MULTIVARIATE BEHAVIORAL RESEARCH, 42(1), 185–227
Copyright © 2007, Lawrence Erlbaum Associates, Inc.
Addressing Moderated Mediation
Hypotheses: Theory, Methods,
and Prescriptions
Kristopher J. Preacher
University of Kansas
Derek D. Rucker
Northwestern University
Andrew F. Hayes
The Ohio St ate University
This article provides researchers with a guide to properly construe and cond uct
analyses of conditional indirect effects, commo nly known as moderated media-
tion effects. We disentangle conflicting definitions of moderated mediation and
describe approach es for estimating and testing a variety of hypotheses involving
con ditional indirect effects. We introduce standard errors for hypothesis testing and
con struction of confidence intervals in large samples but advocate that res earchers
use bootstrapping whenever possible. We also des cribe methods for p robing sig-
nificant conditional indirect effects by employing direct extensions of the simple
slopes me thod and John son-Neyman technique for p robing s ignificant interactions.
Finally, we provide an SPSS macro to facilitate the implementation of the recom-
mended asymptotic and bootstrapping methods. We illustrate the application of
these methods with an example drawn from the Michigan Study of Adolescent
Life Transitions, showing that the indirect e ffect of intrinsic student interest on
mathematics performance through teac her perceptions of talent is moderated by
student math self-concept.
Corresponde nce con cerning this article should be addressed to Kristopher J. Preache r, University
of Kansas, Department of Psychology, 1415 Jayhaw k Boulevard, Room 426, Lawrence, KS 66045-
7556. E-mail: preacher@ku.edu
185
186 PREACHER, RUCKER, HAYES
Mediation, or an indirect effect, is said to occur when the causal effect of an in-
dependent variable (X) on a dependent variable (Y ) is transmitted by a mediator
(M ). In other words, X affects Y because X affects M , and M , in tur n, affects
Y . Mediation effect and indirect effect are often used interchangeably (as they
are here), alt hough some authors have drawn distinctions between them (e.g.,
Holmbeck, 199 7). Methods to assess mediation became particularly p opular in
psychology after publi cations by Judd and Kenny (1981) and Baron and Kenny
(1986). Today, examples of this simple typ e of mediation effect are so numer-
ous that one can open an issue of virt ually any major social science jou rnal and
find at least one test of mediation. For example, Fredrickson, Tugade, Waugh,
and Larkin (2003) hypothesized that positive emotions mediate the effect of
psychological resilience on residual resources (lif e satisfaction, optimism, and
tranquility). Calvete and Cardenoso (2005) demonstrated that the effect of gender
on depressive symptoms is mediated by need for acceptance, positive thinking,
self-focused negative cognitions, and negative problem orientation. Hund reds
of new mediat ion hypotheses are proposed and t ested in the literature every
year. In response to high demand for appropriate metho ds, a large literature now
exists that detail s methods by which mediation may be assessed in models of
ever-increasing complexity.
It is often of critical interest to determine whether or not a mediation effect
remains constant across different contexts, groups of individuals, and values of
the independent variable. For example, perhaps M mediates the X ! Y r el a-
tionship for boys but not for girls. More generally, the strength of an ind irect
effect may depend linearly upon the value of a moderator (W ) that is mea-
sured on an interval or ratio scale. Of course, testing such additional hypotheses
requires th e development of appropriate statistical tests. In recogniti on of th is
requirement, this article aims to educate and help researchers with regard to
how to analyze indirect effects that depend on other variables in the mod el un-
der scrutiny. There are several ways in which hypotheses combining mediation
and moderation may be modeled. Various sources refer to some of these effects
as mediated moderation or moderated mediation (e.g., Baron & Kenny, 1986),
but there is a fair amount of confusion over precisely what pattern of causal
relationships constitutes each kind of effect and how to assess th e presence,
strength, and significance of these effects. For simplicity, we gather such effects
under the general rubric cond itional indirect effects. We define a conditional
indirect effect as the magnitude of an indirect effect at a particular value of a
moderator (or at particular values of more than one mod erato r).
Examples of conditional indirect effect hy potheses are common in the litera-
ture. For example, the mediation effects found by Calvete and Cardenoso (2005)
mentioned previousl y were further hypothesized to be moderated by age. Al-
though studies investigating mediation, mod eration, or both are abundant, fo rmal
tests of conditional indirect effects are less common. We surmise that conditional
ADDRESSING MODERATED MEDIATION HYPOTHESES 187
indirect effects may be relevant and interesting in many settings, but generally
may go unnoticed and unexamined because clear methods have not yet been
articulated in the literature for investigating whether (and, if so, how) an indi-
rect effect varies systematically as a function of another variable. In addition
to introducing methods that can be used to investigate conditional indirect ef-
fects, we illustrate these methods using an example d rawn fr om the Michigan
Study of Adol escent Life Transition s (MSALT). Specificall y, we show how the
indirect effect of intrinsic student interest in math (the independent variabl e) on
mathematics perfor mance (the dependent variable) through teacher perceptions
of talent (a mediator) is moderated by stu dent math self-concept.
