Mathieu and Taylor

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Clarifying conditions and decision pointsfor mediational type inferences inOrganizational Behaviory

JOHN E. MATHIEU* AND SCOTT R. TAYLOR

University of Connecticut, Storrs, Connecticut, U.S.A.

Summary Although mediational designs and analyses are quite popular in Organizational Behavior

research, there is much confusion surrounding the basis of causal inferences. We reviewtheoretical, research design, and construct validity issues that are important for drawinginferences from mediational analyses. We then distinguish between indirect effects, and partialand full mediational hypotheses and outline decision points for drawing inferences of eachtype. An empirical illustration is provided using structural equation modeling (SEM)techniques, and we discuss extensions and directions for future research. Copyright #2006 John Wiley & Sons, Ltd.

Introduction

Over 20 years ago, Baron and Kenny (1986) and James and Brett (1984) published papers that have had

a profound influence on Organizational Behavior research and theory. Those authors advanced atheoretical foundation and analytic guidelines for drawing mediational inferences—theories, methods,

and analyses that elucidate the underlying mechanisms linking antecedents and their consequences. At

issue in this approach are research questions that seek to better understand how some antecedent (X)

variable influences some criterion (Y) variable, as transmitted through some mediating (M) variable. In

this sense, mediators are explanatory variables that provide substantive interpretations of the

underlying nature of an X!Y relationship.

Mediational designs have become ubiquitous in the organizational literature. Wood, Goodman,

Cook, and Beckman (in press) reviewed five leading management journals over the years 1981–2005

and identified 381 studies that tested mediational relationships. Of these, over 60 per cent of the studies

followed prescriptions offered by Baron and Kenny (1986) or James and Brett (1984). However, the

state of the art in mediational analysis is far from consistent. The fact that mediational designs have

developed in different disciplines has only exacerbated the situation (Alwin & Hauser, 1975; Baron &

Kenny, 1986; Frazier, Tix, & Barron, 2004; Holmbeck, 1997; James & Brett, 1984). Indeed,

Journal of Organizational Behavior

J. Organiz. Behav. 27, 1031–1056 (2006)

Published online 7 September 2006 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/job.406

* Correspondence to: John E. Mathieu, University of Connecticut, 2100 Hillside road, Unit 1041, Storrs, CT 06269-1041, U.S.A.E-mail: [email protected] article was published online on 7 September 2006. An error was subsequently identified and corrected by an Erratum noticethat was published online only on 13 October 2006; DOI: 10.1002/job.426. This printed version incorporates the amendmentsidentified by the Erratum notice.

Copyright # 2006 John Wiley & Sons, Ltd. Received 29 April 2006

Accepted 5 May 2006



MacKinnon, Lockwood, Hoffman, West, and Sheets (2002) noted that ‘Reflecting their diverse

disciplinary origins, the procedures [for testing mediating variables] vary in their conceptual basis, the

null hypothesis being tested, their assumptions, and statistical methods of estimation (p. 84).’

Mediational designs come in a variety of forms that differ in terms of the nature of the variables

involved in this X!M!Y chain. For example, Judd and Kenny (1981) discussed the influence of

psychological treatments on individuals’ behavior as mediated by their knowledge. Saks (1995) studiedthe influence of training on newcomer adjustments, as mediated by their post-training self-efficacy.

Mayer and Gavin (2005) considered how employees’ trust in their management influenced their in-role

performance and organizational citizenship behaviors, as mediated by their ability to focus their

attention on work activities. Chen, Gully, Whiteman, and Kilcullen (2000) tested the influence of

individuals’ psychological traits on their behavior, as mediated by their psychological states.

Claessens, Eerde, Rutte, and Roe (2004) considered the influence of individuals’ planning behavior and

work characteristics on their work outcomes such as strain, job satisfaction, and performance, as

mediated by their perceived control of time. In all instances, mediational models advance an

X!M!Y causal sequence, and seek to illustrate the mechanisms through which X and Yare related.

However, there are important nuances in such designs that are often not appreciated, such as whether a

mediator variable partially or full accounts for an X!Y relationship, or whether it merely serves as a

linking mechanism between variables. This important distinction along with other aspects of mediational designs constitutes our focus.

Given the diversity of approaches and statistical techniques that currently exist for testing mediation,

our aims for this paper are to: (1) revisit the research design and measurement preconditions that must

be met in order for tests of mediational relations to be meaningful; (2) review definitions of mediators

and related concepts, and in so doing distinguish between indirect effects, and partial and full

mediational models; (3) distinguish the different statistical tests and decision points that apply,

depending on what type of relationship is hypothesized; and (4) provide an empirical example that

illustrates such differences. We conclude with a discussion of directions for future research and theory

incorporating these distinctions. We note at the onset that many of the points we make below have been

voiced previously. However, a quick perusal of the literature will reveal that some conventional bits of

wisdom have been routinely ignored by many authors, and there remains a lack of consensus regarding

how mediational hypotheses should be framed and tested (Wood et al., in press). Our hope is that this

presentation can serve as a guide for those wishing to advance and to test mediational type relations.

Preconditions for Mediation Tests

The basic mediational design tests whether some antecedent condition ‘X’ has a relationship with some

criterion ‘Y’ through some intervening mechanism ‘M.’ In other words, mediational design advance an

X!M!Y style causal chain. Later we will distinguish different types of such designs and argue that

they advance different a priori hypotheses. Nevertheless, the important point to emphasize here is thatmediational designs implicitly depict a causal X!M!Y chain. Whereas substantial development

has occurred surrounding statistical tests of mediated relationships, far less attention has been devoted

to conditions for strong causal inference in such designs. We submit that inferences of mediation are

founded first and foremost in terms of theory, research design, and the construct validity of measures

employed, and second in terms of statistical evidence of relationships . The greatest challenges for

deriving mediational inferences relates to the specification of causal order among variables, and the

construct validity of the measures employed to operationalize X, M, and Y. In this sense, the

Copyright # 2006 John Wiley & Sons, Ltd. J. Organiz. Behav. 27, 1031–1056 (2006)

1032 J. E. MATHIEU AND S. R. TAYLOR



preconditions for mediation tests are quite similar to those involved in specifying and testing causal

(i.e., structural) models (see James, Mulaik, & Brett, 1982; Kenny, 1979).1

Causal sequence

Perhaps most fundamentally, inferences concerning mediational X!M!Y relationships hinge on

the validity of the assertion that the relationships depicted unfold in that sequence (Stone-Romero &

Rosopa, 2004). In other words, as with structural modeling techniques, multiple qualitatively different

models can be fit equally well to the same covariance matrix. Using the exact same data, one could as

easily ‘confirm’ a Y!M!X mediational chain as one can an X!M!Y sequence (MacCallum,

Wegener, Uchino, & Fabrigar, 1993; Stezl, 1986; Stone-Romero & Rosopa, 2004). Despite passionate

pleas to the contrary by Mitchell (1985) and others, a clear trend away from the use of experimental

designs and a parallel increase in correlational designs has been evident in organizational research in

the past two decades (Scandura & Williams, 2000). Indeed, commenting upon that current state of the

literature, Spencer, Zanna, and Fong (2005, p. 845) lamented ‘that this [correlational mediational]

analysis strategy is overused and has perhaps been elevated as the gold standard of tests of

psychological processes and may even be seen in some quarters as the only legitimate way to examinethem.’ In short, no statistical analysis can unequivocally differentiate one causal sequence from

another. Theorists and researchers must then rely on other means to justify the sequence of effects. The

most valuable bases to advance such inference come from: (1) experimental design features; (2)

temporal precedence; and (3) theoretical rationales.

Experimental designs

Naturally, experimental designs afford the strongest foundation for making causal inferences.

Hallmarks of randomized experimental designs include random assignment of participants to

conditions, control of extraneous variables, and experimenter control of the independent variable .

Indeed, the philosophy of experimental designs is to isolate and test, as best as possible, X !Y

relationships from competing sources of influence. In mediational designs, however, this focus is

extended to a three phase X!M!Y causal sequence. The benefits of conducting randomized

experiments for testing such sequences has long been recognized. For example, Baron and Kenny

(1986) described a design (based on Smith, 1982) whereby one introduces two experimental

manipulations: (1) one presumed to influence the mediator and not the criterion; and (2) one presumed

to influence the criterion yet not the mediator. Analyses of such designs would permit one to distinguish

factors that exert influence directly on a criterion versus those that are carried through an intervening

mechanism.

