A Primer on Moderated Mediation Analysis: Exploring Logistics Involvement in New Product Development

• Author: Hanieh Sardashti,Roger Calantone,Joyce (Feng) Wang,Jason W. Miller,Judith M. Whipple
• Published date: 01 September 2017
• Date: 01 September 2017
• DOI: http://doi.org/10.1111/jbl.12166

A Primer on Moderated Mediation Analysis: Exploring Logistics

Involvement in New Product Development

Roger Calantone, Judith M. Whipple, Joyce (Feng) Wang, Hanieh Sardashti, and

Jason W. Miller

Michigan State University Broad College of Business

Theorizing and empirically testing moderated mediation hypotheses allows logistics and supply chain management (L&SCM) scholars to

extend the boundaries of our current understanding by examining how, when, and why relationships arise between constructs central to

our theories. However, while moderated mediation analyses can enrich theory in L&SCM, they are few in number, likely due to the complexi-

ties associated with their execution. In this article, we provide a didactic treatment for executing moderated mediation analysis. We do so using

primary data regarding logistics involvement in new product development. In the hopes of spurring greater application of moderated mediation

in L&SCM, we devise a series of recommendations that guide scholars through the process of conducting such analyses. These recommenda-

tions extend prior treatments by explaining how to address challenges associated with devising theories to undergird moderated mediation

hypotheses, measuring constructs using multiple indicators, providing guidance for detecting influential cases that can unduly affect results, and

integrating what results should be reported.

Keywords: structural equation modeling; moderation; mediation; moderated mediation; simultaneous equations

INTRODUCTION

Logistics and supply chain management (L&SCM) scholars

increasingly test mediation hypotheses in an effort to understand

the processes through which relationships arise in experimental

and observational settings (Malhotra et al. 2014; Rungtusanatham

et al. 2014). One type of mediation hypothesis garnering

increased attention is moderated mediation that examines how

the indirect effect of a focal predictor on an outcome variable,

through one or more mediators, is contingent on one or more

moderators (Edwards and Lambert 2007; Preacher et al. 2007).

For example, Peinkofer et al. (2015) examine how the indirect

effect of inventory availability level on satisfaction through

expected customer competition was contingent on sales prone-

ness and a measure of item stock availability. Testing moderated

mediation hypotheses provides one way for scholars to push the

boundaries of L&SCM knowledge by probing both the processes

through which relationships arise (Rungtusanatham et al. 2014)

and, simultaneously, examining the boundary conditions of these

processes (Malhotra et al. 2014).

One of the central challenges L&SCM scholars face with testing

moderated mediation hypotheses is that existing didactic treat-

ments (1) rely on automated procedures, such as the PROCESS

macro (Hayes 2013), that limit the types of models that can be

tested; and (2) present moderated mediation in a cursory manner

(Malhotra et al. 2014). Furthermore, existing presentations, such

as Preacher et al.’s (2007) seminal work, do not provide a unified

treatment of various moderated mediation models and, instead,

utilize different research settings as contexts for these distinct mod-

els, making comparisons across the models more difficult to assess.

Extant works also give little guidance for conducting these analy-

ses when measuring constructs using multiple indicators. For

example, if constructs are reflective and measured by multiple

items, should observed measures be created by averaging indica-

tors, calculating factor scores, or applying nonlinear structural

equation modeling techniques to calculate moderation effects at

the latent variable level? Similarly, how should formative con-

structs be used? Last, the moderated mediation literature has given

little heed to how scholars should investigate the presence of

influential cases that may unduly affect results. This issue is parti-

cularly important given that interaction effects, which are central

to moderated mediation analysis, can be sensitive to influential

cases (Cohen et al. 2003). Apart from these statistical issues, the

extant literature gives limited coverage for devising theoretical

explanations for moderated mediation hypotheses.

This article seeks to provide an accessible treatment of moder-

ated mediation analyses to address these issues. This paper begins

with a brief presentation of mediation and moderation from both a

theoretical and statistical standpoint to provide a springboard for

discussing moderated mediation. Focus then shifts to explaining

the data that we utilize to execute moderated mediation analyses.

Our analyses follow, with emphasis placed on offering a system-

atic procedure for conducting such analyses. We conclude with a

summary of how to report the results of these analyses and offer

additional suggestions for how to best utilize moderated mediation

models to advance knowledge in L&SCM.

OVERVIEW OF MEDIATION, MODERATION, AND

MODERATED MEDIATION

Mediation

Mediation concerns how a focal predictor (X) affects an

ultimate outcome variable (Y) through one or more

Corresponding author:

Judith M. Whipple, Supply Chain Management Department, Michi-

gan State University, Broad College of Business, 325 N Business

College Complex, East Lansing, MI 48824, USA;

E-mail: whipple@broad.msu.edu

All co-authors contributed substantially to this project. Many pages

of writing were left on the edit room floor. The order of authors is

the order they joined the project.

Journal of Business Logistics, 2017, 38(3): 151–169 doi: 10.1111/jbl.12166

© Council of Supply Chain Management Professionals

mediators

1

(M

1

M

k

) (Preacher and Hayes 2004). To draw con-

clusions regarding the presence or absence of a specific media-

tion processes (i.e., the indirect effect of Xon Ythrough a

specific mediator), scholars should test whether the indirect effect

of Xon Ythrough the mediator in question differs from zero

(Zhao et al. 2010). A quintessential example of a mediation pro-

cess in L&SCM research concerns understanding how logistics

service quality (X) affects customer loyalty (Y) through customer

satisfaction (M) (Stank et al. 1999; Davis-Sramek et al. 2008).

