Study Sample

Variable Mean (SD) Range

1. BMI z-score 1.01 (1.12) �1.77, 3.27

2. Child age 11.67 (2.57) 8, 17

3. Parent BMI 31.91 (8.4) 18.89, 53.74

4. Maternal encouragement

to diet

1.96 (1.06) 1, 4

5. Body dissatisfaction 0.783 (1.57) �2, 8

Note. BMI¼ body mass index.

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dissatisfaction when parents were not overweight or obese

(i.e., parent BMI <25).

Discussion

Holmbeck, Zebracki, and McGordon (2009) recently of-

fered six recommendations for guiding pediatric psycholo-

gists in their applied statistical analyses. The concepts and

associated statistical analyses of mediation, moderation,

and their integration directly address three of these recom-

mendations: (a) ‘‘. . . go beyond examining bivariate

associations between predictors and outcomes . . .’’; (b)

‘‘. . . examine the influence of moderators . . .’’; (c)

‘‘. . . begin to theorize about variables that may explain

(or mediate) . . .’’ (p. 67). While basic mediation and

moderation analyses also fulfill these recommendations,

we believe that pediatric psychologists can advance con-

ceptualizations of their research areas by integrating medi-

ation and moderation. That is the point that we wish to

emphasize here.

Advances in statistical analyses of mediation, modera-

tion, and their integration have been developed over the

past decade (e.g., Hayes, 2013a). We believe these analyt-

ical strategies will only be fruitful in the context of well-

articulated conceptual paradigms. By integrating mediation

and moderation, pediatric psychologists will be able to ad-

vance their research questions. For example, where media-

tion is well-established, researchers can begin asking if the

mediation process is universal, and if not, what factors

might moderate the strength of the mediating effects.

Where moderation is established, researchers can begin ex-

amining the processes through which moderation occurs.

Considering the integration of mediation and moder-

ation can also have important clinical applications. The

clinical implications of the demonstration in this study

include assessing and addressing maternal encouragement

to diet behaviors and educating parents about effective

ways to support healthy eating and exercise habits for

adolescents. Additionally, practitioners should take into

account parent weight when assessing maternal encourage-

ment to diet, as it appears that parent weight is influential

in predicting weight-related behaviors and attitudes. Had

mediation been examined absent from the context of the

proposed moderator, we may have concluded erroneously

that the predictor-criterion relationship was relevant to all

children. Instead, our analyses revealed that the context

within which a child lives, which in this case was defined

by parental weight status, plays an important role in the

demonstrated relationships. Further, this finding supports

current trends in obesity interventions, which have inte-

grated parent weight management into family lifestyle in-

tervention programs aimed at ultimately addressing

childhood obesity (Epstein, 1996). More broadly, consid-

ering potential moderators in the context of established

meditational models will offer a framework for tailoring

interventions to specific subpopulations.

Limitations and Additional Considerations

The limitations of analyses of mediation, moderation, and

their integration are linked inextricably to the research

design underlying the analytical techniques. In our analy-

ses, the data were cross-sectional, which may inflate esti-

mations of mediation and precludes any conclusions of

directionality (Maxwell & Cole, 2007). Causality cannot

be assumed in the absence of experimental manipulation

(which would actually be impossible for the predictor in

our analyses). Further, assessment of the mediating vari-

able was based on a single item that may not represent true

properties interval or ratio data.

We need to note that the concepts and methods dis-

cussed in this article are not new. Therefore, there are no

new assumptions or sample size issues to discuss. One

benefit of the bootstrapping approach to moderation anal-

yses is that it overcomes the requirement of ‘‘large’’ sample

sizes of the Sobel approach to assessing mediation. That

said, our analysis was still based on OLS regression, and

thus corresponding assumptions and sample size issues still

apply. Specific to mediation analyses, Fritz and MacKinnon

(2007) offered empirically based estimates of sample sizes

required to achieve adequate statistical power (which they

operationalize as 0.8). Naturally, the sample size required to

demonstrate significant results will vary as a function of

effect size, with larger samples being necessary when the

strength of relations among variables is smaller. According

to Fritz and MacKinnon (2007), sample sizes necessary to

achieve adequate power to detect mediating effects ranges

can vary greatly. They report that only 34 participants are

necessary when bootstrapping techniques are used in the

context of strong associations (b¼ .59) between both the

Table II. 95% BC Confidence Intervals of the Indirect Effect at the

10th, 25th, 50th, 75th, and 90th Percentiles of the Moderator

Parent BMI Point estimate

BC 95% bootstrapped CIa

Lower Upper

21.4644 0.0670 �0.0344 0.2261

24.9956 0.1072 0.0131b 0.2691

29.2000 0.1549 0.0464b 0.3209

34.4531 0.2146 0.0642b 0.3919

44.6240 0.3301 0.0861b 0.5759

Note. BMI¼ body mass index.aBC confidence intervals are bias-corrected.bConfidence intervals that do not contain zero are deemed to be significant.