More recently, Stone-Romero and Rosopa (2004, p. 283) argued that ‘the only way that one can

make credible inferences about mediation is to perform two or more experiments. In the first, the cause

[i.e., X] is manipulated to determine its effect on the mediator [i.e., M]. In the second, the mediator [i.e.,

M] is manipulated to determine its effect on the dependent variable [i.e., Y].’ Certainly such an

approach affords a solid foundation for making causal inferences, but may not be feasible or evendesirable in many applied circumstances. There may well be ethical, logistical, financial, and other

considerations that limit the extent to which researchers can employ randomized experimental designs.

1We should further note that mediation inferences from such designs are predicated not only on the assumptions that X, M, and Yarecausallyordered in that fashion, andtheir relationships arenot attributableto other variables or processes, butalso that they arerelated linearly (see Bollen, 1989; Kenny et al., 1998; Pearl, 2000 for further details). Whereas non-linear relationships, such asmoderation, can be incorporated in mediational frameworks, that takes us beyond the current discussion (see Baron & Kenny,1986; James & Brett, 1984; Muller et al., 2005).


MEDIATIONAL INFERENCES 1033



Spencer et al. (2005) outlined circumstances when experiments offer desirable features for drawing

mediational inferences, as well as instances when they may be less applicable. In short, however,

randomized experimental designs offer the strongest basis for drawing causal inferences and should not

be abandoned so prematurely by applied researchers (Mitchell, 1985; Scandura & Williams, 2000).

Quasi-experimental designs also afford means by which causal order can be established (Cook &

Campbell, 1979; Shadish, Cook, & Campbell, 2002). Because researchers may not be able to randomlyassign participants to conditions, the causal sequence of X!M!Y is vulnerable to any selection

related threats to internal validity (Cook & Campbell, 1979; Shadish et al., 2002). To the extent that

individuals’ status on a mediator or criterion variable may alter their likelihood of experiencing a

treatment, the implied causal sequence may also be compromised. For example, consider a typical:

training! self-efficacy! performance, mediational chain. If participation in training is voluntary, and

more efficacious people are more likely to seek training, then the true sequence of events may well be

self-efficacy! training! performance. If higher performing employees develop greater self-efficacy

(Bandura, 1986), then the sequence could actually be performance! efficacy! training. If efficacy

and performance levels remain fairly stable over time, one could easily misconstrue and find substantial

support for the training! efficacy! performance sequence when the very reverse is actually

occurring.

Researchers also have less control over contaminating variables in quasi-experiments ascompared to randomized experiments. Whereas concerns about contaminating influences and other

threats to internal validity are extensive and well discussed elsewhere (see Cook & Campbell, 1979;

Shadish et al., 2002; West, Biesanz, & Pitts, 2000), our primary focus here concerns threats to the

implied causal sequence of effects in a mediational design. Revisiting our training example, a

misspecification of causal sequence can emanate from the influence of an omitted (sometimes

referred to as unmeasured, third, contaminating, hidden, or confounding) variable. For example, if

employees with greater seniority are first eligible to receive training, and if they also tend to have

higher self-efficacy, then there would be an illusionary training! efficacy relationship unless

seniority is also controlled. The issue here is that one must carefully consider what other variables

might confound the relationships under consideration and account for their influence when

evaluating the specified causal sequence and variable relationships as outline above. Otherwise,

such influences might mask real effects (see MacKinnon, Krull, & Lockwood, 2000) or generate

artifactual relationships.

In summary, our discussion about the advantages of experimental and quasi-experimental designs

converges on the larger issues of justifying the presumed causal order of variables and minimizing the

influence of unmeasured variables. Randomized experiments certainly provide the strongest case for

minimizing the influence of such potential effects but are difficult to implement. Quasi-experiments

offer much as well, but are susceptible to a variety of threats to causal inferences. James (1980) and

James et al. (1982) have well chronicled this issue. They submitted that an omitted variable poses a

threat to causal inferences if it: (a) has a significant unique influence on an effect (i.e., mediator or

criterion); (b) is stable; and (c) is related to at least one other predictor included in the model. In other

words, in mediation analyses, omitted variables represent a significant threat to validity of the X !M

relationship if they are related both to the antecedent and to the mediator, and have a unique influenceon the mediator. Moreover, omitted variables represent a significant threat to inferences involving the

prediction of the criterion, if they have a unique influence on the outcome variable and either the

antecedent or mediator.

Temporal precedence

A mediational framework proposes that the antecedent preceded the mediator, which in turn preceded

the criterion. Implicitly, therefore, mediational designs advance a time-based model of events whereby





X occurs before M which in turn occurs before Y. To the extent that the measures and operations

employed to operationalize variables in a study are aligned with that sequence, one can have more

confidence that the chain of relationships is not compromised. Let us emphasize one point here: it is the

temporal relationships of the underlying phenomena that are at issue, not necessarily the timing of

measurements. Certainly, to the extent that the two different sequences are aligned is of concern.

However, the literature is replete with designs whereby researchers collect a set of observations andthen correlate variables with some record of last year’s performance, whether that was derived from

performance appraisals, performance outputs, sales, or some financial index. In effect, this reverses the

presumed sequence of events and more likely models Y!X!M than it does X!M!Y.

Simply assessing a presumed antecedent before measuring a presumed mediator and criterion in no

way assures that the true underlying causal order is consistent with the order of measurement (James

et al., 1982; Kenny, 1979). Indeed the synchronization of measurement timing and the development of

phenomena over time are critical to the basis of causal inferences (Mitchell & James, 2001). Given that

X!M!Y relationships are presumed to unfold over time, it begs the question of how long does it

take each variable to develop and to change? Consider a work redesign effort intended to empower

employees and thereby to enhance their work motivation with the aim of increasing customer

satisfaction. How long does it take to establish the new work design? Over what duration should we

track employees’ subsequent motivation? If employees are indeed more motivated to perform, howlong will it take for customers to notice and for them to become more satisfied? These questions are not

easy to answer, and in few instances would phenomena readily align with the 3 or 6 month intervals that

organizations are willing to tolerate, even if they are open to multiple data collections. Even worse,

consider the fact that employee motivations (M) in this instance are likely to begin changing before the

work redesign (X) intervention is fully entrenched. And, the appropriate window for sampling

customer reactions may vary widely depending on their frequency of encounters with employees and

other factors. In sum, the guiding point here is that the passage of time between the assessment of X, M,

and Y helps to further strengthen inferences about the causal sequence. To the extent that such

assessments are aligned with the underlying developmental phenomena being studied will strengthen

causal inferences.

Theoretical guidance

Theoretical frameworks usually prescribe a distinct ordering of variables. In fact, it is a hallmark of

good theories that they articulate the how and why variables are ordered in a particular way (e.g., Sutton

& Staw, 1995; Whetten, 1989). This is perhaps the only basis for advancing a particular causal order in

non-experimental studies with simultaneous measurement of the antecedent, mediator, and criterion

variables (i.e., classic cross-sectional designs). For example, Fishbein and Aijzen’s (1975) Theory of

Reasoned Action has long posited that individuals’ attitudes give rise to intentions, which in turn

influence their actual behaviors. This theoretical foundation has been applied extensively to the study

of employees’ absence and turnover behaviors (Hom & Kinicki, 2001; Tett & Meyer, 1993). The job

characteristics model argues that work design features give rise to psychological states which in turn

influence individuals’ reactions (e.g., satisfaction) and behaviors (Hackman & Oldham, 1980). Mathieu

(1991) used Lewinian Field Theory (Lewin, 1943) to submit that variables more psychologicallyremoved from oneself (i.e., distal effects such as perceptions of work characteristics), would influence

more psychologically proximal variables (e.g., role states) and thereby affect work attitudes (e.g.,

satisfaction, organizational commitment). Absent an experimental or longitudinal design, one might

test a mediational model on the basis of the theoretical ordering of variables. Naturally the case would

be stronger if one could also leverage features from a design perspective, but clearly the theory must

articulate a certain causal sequence. And, in cross-sectional studies one often has little else to justify

any particular order.