Considering these three constructs (i.e., excluding control vari-

ables), the following system of linear equations

2

can test this

mediation hypothesis:

M¼a0þa1XþeMð1Þ

Y¼b0þb1Xþb2MþeYð2Þ

As explained by Hayes and Preacher (2010), in the case of a sin-

gle mediator model,

3

the indirect effect of Xon Yis the product of

the first partial derivative of Mwith respect to XðoM=oXÞand the

first partial derivative of Ywith respect to MðoY=oMÞ. In this

example, the indirect effect of Xon Ythrough M, denoted as h

X

,is

a

1

b

2

. While the point estimate of h

X

is easily calculated and the

standard error of h

X

is obtainable through the multivariate delta

method (Bollen 1987), methodologists strongly recommend

against using a Z-test [a.k.a. the Sobel (1982) test] to draw conclu-

sions about the significance of an indirect effect (Preacher and

Hayes 2004). The reason is that the sampling distribution of the

product of two normally distributed random variables is non-

normal, meaning that the sampling distribution of h

X

will inher-

ently be non normal (Preacher and Hayes 2008). Instead, scholars

have recommended that the statistical significance of an indirect

effect be determined through one of four approaches:

4

(1) MacKin-

non et al.’s (2007) distribution of product methods; (2) Monte

Carlo simulation (Preacher and Selig 2012); (3) Bayesian

estimation (Yuan and MacKinnon 2009); or (4) bootstrap resam-

pling (Preacher and Hayes 2004, 2008). Preacher (2015) notes that

simulation research by Hayes and Scharkow (2013) suggests these

four methods display a high level of agreement and, thus, choice

of method is unlikely to affect conclusions. The discussion that h

X

has a non normal sampling distribution is important because it will

affect our statistical significance testing of the indirect effects in

the context of moderated mediation.

Moderation

Moderation occurs when the strength and/or direction of the rela-

tionship between a focal predictor (X) and an outcome variable (Y)

is conditional on the value of one or more moderators (W,Z, etc.)

(Aiken and West 1991). The majority of moderation hypotheses

concern simple two-way interactions, which examine how the

effect of Xon Yvaries across levels of a single W(Goldsby et al.

2013). Richey et al.’s (2004) theorizing that the Reverse Logistics

Program Introduction Timing (X)onEconomic Performance (Y)

would vary across levels of Resource Commitment (W) represents

a simple two-way interaction. Scholars can also test multiple two-

way interactions simultaneously

5

as done by Miller et al. (2013)

who examine how the effect of Technology Control (X)onOpera-

tional Performance (Y) varied across levels of Activity Control (W)

and Process Control (Z). Even greater complexity exists with

three-way interactions, which occur when the simple slope of the X

across the range of a primary moderator (W) varies across the level

of a secondary moderator (Z) (Hayes and Matthes 2009). It is rec-

ommended that scholars test moderation hypotheses by including a

multiplicative term(s) between the focal predictor and the modera-

tor(s) in generalized linear models (e.g., OLS regression) (Aiken

and West 1991) or nonlinear structural equation models

6

(Kelava

et al. 2011). For example, returning the aforementioned study by

Richey et al. (2004), the linear model for the interaction between

Reverse Logistics Program Introduction Timing (X) and Resource

Commitment (W)onEconomic Performance (Y) is:

Y¼c0þc1Xþc2Wþc3XW þeMð3Þ

Following rules for statistical models (Seber and Wild 1989), the

effect of Xon Yin Equation ( 3)is the first partial derivative of Ywith

respect to X, which we denote as φ

X

,isc

1

+c

3

W. This indicates that

the effect ofXon Yvaries as a function of W(A iken and West 1991)

and, moreover, c

1

is not a “main effect,”but rather represents the

expected change in Ydue to a one-unit change in Xwhen Wis at zero

(Spiller et al. 2013). Given that moderation effects are often dif ficult

to interpret, Aiken and West (1991) encourage the graphical presen-

tation of model-implied effects and the testing of the statistical

1

It is important to note that mediators are distinct from theoret-

ical mechanisms offered as explanations for why constructs are

related (Astbury and Leeuw 2010). Thus, mediators should not

be confused with theoretical mechanisms. We will return to this

point later in the article.

2

For presentation purposes, we assume that these linear equa-

tions have identity link functions and the residuals are approxi-

mately normal (i.e., standard assumptions for ordinary least

squares (OLS) regression or fitting covariance structure models

using normal theory maximum-likelihood [ML] estimation).

These assumptions are not required, as mediation can be tested

by combining linear equations that have different link functions

(e.g., logit) and different residual distributions (e.g., gamma or

exponential) (MacKinnon 2008).

3

When multiple mediators are present, the following discussion

applies to the estimation of a specific indirect effect (Preacher

and Hayes 2008). For more details regarding multiple mediation

models, we refer readers to Rungtusanatham et al. (2014).

4

Rungtusanatham et al. (2014) provide an overview of these

approaches.

5

This approach is most tenable when the moderators and the

focal predictor have limited correlation. In instances of high cor-

relation, it may be more fruitful to test each two-way interaction

separately and include the linear term for each moderator as a

control variable.

6

Creating interactions between continuous latent variables mea-

sured via multiple indicators involves greater complexity. See

Miller et al. (2013) and Saldanha et al. (2014) for L&SCM

applications of these techniques.

152 R. Calantone et al.