Post on 13-May-2023
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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