To summarize, the specification of the causal order of variables is absolutely critical to inferences

about mediational relationships. This is first and foremost a theoretical exercise. Research design

features in terms of experimental control and temporal precedence provide additional justification for

particular sequences. Notably, there is no panacea for justifying causal sequence. Learned scholars

differ on what they believe is sufficient grounds upon which to claim causal order. On one extreme,

Stone-Romero and Rosopa (2004) submitted that anything short of a randomized experiment isinsufficient to claim justified causal order. Their position is ‘tests of mediation models that are based

upon data from non-experimental studies have little or no capacity to serve as a basis for valid

inferences about mediation (Stone-Romero & Rosopa, 2004; p. 250).’ On the other extreme, a perusal

of journal articles will quickly reveal numerous instances of authors claiming ‘causal’ connections

from mediational analyses of cross-sectional data collected in a single survey as related to last year’s

performance indices. Reasonable people can disagree, and we personally believe that both of the above

extreme positions are probably overstated. In any case, to the extent that one’s work is: (a) grounded in

strong theory; (b) employs true or quasi-experimental designs; and (c) assesses variables over time in

the proper sequence and intervals, confidence in the causal sequence of variables in a particular model

is enhanced.

Measurement related issues

As with any research investigation, the construct validity of measures employed are of concern in tests

of mediation. Schwab (1980) submitted ‘Construct validity is defined as representing the

correspondence between a construct (conceptual definition of a variable) and the operational

procedure to measure or manipulate that construct’ (pp. 5–6). Of note in particular for mediational

analyses, attention should be directed at the convergent and discriminant validity of measures.

Convergent validity

Convergent validity essentially concerns the extent to which different measures of the same construct

‘hold together’ or converge on the intended construct. Usually convergent validity is assessed using

techniques such as factor analyses and other approaches that evaluate how well different observations

relate to a latent variable. Naturally, this concept is related to reliability concepts such as internal

consistency estimates, alternative forms/methods, interrater, or test-retest. Depending on the nature of

the constructs involved in the X!M!Y relationship, any combination of reliability estimates may

be applicable (see Nunnally, 1978). Of note for the present discussion is the fact that measurement

unreliability, particularly that of the mediator, can bias mediational analyses. As Hoyle and Kenny

(1999) have demonstrated, assuming all positive paths, to the extent that a mediator is measured with less

than perfect reliability, the M!Y relationship would likely be underestimated, whereas the X!Y would

likely be overestimated when the antecedent and mediator are considered simultaneously. Whereas latent

variable modeling can help to compensate for measurement shortcomings, the technique is certainly not a

panacea. Consequently, the message here is clear: it is critical to use reliable measures when testing

mediation, particularly when it comes to the mediator variable.

Discriminant validity

Discriminant validity of measures is another concern for all research investigations, yet particularly for

tests of mediation. Discriminant validity refers to the extent to which measures of different constructs

are empirically and theoretically distinguishable. Note that discriminant validity must be gauged in the

context of the larger nomological network within which the relationships being considered are believed

to reside. Discriminant validity does not imply that measures of different constructs are uncorrelated;





indeed if that were the case there would be no mediational covariance to be modeled. The issue is

whether measures of different variables are so highly correlated as to raise questions about whether

they are assessing different constructs.

If measures of an antecedent variable and a mediator are not sufficiently distinguishable, then they

are in effect tapping the same underlying domain. Consequently, any attempt to parse their independent

contributions to a criterion variable will be futile. For example, if X and M fail to evidence discriminantvalidity, any sequential analysis of their substantive relationship will conclude that the mediator carries

the influence of X on Y. The same conclusion would follow in situations where the mediator and

criterion and not distinguishable. This problem is akin to the notion of multi-collinearity between either

the X and M variables, or between the M and Y variables. Consequently, it is incumbent on researchers

to demonstrate that their measures of X, M, and Y evidence acceptable discriminant validity before any

mediational tests are justified. This may be done in a variety of fashions ranging from exploratory factor

analyses to more powerful multi-trait, multi-method approaches, and confirmatory factor analyses. In

sum, a lack of discriminant validity between either X and M, or between M and Y, will lead to an

illusionary mediational relationship that amounts to nothing more than correlating some measure of a

construct with another measure of the same construct.

Distinguishing indirect and mediating relationships

Up to this point we have employed the term mediating variable in a very general sense. Unfortunately,

different authors define mediation in many different ways and often use terms such as indirect effects,

intervening variables, intermediate endpoint, and so forth interchangeably with mediators. (see

MacKinnon et al., 2002 for a review). Further, although mediational models are pervasive in applied

research and elsewhere, there is some debate concerning the requisite statistical evidence for drawing

inferences about mediation (cf., Baron & Kenny, 1986; Collins, Graham, & Flaherty, 1998; Frazier

et al, 2004; Holmbeck, 1997; James & Brett, 1984; James, Mulaik, & Brett, 2006; Kenny, Kashy, &

Bolger, 1998; MacKinnon, et al., 2000, 2002; Preacher & Hayes, 2004; Shrout & Bolger, 2002). We

believe that root causes of such controversies lie in differences of opinion regarding: (1) definitions of mediators and related concepts; (2) the necessity of first demonstrating a significant total X!Y

relationship; and (3) the appropriate base model for tests of different forms of mediation.

The first two points of contention are closely intertwined. Some have submitted that a precondition

for tests of mediation is that the antecedent must exhibit a significant ‘total’ relationship with a criterion

when considered alone (i.e., X!Y, see Baron & Kenny, 1986; Judd & Kenny, 1981; Preacher &

Hayes, 2004). Others have relaxed this precondition, and argued that mediation inferences are justified

if the indirect effect carried by the X!M and M!Y paths is significant (e.g., Kenny, et al., 1998;

MacKinnon et al., 2002). Advocates of this latter view often equate mediator variables with indirect

effects (e.g., Alwin & Hauser, 1975; Bollen, 1987; MacKinnon et al., 2002). However, there is an

important distinction between indirect and mediator variables.

For example, MacKinnon et al. (2002, p. 83) suggested that ‘An intervening variable (Mediator)

transmits the effect of an independent variable to a dependent variable [emphasis added].’ In contrast,Baron and Kenny (1986, p. 176) submitted that ‘a given variable may be said to function as a mediator

to the extent that it accounts for the relation between the predictor and the criterion [emphasis added].’

Preacher and Hayes (2004, p.719) explicitly drew a distinction between the two concepts and argued

that mediation is a special, more restrictive, type of intervening relationship.

‘A conclusion that a mediation effect is present implies that the total effect X!Y was present

initially. There is no such assumption in the assessment of indirect effects. It is quite possible to find





that an indirect effect is significant even when there is no evidence for a significant total effect.

Whether or not the effect also represents mediation should be judged through examination of the

total effect.’

In other words, mediator variables are explanatory mechanisms that shed light on the nature of the

relationship that exists between two variables. If no such relationship exists, then there is nothing to bemediated . While a chain of events whereby X!M and M!Y may well be of interest, along with

the extent to which variance in Y can be attributed to the indirect effect of X, we submit that sequence

represents a qualitatively different phenomenon than mediation. We prefer to label such relationships

as indirect effects.

We readily acknowledge that there is another reason why some researchers (e.g., MacKinnon et al.,

2000) advocate dropping the X!Y precondition for mediational inferences. This second position

centers around the fact that confounding, suppression, and interactive effects could attenuate overall

X!Y relationships (see MacKinnon et al., 2000).2 Similarly, others have argued that competing

effects might mitigate total X!Y relationships, when opposite signed direct and indirect effects are

present (e.g., when X and M are both positively related to Y, yet X and M are negatively related).

Notably, the common thread through all of these positions is that ‘some’ other variable, including

perhaps the mediator, serves to contaminate the total X!Y relationship when viewed in isolation. Inother words, the opposite signs and mediator as a suppressor arguments both suggest that the true

underlying model is a partially mediated one whereby the direct effect of X!Y can only be interpreted

in the context of a model that also includes the M!Y path. This raises a central point about the

importance of the base model that one hypothesizes.

James et al. (2006) underscored the importance of the base model that one adopts for tests of

mediation. In the case of full mediation, M is hypothesized to fully account for the significant total

effect of X!Y. In other words, the direct effect of X!Y is no longer significant once M!Y has been

included. In contrast, in the case of partial mediation, M is believed to account for a significant portion

of the total X!Y, but a significant direct effect also remains. In other words, both M !Yand X!Y

are significant when considered simultaneously. Of course, both partial and full mediation models are

predicated on a significant X!M relationship. James et al. (2006) and Shrout and Bolger (2002) noted

that full and partial mediational inferences rely on different types of statistical tests. Consequently,

which model one hypothesizes may lead to different conclusions in many instances.