OVERVIEW OF OBJECTIVES
We have several objectives in this article. First, consistent with recent efforts
to disentangle confusion over moderated mediation (e.g., Muller, Judd, & Yzer-
byt, 2005), we provide a guide to help resolve the confusion that persists in
the literature regarding confli cting definitio ns of moderated mediati on. Second,
as called for by Muller et al. (2005), we provide intuitive approaches fo r test-
ing hypotheses of conditional indirect effects. To this end, we introduce stan-
dard errors (SEs) for various conditional indirect effects and discuss the utility
of bootstrapping and normal-theory methods. Thi rd, we describe methods for
probing moderated mediation effects by employing direct extensions of methods
familiar to many researchers in the context of probing significant interactions.
Specifically, we implement a direct extension of the si m ple slopes procedure
(Aiken & West, 1991) to probe moderated mediation effects. We also suggest
that the regions of significance approach (or the Johnson-Neyman technique)
be extended to probing moderated mediation effects, identifyin g ranges of the
moderator for which an indirect effect i s statistically significant. Finally, we
provide an SPSS macro to facilitate the implementation of the recommended
asymptotic and bootstrapping methods, illustrating its use with a real-world ex-
ample. Our procedures are illustrated within a regression or path- analytic frame-
work (with no latent variables), but our strategies can be easily applied in more
complex structural equation models (SEMs). This article is aimed primarily at
the appli ed researcher to whom the methods will be most useful, but there is
also much that will be of interest to methodologists. The ultimate goal and
contribution of this arti cl e is to offer researchers and practitioners an intuitive
guide to constru e and conduct complex mediation analyses involvi ng conditi onal
indirect effects.
Before discussing conditional indirect effects, we briefly review simple me-
diation and moderation and discuss methods traditionally used to investigate
their presence. We then present methods for assessing the presence, strength,
188 PREACHER, RUCKER, HAYES
and significance of conditional indirect effects to facilitate the understanding o f
moderated mediation.
SIMPLE MEDIATION
Mediation analysis permits examination of process, al lowing the researcher to in-
vestigate by what means X exerts i ts effect on Y . Although systems of equations
linking X to Y through multiple mediators are possible to specify (MacKinn on,
2000), we focus on models in which o nly a single mediator (M ) is posited. We
term this three-variable system simple mediati on. Simple mediation is illustrated
in the path diagram in Figure 1. In the figure, a
1
refers to the (unstandardized)
slope coefficient of M regressed on X, and b
1
and c
0
denote the conditional
coefficients of Y regressed on M and X, respectively, when both are included
as simultaneous predictors of Y . Letting c represent the effect of X on Y in the
absence of M , the indirect effect is traditionall y quantified as c c
0
, which is
ordinarily equivalent to a
1
b
1
(MacKinnon, Warsi, & Dwyer, 1995).
The coefficients previously described are commonly obtained using least-
squares regression. Specifically, coefficients a
1
and b
1
may be obtained from
the regression equations:
M D a
0
C a
1
X C r (1)
Y D b
0
C c
0
X C b
1
M C r (2)
where a
0
and b
0
are intercept terms and r is a regression residual. The coeffi-
cients a
1
and b
1
are then used to assess the presence, strength, and significance
of the indirect effect of X on Y via M . All of the models considered here
FIGURE 1 Simple mediation.
ADDRESSING MODERATED MEDIATION HYPOTHESES 189
may be assessed using SEM software or standard least-squares or maximum
likelihood regression routines.
ASSESSING THE PRESENCE, STRENGTH, AND
SIGNIFI C ANCE OF INDIRECT EFFECTS
MacKinnon and colleagues (MacKinnon, Lockwood, Hoffman, West, & Sheets,
2002; MacKinnon , Lockwood , & Williams, 2004) r eview a variety of strategies
to gauge th e extent and signi ficance of indi rect effects. The most popular of
these strategies are the causal steps strategy, distribution of the prod uct strate-
gies, resampling or bootstrapping strategies, and various p roduct of coefficients
strategies. We do not dwell o n all four approaches here. The causal steps strat-
egy suffers from low power and does not directly address the hypothesis of
interest (MacKinnon et al., 2002 ). Most methodologists agree that the prod uct
term a
1
b
1
, the quantity of interest in the remaining three strategies, is a proper
quantification of the indi rect effect. The distribution of the product strategy is
probably the most accurate analytic method available for determining the signif-
icance of, and confidence intervals (C Is) for, a
1
b
1
in simpl e mediation models
(MacKinnon et al., 2004). However, extending this method to the study of con-
ditional indirect effects will involve extensive analytic work and programming
because the expressions for condit ional indir ect effects are more complex than
those for simple mediation effects. We therefore limit our attention to the prod-
uct of coefficients and bootstrapping strategies. We briefly explore each of these
strategies in turn because each h as implications for how con ditional indirect
effects can be appropriately assessed.
Product of Coefficients Strat egies
An ind irect effect is conceptuali zed as a popu lation quantity that must b e es-
timated in th e sample. Sample indirect effects are quantified as products of
sample estimates of regression coefficients. I n the case of simple mediation, the
point estimate of the indirect effect is Oa
1
O
b
1
, where the hat notation denotes a
sample estimate of a population quantit y. Under the assumpti ons of maximum
likelihood and ordinary least sq uares, Oa
1
and
O
b
1
are asympto tically independent
and normally distributed. When i t is further assumed that the product Oa
1
O
b
1
is
normally dist ributed, the exact SE (Aroian, 1947; Craig, 1936; Goodman, 1960)
is:
SE
Oa
1
O
b
1
D
r
Oa
2
1
s
2
O
b
1
C
O
b
2
1
s
2
Oa
1
C s
2
Oa
1
s
2
O
b
1
(3)