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predictor and mediator (path ‘‘a’’) and between the medi-

ator and criterion (path ‘‘b’’). However, in the context of

small associations (b¼ .14) for both the ‘‘a’’ and ‘‘b’’ paths,

>500 participants are required when adopting the Baron

and Kenny (1986) approach for assessing mediation.

Notably, sample size requirements reported by Fritz and

MacKinnon (2007) were always smaller when bootstrap-

ping methods were used, but samples >450 may still be

necessary when the strength of relations among variables is

small. Naturally, more complex models that incorporate

multiple mediators and moderators will require larger

sample sizes.

In addition to sample size issues, researchers should

be cognizant of statistical assumptions that underlie ana-

lytical approaches that they adopt. In our regression-based

illustration, the same assumptions of OLS regression

remain relevant. These include normality of residuals, ho-

moscedasticity, and linearity. OLS regression tends to be a

fairly robust technique when these assumptions are vio-

lated, particularly when the violations are relatively minor

(e.g., Hayes, 2013a; Tabachnick & Fidell, 2013).

With respect to our adoption of the PROCESS macro,

we would also like to discuss briefly some of the available

extensions of PROCESS, as well as some of its limitations.

We examined a continuous criterion in this illustration, but

the macro is fully functional with dichotomous outcomes as

well (i.e., logistic regression). Pediatric psychologists are

often faced with distributions that are neither dichotomous

nor normally distributed (such as ordinal data or count

outcomes; Karazsia & van Dulmen, 2008), and in such

situations, the regression analyses that incorporate media-

tion and or moderation will need to be conducted with an

appropriate estimation method (e.g., Poisson regression,

Probit regression) not currently available in PROCESS.

When researchers test models with multiple outcome vari-

ables, PROCESS can be adapted accordingly (see Hayes,

2013a). However, PROCESS currently handles models for

which the criterion is observed. This limitation is relevant to

pediatric psychologists who may model latent (unobserved)

variables. Alternative analytic approaches, such as

Structural Equation Modeling (SEM), offer the flexibility

for testing such models (see Nelson, Aylward, & Steele,

2008, for overview of the relevance of SEM to pediatric

psychologists). Although modeling interaction terms can

introduce a degree of complexity in SEM (Edwards,

2009), step-by-step resources applicable to SEM software

do exist for examining both mediation and moderation

(Little, Card, Bovaird, Preacher, & Crandall, 2007).

In light of limitations of our demonstration in this

article, we hope that our illustration inspires pediatric psy-

chologists to consider ways in which their research pro-

grams and clinical practices might be advanced by being

cognizant of the ways in which mediation and moderation

may be integrated. The reader interested in integrating me-

diation and moderation in her own work is encouraged to

consult sources referenced throughout this document.

Funding

Conflicts of interest: None declared.

Appendix

Run MATRIX procedure:

**************** PROCESS Procedure for SPSS Release 2.041 ****************

Written by Andrew F. Hayes, Ph.D. http://www.afhayes.com ************************************************************************** Model = 7 Y = BodyDiss X = BMIZHD M = MomETDHD W = Parent_B

Sample size 117 ************************************************************************** Outcome: MomETDHD

Model Summary R R-sq F df1 df2 p .5687 .3234 18.0028 3.0000 113.0000 .0000

Model coeff se t p LLCI ULCI constant 2.1069 .4255 4.9520 .0000 1.2640 2.9498 BMIZHD -.4557 .2939 -1.5503 .1239 -1.0380 .1266 Parent_B -.0216 .0142 -1.5223 .1307 -.0497 .0065 int_1 .0293 .0091 3.2013 .0018 .0112 .0474

(Continued)

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Direct effect of X on Y Effect SE t p LLCI ULCI .4510 .1369 3.2952 .0013 .1799 .7221 Conditional indirect effect(s) of X on Y at values of the moderator(s)

Mediator Parent_B Effect Boot SE BootLLCI BootULCI MomETDHD 21.4644 .0670 .0631 -.0344 .2261 MomETDHD 24.9956 .1072 .0627 .0131 .2691 MomETDHD 29.2000 .1549 .0686 .0464 .3209 MomETDHD 34.4531 .2146 .0836 .0642 .3919 MomETDHD 44.6240 .3301 .1245 .0861 .5759

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******************** DIRECT AND INDIRECT EFFECTS *************************

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