James et al. (2006) noted that the Baron and Kenny (1986) approach implicitly advocates partial

mediation as the base model for tests of mediation. Alternatively, James and Brett (1984), and James

et al. (2006) prefer the axiom of parsimony and advocate the full mediation base model. All agreed that

substantive reasoning should guide which is adopted in any given circumstance; but the important point

is that the a priori model that one advances has important implications for confirmatory and

disconfirming statistical evidence. We extend this logic and submit that the specification of one’s

hypothesized base model has implications for indirect effects along with partial and full mediation.

Moreover, such relations can be examined in the context of larger structural models where the

influences of other variables of interest are also considered. Nevertheless, the evidential basis for

drawing inferences of each type remains consistent and is outlined below.In summary, we believe that there are different types of relationships that fall under the general

heading of intervening effects. Accordingly, we use the term intervening effects to describe any type of

2Concerns about the influence of interactive or confounding variables imply the presence of non-linear relationships whichviolates an assumption of testing indirect or mediated relations, unless one is also hypothesizing moderation (see Footnote 1).Further, extraneous, omitted, or 3rd variablesrepresentspecification errorsthat always must be accountedfor, through theoretical,methodological, or empirical means, whenever a causal sequence of effects is advanced (James et al., 1982; Stone-Romero &Rosopa, 2004). We elaborate more fully on this and related points below.





linking mechanism ‘M’ that ties an antecedent with a criterion. Indirect effects are a special form of

intervening effect whereby X and Y are not related directly (i.e., are uncorrelated), but they are

indirectly related through significant relationships with a linking mechanism. In contrast, mediation

refers to instances where the significant total relationship that exists between an antecedent and a

criterion, is accounted for in part ( partial mediation) or completely ( full mediation) by a mediator

variable.

Estimation Guidelines and Decision Rules

We submit that different statistical rules of evidence apply depending on whether one anticipates an

indirect effect versus partial or full mediation. We argue that researchers are obliged to specify, a priori,

which type of intervening process that they anticipate. Importantly, the nature of the hypothesized

relationship leads to different sources of confirmatory and disconfirming evidence. In this sense, what

we are advocating is an approach that is similar to that of structural equation modeling (SEM).Accordingly, a failure to reject a hypothesized model hinges on two types of tests: (1) confirmation of

hypothesized relations (i.e., relationships that were hypothesized to exist are indeed significant and in

the hypothesized directions); and (2) disconfirmation of non-hypothesized paths (i.e., sufficient model

fit indices, which indicate that the paths that were hypothesized to be absent are indeed not significant).

Moreover, because different competing models can be fit to the same data, we advocate contrasting

one’s hypothesized model against viable alternative models (see Anderson & Gerbing, 1988, for a good

background on this general approach).

Figure 1 presents three alternative models containing intervening effects and their respective

parameters. In this sense, the indirect effects model is the most constrained or parsimonious, as it

implies that the only significant relationships observed are the combined effect (bmxbym). This

implies that both the X!M (bmx)andM!Y (bym) paths are significant, although the combined effect

is best tested using approaches such as the Sobel test (see MacKinnon et al., 2002; Shrout & Bolger,

YMX

YMX

YMX

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noitaideMlluF

tcef f Etcer idnI

β xm

β xm

β xm

βym

βym

βy x.m

βy m.x

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Figure 1. Alternative intervening models





2002 for details). Importantly, an indirect effect hypothesis also implicitly suggests that the total X!Y

relationship (byx) is absent. The full mediation model is the next most parsimonious. This model also

includes significant X!M (bmx) a n d M!Y (bym) paths. However, the dashed line from X!Y in this

model is meant to imply a significant total X!Y (byx) relationship that becomes non-significant when

M!Y (bym) is included. In other words, a hypothesis of full mediation also requires a non-significant

byx.m effect. Last, the partial mediation model is the least parsimonious and implies that X!M (bmx),as well as both M!Yand X!Y will be significant when considered simultaneously (bym.x and byx.m,

respectively).

The three panels of Figure 2 specify sequences of effects to be considered in order for each of the

hypothesized models to be supported. Later we will describe analytic techniques which provide

information regarding these effects. The columns of rectangles in Figure 2 depicts the various

conditions that must hold for each model to be accepted, whereas the branches containing circles depict

guided alternative hypotheses that might be considered if a hypothesized condition is disconfirmed.

Notably, by ‘accepted models’ we mean that the data fail to reject the hypothesized model. As is always

the case, this does not mean that a hypothesized model has been proven; simply that it is not

inconsistent with the data. Similarly, once any facet of a hypothesized model is rejected, one enters an

exploratory mode as alternative models are considered. Consequently, any conclusions that are derived

from such searches are tentative at best and need to be validated on a new sample.

Indirect effects

As shown in Panel 1 of Figure 2, the pivotal test of the indirect model is simply (bmxbym) using

methods such as the Sobel (1982) test or more sophisticated approaches employing bootstrapping

techniques (see, MacKinnon et al., 2002; Preacher & Hayes, 2004; Shrout & Bolger, 2002). If such a

test is not significant, then one should reject the indirect effect hypothesis and consider viable

alternatives. A more parsimonious alternative in such instances would be to consider simply a direct

Figure 2. Decision tree for evidence supporting different intervening effects





X!Y (byx) relationship. Moreover, even if the indirect effect was significant , researchers should

consider whether alternative models such as a partially or fully mediated model are suggested by the

data. For example, if the overall X!Y relationship was significant (byx), and X does not contribute to

the prediction of Yonce M has been considered (byx.m), then the hypothesis of an indirect effect would

be rejected in lieu of an alternative model of full mediation.

This approach echoes our earlier comments about researchers’ casual dismissal of the preconditionof a total X!Y effect for tests of mediation. Our reading of the literature suggests that there are very

few instances where researchers actually hypothesized a priori that the total X!Y relationship would

be non-significant. Rather, it appears as though many evoke a waiver of the X!Y precondition when it

fails to materialize in their data, and then simply proceed to test the significance of the indirect effect.

This has occurred even when there was no evidence to suggest suppression or counter-acting signs of

direct and indirect effects. Such tactics, in our opinion, moves one away from confirmatory hypothesis

testing and into the exploratory realm. In summary, we submit that the presence of a significant total

X!Y relationship leads to the rejection of a hypothesis of an indirect effect and should trigger a

consideration of an alternative partial mediation hypothesis (if suppression or counter-acting effects are

suspected), and thereby perhaps, to a full mediation explanation.

Full mediation

As depicted in the second panel of Figure 2, a hypothesis of full mediation is predicated on a significant

total X!Y (byx) relationship. Failing that, one might consider an alternative hypothesis of an indirect

effect. If suppression is evident, then one might consider the alternative hypothesis of a partially

mediated relationship. Assuming the total effect was present, one proceeds to test the X!M (bmx) and

M!Y (bym) relationships. If either fails to exist, then the evidence is consistent with the alternative

hypothesis of a direct effect. Moreover, full mediation depends on the non-significance of direct effect

of X!Y when the M!Y path is included (i.e., a non-significant byx.m). If the direct X!Y path is

significant in this context, then the hypothesis of full mediation should be rejected and the researcher

should consider the alternative hypothesis of partial mediation. We should note that there may be caseswhere adding the byx.m parameter attenuates the M!Y relationship (bym.x) to a non-significant level.

If the X!Y relationship (byx.m) is significant in such an instance, then the full mediational hypothesis

should be rejected in lieu of an alternative hypothesis of a direct effect. Alternatively, if neither byx.m or

bym.x are significant, and the previous conditions were satisfied, then the data are consistent with the

hypothesis of full mediation. This follows from the fact that the relevant M !Y parameter for the full

mediation hypothesis is bym not bym.x (see James et al., 2006).

Partial mediation

A partial mediation hypothesis, as shown in Panel 3 of Figure 1, is the least constrained and rests on thesignificance of all three paths: X!M (bmx) and both X!Y (byx.m) and M!Y (bym.x) when

considered simultaneously. Given the presumed causal order of variables, if the X!Y (byx.m) path is

not significant in this model, then the hypothesis of partial mediation should be rejected and one should,

perhaps, consider an alternative hypothesis of full mediation. Alternatively, if the X!M (bmx) or the

M!Y (bym.x) paths are not significant, then the partial mediation hypothesis should be rejected in lieu

of the alternative hypothesis of simply a direct effect. The partial mediation hypothesis would only be

supported if all three hypothesized paths are significant.





Caveats

We should highlight two other related concerns for the tests outlined above. First, our various decision

points pivot on tests of statistical significance, just as any SEM nested model comparisons do (see

Anderson & Gerbing, 1988). Nevertheless, tests of statistical significance must be considered in light of

related issues such as sample size and measurement reliability (Hoyle & Kenny, 1999). In other words,significance tests must be tempered by considerations of power and effect size estimates. Enormous

sample sizes can yield statistically significant results that are virtually meaningless in practice and also

easily lead to the rejection of full mediation hypotheses. Alternatively, small sample sizes can easily

lead to inferences of full mediation in instances where there is not sufficient power to adequately test for

partial mediation. The summary point is that sufficient power must exist to adequately test various

relationships, and researchers should balance conclusions about statistical significance with those

about practical significance.

A second, and related caveat, concerns the relative power of different tests. MacKinnon et al. (2002)

have argued that a direct test of intervening effects (bmxbym) has greater power as compared to causal

steps approaches such as those outlined by Baron and Kenny (1986). However, recall that MacKinnon

et al. (2002) equated indirect effects with mediation, and argued that ‘overall, the step requiring a

significant total effect of X on Y led to the most Type II errors, (p. 96).’ In other words, thedistinguishing feature between indirect and mediator relations is what accounts for the fact that tests of

the latter are more conservative than the former. The fact that mediators rely on the presence of a total

direct effect represents a greater statistical burden, however, so we believe that the corresponding lower

power is totally appropriate. In other words, the combined tests of indirect effects appear to have greater

statistical power simply as a consequence of comparing them with qualitatively different types of

relationships—namely, mediation.

Summary

Tests of intervening effects are predicated on the assumption that the causal sequence of variables is

sufficiently justified and the measures employed to represent the constructs possess sufficient construct

validity. While not particularly controversial, we believe these preconditions are often overlooked and

should be afforded more attention by scholars. Less clarity surrounds the ‘rules of evidence’ for

mediational type inferences and associated statistical tests. A key to most of this confusion is the fact

that X!M!Y models may represent full mediation, partial mediation, or indirect effects—all of

which are confirmed or disconfirmed in slightly different ways. We submit that researchers are obliged

to a priori specify the nature of the relationship(s) that they anticipate, and then to conduct the

corresponding tests to demonstrate both confirmatory and disconfirming evidence. To better illustrate

how this works in practice, we offer the following example.

Empirical Illustration

The purpose of this illustration is to demonstrate the steps and evidential basis involved in testing

indirect effects, and partial and fully mediated relationships. Our example focuses on the concept of





self-efficacy as a mediator of the influences of individual differences and situational cues on

individuals’ performance and is illustrated in Figure 3. Self-efficacy is defined as ‘people’s judgments

of their capabilities to organize and execute courses of action required to attain designated types of

performances’ (Bandura, 1986, p. 391). The positive relationship between self-efficacy and

performance has been demonstrated time and again and summarized in narrative reviews (e.g.,

Bandura & Locke, 2003) and in meta-analyses (e.g., Stajkovic & Luthans, 1998). Hence, there isabundant support for viewing it as an influence on performance.

Bandura (1977) has long theorized that self-efficacy is determined mostly by the cognitive appraisal

and integration of information cues. Two of the most influential of such cues are enactive mastery and

vicarious experience. Enactive mastery develops through repeated performance accomplishments in

the same or similar situations. In other words, to the extent that individuals have performed well in a

particular situation in the past, it is reasonable to expect that their efficacy expectations will be higher.

Further, naturally one would expect that individuals’ past performance would correlate positively with

their future performance for reasons other than simply their efficacy expectations (e.g., because ability

influences both). Consequently, as depicted in Figure 3, we would hypothesize that self-efficacy would

partially mediate the relationship between previous (i.e., baseline) performance and subsequent

performance.

Vicarious experience is gained through direct observation or information about how well others’

have performed in a situation. However, there is no reason to expect that vicarious experience

would influence individuals’ performance unless they internalized such information in terms of

their efficacy expectations. Consequently, we hypothesized that self-efficacy would fully mediate

the relationship between normative information and individuals’ performance. Indeed, previous

research has been consistent with this expectation (e.g., Mathieu & Button, 1992; Weiss, Suckow, &

Rakestraw, 1999).

Finally, recent theorizing and research have argued that relatively stable individual differences may

influence efficacy expectations. For example, Phillips and Gully (1997) found support for a positive

correlation between individuals’ learning goal orientation and their self-efficacy in an academic setting.

Individuals who are high on learning goal-orientation strive to understand something new or to increase

their level of competence in a given activity (Button, Mathieu, & Zajac, 1996). Whereas a learning goalorientation may contribute directly to performance, it is more likely to help shape specific task-related

perceptions such as self-efficacy. Although some previous researchers have found results that are

consistent with a hypothesis of full mediation (e.g., Phillips & Gully, 1997), others have found

relationships more consistent with an indirect effect inference (e.g., Chen et al., 2000; Diefendorff,

2004; Potosky & Ramakrishna, 2002). Which interpretation is most appropriate is debatable. However,

for present illustration purposes, we hypothesized that learning goal orientation would exhibit a

positive indirect effect with performance via self-efficacy.

Figure 3. Hypothesized intervening effects





Method

Participants

Two hundred and one undergraduates were recruited from introductory psychology courses at a largenortheastern University and received extra credit toward their course grade for participation. The

sample was 61 per cent female, and their average age was 18.65 (SD¼ 1.97). Participants were invited

to attend experimental sessions where they were randomly assigned to one of the three normative

information conditions (n¼ 67 per condition) as described below.

Task and procedure

The task was identical to the one used by Mathieu and Button (1992). It involved the creation of words

containing three or more letters drawn from a list of 10 letters: four vowels (worth 1 point each), two

consonants (worth 1 point each), and four additional consonants worth 2, 3, 4, and 10 points,

respectively. The point values associated with each letter correspond to those used in the game‘Scrabble.’ The object of the task was to score as many points as possible during a 10-minutes session

by forming words containing three or more letters from the list provided, excluding proper nouns and

slang. Points were awarded according to the point values associated with letters used in each word

generated.

Upon arrival at the experimental session, participants completed an informed consent form and a

survey that contained demographic items and a measure of learning goal orientation from Button et al.

(1996). Once the survey was completed, the experimental task was explained to participants and they

completed a 5-minutes practice exercise. They then calculated their own score on the practice exercise

and were told that they would perform a 10-minutes experimental trial after answering some survey

questions. The first page of the survey instrument presented the normative information manipulation

using the following statement. ‘In previous testing we have found that students like you score about 115

[175, 235] points on the task you are about to complete [emphasis in instructions].’ The middle value

corresponded to pilot subjects’ average performance, whereas the low- and high-point values were set

one standard deviation from the mean, based on pilot data. They then completed several survey items

that included their self-efficacy and a manipulation check, and then completed the 10-minutes task,

were debriefed and given their extra credit slips, and dismissed.

Measures

Manipulation check

A manipulation check identical to that used by Mathieu and Button (1992) was administered after the

survey items. It asked participants how many points they thought most people would score on the task they were about to complete. As anticipated, their responses differed significantly across the normative

information conditions (F (2,194)¼ 189.16, p< 0.001) and all means differed significantly from each

other in the anticipated fashion.

Performance

Participants’ practice and task performances were simply the total number of points they earned during

each of the timed periods. Individuals scored their own practice trail in order to provide clear and





immediate feedback. Their calculations were later checked by a coder, blind to manipulated normative

information, and found to be highly accurate.

Self-efficacy

Self-efficacy was assessed using a nine-item graduated scale identical to that employed by Mathieu and

Button (1992). The 9-point scale spanned two standard deviations above and below the mean pointobtained in the pilot sessions. Participants rated the extent to which they believed that they could score

at least each of the point values using a Likert-type 7-point scale, ranging from 1 ( virtually no

possibility) through 4 (about a 50/50 chance) to 7 (complete certainty). Thus, higher scores represent

greater levels of self-efficacy (a¼ 0.95). We created three ‘parcels’ (i.e., subscales) for use in the SEM

analysis by averaging the highest, lowest, and midpoint rating to form one indicator, the next highest,

lowest, and middle value to form a second, and the remaining three ratings to form a third.3

Learning goal orientation

Learning goal orientation was assessed using six items from Button et al. (1996). An example item is ‘I

prefer to work on tasks that force me to learn new things.’ Participants responded to each item using a

1–7 agreement scale with higher values representing greater learning orientation (a¼ 0.77). We also

created three ‘parcels’ for this measure, by first fitting them to a single factor model and then averagingthe highest and lowest loading items to form one composite, and so forth as described above.

Analytic overview

We employed Anderson and Gerbing’s (1988) two-step SEM strategy to test the model depicted in

Figure 1 using LISREL 8.54 (Joreskog, Sorbom, du Toit, & du Toit, 2000). SEM techniques have long

been advocated as preferable to regression techniques for testing mediational relationships because

they permit one to model both measurement and structural relationships and yield overall fit indices

(cf., Baron & Kenny, 1986; James & Brett, 1984; James et al., 2006; Kenny et al., 1998). Accordingly,

we first fit a confirmatory factor analytic (CFA) measurement model followed by a series of structural

models testing our hypothesized relationships.

In order to gauge model fit, we report the Standardized Root Mean Square Residual (SRMSR),

Goodness of Fit index (GFI; Joreskog et al., 2000), and the Comparative Fit Index (CFI; Bentler, 1990).

We also report x2 values which provide a statistical basis for comparing the relative fit of nested models.

SRMSR is a measure of the standardized difference between the observed covariance and predicted

covariance. Usually, SRMSR values¼ 0.08 are considered a ‘relatively good fit for the model,’ and

values¼ 0.10 considered ‘fair’ (Browne & Cudeck, 1989). The CFI is an incremental fit index that

contrasts the fit of a hypothesized SEM model against a baseline (uncorrelated indicators) model.

Historically, SEM model incremental fit indices such as GFI and CFI < 0.90 have been considered

wanting and likely to be improved substantially. More recently, however, Hu and Bentler (1999)

proposed that use of combined cutoffs such as CFI 0.95 and SRMSR 0.08 results in better

balance of rejection rates for misspecified models under different conditions. In contrast, Marsh,Kit-Tai, and Wen (2004), Beauducel and Wittmann (2005), Fan and Sivo (2005) illustrated that

deciding on the most appropriate index and cutoff is a complex function of the nature of model

3This parceling approach helps to reduce the ratio of estimated parameters to sample size in SEM analyses (Hagtvet & Nasser,2004; Hall, Snell, & Foust, 1999; Landis, Beal, & Tesluk, 2000). It is also true that graduated self-efficacy items such as theseyield notoriously positively skewed distributions for the highest levels rated and negatively skewed distributions for the lowestlevels rated. Combining the ratings in this fashion yields parcels that better fulfill the normal distribution assumptions of SEMindicators.





misspecifications, sample sizes, balances between Type I and Type II tradeoffs, and a host of other

factors. All authors also emphasized that the acceptability of models rests heavily on the extent to

which hypothesized parameters are significant and in the anticipated directions, as well as issues such

as parsimony. Given such controversy and the complexity of issues surrounding cutoff values for model

fit indices, along with our study characteristics, we will consider models with CFI values <0.90 and

SRMSR values>0.10 as deficient , those with CFI 0.90 to<0.95 and SRMSR>0.08 to0.10 rangesas acceptable, and ones with CFI 0.95 and SRMSR<0.08 ranges as excellent .

Results

Confirmatory factor analysis model

Descriptive statistics and variable correlations are presented in Table 1. Table 2 presents a summary of

the fit indices for the various models that we tested. Using the covariance matrix, we estimated a five-

factor CFA model. In effect, this model amounts to testing the discriminant validity of three self-efficacy and three learning goal orientation parcels, as the remaining three latent variables (i.e.,

normative information manipulation, baseline, and final performance) were set equal to their observed

scores. The five-factor CFA evidenced excellent fit indices [x2(20)¼ 19.04, n.s.; GFI¼ 0.98;

CFI¼ 1.00; SRMSR¼ 0.019] with all six parcels exhibiting significant ( p< 0.05) relationships with

their intended latent variable.

To further test the discriminant validity of the self-efficacy and learning goal orientation measures,

we fit a four-factor CFA model by constraining their latent variables to unity. This four-factor model,

which is nested in the five-factor model, exhibited a deficient and significantly worse model fit [Dx2

(1)¼ 27.24, p< 0.001; x2(21)¼ 46.28, p< 0.01; GFI¼ 0.95; CFI¼ 0.98; SRMSR¼ 0.11]. Finally, we

fit a null latent CFA model (which constrains the correlations among the latent variables to zero) to the

data [x2(30)¼ 157.42, p< 0.001; GFI¼ 0.85; CFI¼ 0.89; SRMSR¼ 0.19] and obtained a

significantly worse fit [Dx2(10)¼ 138.38, p< 0.001] as compared to the five-factor model.

Table 1. Variable descriptive statistics and correlations

Variables

LLGO LSE

Mean SD 1 2 3 4 5 6 7 8

1. Baseline performance 69.93 3 1.26 — 0.07 0.490.08 0.50

2. Normative informationa 2.00 0.82 0.07 — 0.160.05 0.16

3. Performance 84.55 32.31 0.49 0.16 — 0.03 0.39

4. LGO-1 5.36 0.93 0.04 0.02 0.05 — 0.18

5. LGO-2 5.48 0.79 0.06 0.08 0.04 0.53 —

6. LGO-3 5.95 0.70

0.06 0.01

0.04 0.44

0.55

—7. Self-efficacy-1 5.07 1.04 0.47 0.17 0.38 0.09 0.17 0.12 —8. Self-efficacy-2 4.94 1.17 0.50 0.16 0.38 0.09 0.14 0.11 0.96 —9. Self-efficacy-3 5.46 1.19 0.49 0.14 0.39 0.09 0.15 0.12 0.91 0.92

p< 0.05.aCoded: 1¼Low, 2¼Moderate, 3¼High.

Notes: Lower diagonal contains indicator correlations, upper diagonal contains latent variable correlations.LLGO¼Latent learning goal orientation, LSE¼Latent self-efficacy N ¼ 201.





Collectively, these results indicate that the measurement properties fit quite well and there is sufficient

covariance among the latent variables to warrant examining the different intervening effects. We should

also highlight that the fit of the five-factor CFA is equivalent to a ‘saturated structural model’—or onethat includes direct paths from all antecedents to both the mediator (i.e., self-efficacy) and to the

criterion (i.e., performance). This saturated model provides a useful comparison against which to gauge

the fit of other models.

Structural models

Below we fit different structural models to test the three different types of intervening effects that were

hypothesized. In effect, we isolate the direct and indirect effects for each of the three antecedents.

However, we first fit ‘only directs’ and ‘no directs’ models to serve as additional bases of comparison.

The only directs model estimates direct relationships from all antecedents to performance, with no

paths leading to or stemming from the self-efficacy mediator (although self-efficacy remains as a latent

variable in the model). This model exhibited deficient fit indices [x2(24)¼ 96.36, p< 0.001;

GFI¼ 0.92; CFI¼ 0.94; SRMSR¼ 0.170] and differed significantly from the CFA model

[Dx2(4)¼ 77.32, p<0.001]. This indicates that at least one of the antecedents has a significant

direct effect with self-efficacy, or efficacy related significantly with performance. In other words, these

results attest to the importance of the mediator variable. In the context of this model, both normative

information (b yx¼ 0.12, p< 0.05) and baseline performance (b yx¼ 0.48, p<0.01) related significantly

to performance, whereas learning goal orientation (b yx¼ 0.02, n.s.) did not. These findings are

consistent with the anticipated forms of intervening effects.

The no direct effects model estimated paths from each of the antecedents to self-efficacy, and from

efficacy to performance, but contained no direct effects from the antecedents to performance. This

model exhibited acceptable fit indices [x2(23)¼ 51.32, p< 0.01; GFI¼ 0.95; CFI¼ 0.98;

SRMSR¼ 0.052] but did differ significantly from the CFA model [Dx

2

(3)¼ 32.28, p<

0.001]. Thislack of fit indicates that one or more of the antecedents has a significant direct effect with performance.

In the context of this model, all three antecedents related significantly with self-efficacy (learning goal

orientation bmx¼ 0.22, p< 0.05; normative information bmx¼ 0.14, p< 0.05; and baseline

performance bmx¼ 0.51, p< 0.01), and self-efficacy exhibited a significant relationship with

performance (bym¼ 0.19, p<0.05). Therefore, the X!M relationship (bmx) is evident for all three

intervening effects, and the M!Y relationship holds, at least when considered alone. Notably, self-

efficacy retained its significant relationship with performance in all models that we examined. In

Table 2. Summary of structural equation modeling analyses

Models

Fit indices

DF x2 GFI CFI SRMSR

Saturated model 20 19.04 0.98 1.00 0.019Learning goal direct 22 48.79 0.95 0.98 0.047Normative informationa direct 22 49.20 0.95 0.98 0.050Baseline performance direct 22 21.90 0.98 1.00 0.024No directs 23 51.32 0.95 0.98 0.052Only directs 24 96.36 0.92 0.94 0.170Null latent 30 157.42 0.85 0.89 0.190

p< 0.01.aCoded: 1¼Low, 2¼Moderate, 3¼High. Notes: N ¼ 201.





addition, the indirect effects of all the antecedents to performance via self-efficacy (bmxbym) were

significant in this model: learning goal orientation: b¼ 0.09, Sobel¼ 4.70, SE¼ 1.69, p< 0.05;

normative information b¼ 0.05, Sobel¼ 2.14, SE¼ 0.99, p< 0.05; and baseline performance

b¼ 0.20, Sobel¼ 0.21, SE¼ 0.04, p< 0.01.

In summary, these two base models provide us with valuable information about the significance of

the parameters associated with the different intervening effects. From the ‘only directs’ model weascertained that the mediator variable plays an important role in the context of our model. From the ‘no

directs’ model we learned that the indirect effect of each antecedent with performance was significant,

as transmitted through the self-efficacy mediator. We now turn to additional models that complete the

picture for the three different relationships that were hypothesized.

Indirect effect

Recall that learning goal orientation was hypothesized to have only an indirect effect with performance

via self-efficacy. As shown in the upper triangle of Table 1, the correlation (i.e., total effect, byx)

between the latent learning goal orientation variable and performance was not significant (r ¼0.03,

ns), as anticipated. Using the no directs model as a base, we next fit a ‘learning goal direct ’ model by

adding a path from learning goal orientation to performance. Although this model exhibited excellent

fit indices, [x2(22)¼ 48.79, p< 0.01; GFI¼ 0.95; CFI¼ 0.98; SRMSR¼ 0.047], it was not asignificant improvement over the no direct model [Dx2(1)¼ 2.53, n.s.] and it differed significantly from

the saturated model [Dx2(2)¼ 29.75, p<0.001]. This implies that the direct effect of learning goal

orientation to performance was not significant, and indeed it was not (bym.x¼0.12, n.s.). In contrast,

the indirect effect of learning goal orientation to performance via self-efficacy was significant in this

model (bmxbym.x¼ 0.09, Sobel¼ 5.18, SE¼ 1.83, p< 0.05). In summary, the indirect effect

(bmxb ym) was significant in this model, whereas the direct X !Y relationship (b yx.m) was not. Given

that the total (b yx) was also not significant, these results are consistent with the hypothesis of an indirect

effect.

Fully mediated effect

We hypothesized that the influence of the normative information manipulation on performance would

be fully mediated by self-efficacy. As illustrated in the upper triangle of Table 1, the correlation

between the normative information manipulation and performance was significant (r ¼ 0.16, p< 0.05),

as anticipated. Therefore, the total (byx) condition was fulfilled. Next, again using the no directs model

as a base, next fit a ‘normative information direct ’ model by adding a path from normative information

to performance. This model also exhibited excellent fit indices, [x2(22)¼ 49.20, p< 0.01; GFI¼ 0.95;

CFI¼ 0.98; SRMSR¼ 0.050], but was also not a significant improvement over the no direct model

[Dx2(1)¼ 2.12, n.s.], and differed significantly from the saturated model [Dx2(2)¼ 30.16, p< 0.001].

Thus, the direct effect of normative information to performance was not significant (byx.m¼ 0.10, n.s.)

although the indirect effect was (bmxbym.x¼ 0.05, Sobel¼ 2.04, SE¼ 0.95, p< 0.05). In summary,

the results of this model indicate that normative information has a direct effect on the self-efficacy

mediator (bmx), self-efficacy has a significant relationship with performance (b ym), and that the direct

effect of normative information to performance (byx.m) is no longer significant. Given the earlier significant total X ! Y effect (b yx), these results are consistent with the hypothesis of a full mediation.

Partially mediated effect

Last, we hypothesized that the influence of the baseline performance on the experimental trial

performance would be partially mediated by self-efficacy. Accordingly, using the no directs model

again as a base, we fit a ‘baseline performance direct ’ model by adding a path from baseline

performance to performance. This model exhibited excellent fit indices [x2(22)¼ 21.90, n.s.;





GFI¼ 0.98; CFI¼ 1.00; SRMSR¼ 0.024], was a significant improvement over the no directs model

[Dx2(1)¼ 29.42, p< 0.01], and did not differ significantly from the saturated model [Dx2(2)¼ 2.86,

n.s.]. This implies that the direct effect of baseline performance to performance was significant, and in

fact it was (byx.m¼ 0.40, p< 0.01), as was the indirect effect via self-efficacy (bmxbym.x¼ 0.10,Sobel¼ 0.10, SE¼ 0.04, p<0.01). Moreover, baseline performance evidenced a significant direct

effect with the self-efficacy mediator (bmx), and self-efficacy had a significant relationship with

performance (bym.x). These findings are consistent with the hypothesis of a partially mediated effect .

The results of this model, which in effect constitutes the hypothesized model when all three intervening

hypotheses are considered together, are presented in Figure 4.

Summary

The series of model tests illustrated the chain of evidence required for different types of intervening

effects. It is noteworthy that the overall fit indices were excellent for all but the ‘directs only,’ ‘no

directs,’ and the ‘null latent’ models. The series of tests made clear that the lack of fit stemmed from

significant relationships between: (1) all three antecedents and the self-efficacy mediator; (2) the

efficacy mediator and the performance outcome; and (3) baseline performance and the performance

outcome, directly. Inclusion of these relations fully accounted for the covariance among the latent

variables. It is also worth noting that the indirect effects tests were significant for all three antecedents

in both the ‘no directs’ model, as well as when considered individually in the ‘direct effects’ models.

Discussion

The purpose of this paper was to revisit the popular question of ‘how do you test mediatedrelationships?’ We submitted that researchers should consider issues related to the theory that they are

testing, the research design that they are employing, and the construct validity of the measures that they

collect. We argued that mediational inferences hinge on the ability of researchers to: (1) justify the

causal order of variables; (2) reasonably exclude the influence of outside factors; (3) demonstrate

acceptable construct validity of their measures; (4) articulate, a priori, the nature of the intervening

effects that they anticipate; and (5) obtain a pattern of effects that are consistent with their anticipated

relationships while also disconfirming alternative hypotheses.

Figure 4. Model results of different intervening effects





Research design factors are paramount for reasonable mediational inferences to be drawn. If the

causal order of variables is compromised, then it matters little how well the measures perform or the

covariances are partitioned. Because no analytic technique can discern the ‘true’ causal order of

variables, establishing the internal validity of a study is critical. Adequately ruling out the influence of

alternative explanations is also vital for drawing mediational inferences. Randomized field experiments

afford the greatest control over such concerns, yet they may not be feasible for a number of reasons.Nevertheless, they remain the ‘gold standard’ and should be pursued whenever possible. Quasi-

experimental designs offer reasonable ‘fall back’ options, but as Campbell and Stanley (1966) long ago

warned, are fraught with threats to internal validity. Lacking the ability to perform any type of

experiment, temporal precedence, and strong theory offer some bases for specifying causal order, but

they are certainly not the strongest positions to defend. In the end, journal editors, reviewers, and

consumers of research will no doubt have greater confidence in studies that leverage strong theory and

experimental design features, reasonable exclusion of alternative explanations for effects, measures

that have good construct validity and were gathered in the proper temporal precedence, and results that

were consistent with the hypothesized relationships.

In our empirical illustration, we justified the causal order of variables using a combination of

techniques. First, an individual difference variable (learning goal orientation) was collected before the

experiment was even introduced. Second, participants completed a practice exercise to familiarizethemselves with the task and to establish a baseline. Third, we then randomly assigned participants to

normative information experimental conditions, after which we assessed their self-efficacy before they

completed the performance trial. We reported confirmatory factor analysis results that supported the

measurement properties of the scales we employed, and then described a series of competing structural

models that homed in on the parameters of interest for different intervening relationships. Given the

strong theoretical foundation concerning self-efficacy, the combination of experimental design

features, temporal precedence, measurement quality, and focused analyses represents a fairly strong

position from which to draw mediational inferences.

We also sought to differentiate indirect effects, partial mediation, and full mediation. Clearly they are

similar in the sense that they all describe an intervening process linking antecedents with an outcome.

However, we submitted that there are important, albeit subtle, differences between the nature of the

relationship that they each advance. Moreover, we argued that different types of confirmatory and

disconfirming evidence are warranted for each type of relationships. Most importantly, we argued that

researchers should articulate a priori hypotheses concerning the nature of the relationship(s) that they

anticipate. This underscores the importance of adopting a confirmatory approach toward tests of

intervening effects. As illustrated in the panels of Figure 2, the base model(s) that one chooses presents

important guidelines for the evidential basis of different types of inferences. Moreover, when

considered collectively in a larger structural model, which parameters are included has implications

for tests of indirect and mediated relations. For example, a close examination of the results we reported

will reveal that the magnitude of any given direct and indirect effect varied as a function of what other

parameters were being modeled. In practice, it could well be that the significance of a given parameter

will change depending on the nature of the entire network of model relations. Therefore, we encourage

researchers to articulate an a priori model (including any potential co-variates of interest), and to reportthe parameter estimates for that model. Naturally, a revised model may be suggested by the data; in

which case it is informative to report the parameter estimates from that context as well. Of course,

revised models need to be validated on a new sample.

We provided an empirical illustration of the three types of intervening relationships. In so doing, we

outlined how a series of structural equation models could be employed to test the relevant parameters

for each relationship. This could have just as easily been done using standard multiple regression

techniques. However, SEM techniques offer three critical advantages over multiple regression





approaches. First, using a two-stage SEM approach, researchers explicitly address the measurement

properties of the variables that they have collected before the consideration of the more substantive

relations. Whereas SEM does not absolve researchers from the importance of using valid and reliable

measures, it does explicitly account for how measurement properties influence substantive conclusions.

Second, SEM techniques explicitly consider the potential influence of constrained parameters. In other

words, SEM model fit indices hinge on the veracity relationships thought not to exist. For example, ahypothesis of full mediation rests not only on the significance of X !M and M!Y parameters, but

also on whether X fails to relate significantly to Y once M has been considered. The third strength of

SEM analyses derives from the nested model comparisons. Whereas sample size and related factors

determine the power of tests of whether a parameter of interest differs significantly from zero, these are

held relatively constant in the context of nested model tests. In other words, the SEM nested model

comparisons allow one to home in on the specific parameters of interest and to contrast a given pattern

of effects against viable alternatives. Clearly substantive considerations should guide the selection of

alternative models (Anderson & Gerbing, 1988), yet we believe the three types of intervening effects

we described will likely represent fairly viable alternatives for any hypothesis of interest.

While we are clearly echoing previous calls for greater use of SEM techniques in mediational

analyses (Baron & Kenny, 1986; James & Brett, 1984), they are not panaceas. Researchers must still

attend to the preconditions for tests of mediation that we reviewed. Furthermore, the variouscomparison models that we advanced are not all directly comparable. Model contrasts are only valuable

if competing models are nested. In other words, models are nested if one represents a more restrictive

version of the other. Whereas both the saturated model and null latent models provide valuable

universal benchmarks, the directs only and no directs models are only useful for limited comparisons.

Nevertheless, the series of model comparisons enable researchers to test all the relevant parameters

related to intervening effects. We should add that simpler approaches such as regression may well be

applied in circumstances where the assumptions of SEM techniques have not been met (e.g., reasonable

sample sizes).

Extensions

Moderated relationships

Thus far we have been concerned with strictly ‘main effect’ or linear relationships associated with

various intervening effects. However, interactions or moderator relationships can also be incorporated

into this framework. Both James and Brett (1984) and Baron and Kenny (1986) discussed procedures

for testing both mediators and moderators simultaneously. James and Brett (1984), and more recently,

Muller, Judd, and Yzerbyt (2005), further differentiated different forms that combinations of mediators

and moderators may take. First, they described mediated moderation as the situation where an

interaction between two antecedents, as related to a criterion variable, passes through a mediator. In

effect, this implies that the moderator influences the X!M link of a mediated relationship. For

example, the influence of normative information on individuals’ self-efficacy might be contingent on

the extent to which participants identify with the normative group. In other words, normativeperformance information about ‘people just like me’ is likely to influence a person’s self-efficacy far

more than is information about ‘people much different than me.’ Tests of this moderation, whether they

be conducted using moderated regression or more sophisticated SEM techniques (Cortina, Chen, &

Dunlap, 2001), would follow the analytic approach that we outlined earlier, while also considering

interactions involving the antecedent variable(s) and the moderator.

The other combination of variables is referred to as moderated mediation (James & Brett, 1984). In

this case, the moderator exerts its influence on the M!Y path in the X!M!Y sequence. For





example, individuals’ self-efficacy is likely to have a stronger relationship with their performance in

weak or unconstrained environments, whereas strong environments or ones with abundant situational

constraints would likely attenuate self-efficacy! performance relations. Here again, the standard

evidential basis for establishing mediated relations is followed; only the moderator’s influence on tests

including the M!Y combination is also considered. In short, the difference between the two types of

combinations follows from whether the moderator exerts its influence on the X!M link (mediatedmoderation) or on the M!Y link (moderated mediation) in the X!M!Y sequence.

Multiple mediators

To this point we have been discussing relationships between antecedents and an outcome via a single

mediator. However, there are many circumstances where multiple mediators may be in operation.

There are two different varieties of multiple mediation. The first instance of multiple mediation simply

involves a longer causal chain such as X!M1 !M2 !Y. For example, self-set goals have long been

considered as a mediating mechanism linking self-efficacy in performance (Bandura & Locke, 2003).

Consequently, the fully mediated relationship between normative information and performance that we

illustrated would be transmitted through a self-efficacy! self-set goals! performance chain.

Whether the relationship between self-efficacy and performance is partially or fully mediated by goals

must be hypothesized and analyzed accordingly, as does the normative information! self-efficacy! self-set goals sequence. Analytic techniques to address the relative contribution of some

X variable on some distal Y variable as transmitted by two (or more) sequential mediators are still

evolving (see Shrout & Bolger, 2002). Nevertheless, the preconditions for testing mediational type

inferences that we outlined would apply.

The second form of multiple mediation concerns two or more ‘stacked’ mediators. For example,

Kohler and Mathieu (1993) advanced a model whereby individual resource variables and work related

perceptions where associated with different forms of absenteeism as mediated by three work attitudes

(e.g., job satisfaction) and three forms of work stress (e.g., somatic tensions). These authors considered

the work attitudes and stresses as co-occurring in the sense that they advanced no causal sequence

among them. Kohler and Mathieu (1993) tested mediational relations using a ‘block’ of mediators

considered together as a set. More recently, Preacher and Hayes (2005) have advanced techniques to

not only assess the extent to which blocks of such mediators convey indirect effects, but also enable

researchers to differentiate the extent to which the collective indirect effects are attributable to each of

the mediators considered.

Multi-level approaches

Throughout this paper we have assumed that all variables of interest were indexed at the same level of

analysis. However, mediational inferences can also be considered in the context of multi-level designs.

Generally, multi-level designs come in two varieties: (1) nested entities; and (2) longitudinal

approaches. In nested entity designs, some focal level-1 of analysis (e.g., individuals) is considered in

the context of higher level-2 units (e.g., teams). In these designs, antecedents and mediators may

emanate from different levels of analysis and combine to influence a lower-level criterion (see Mathieu

& Taylor, in press). For example, team characteristics (X) may influence members’ individualperformances as mediated by level-2 team processes (M) or perhaps by their level-1 identification with

the team.

A second type of multi-level design is commonly referred to as within-subject (Judd, Kenny, &

McClelland, 2001), growth-curve modeling (e.g., Bliese & Polyhart, 2002), or repeated measures (e.g.,

Moskowitz & Hershberger, 2002) designs. In these designs, the lower level-1 variables are represented

as repeated observations of the same unit of analysis (e.g., individual) over time. For example, one

might consider the influence of level-2 individuals’ personality traits (X) on their individual level-1





performance overtime (Y), as mediated by their work attitudes. Mediators (M) in this context could be

relatively stable level-2 work attitudes (e.g., organizational commitment) assessed at a single point in

time, or temporally changing level-1 variables (e.g., moods) assessed using time sampling techniques.

Plenty of good work is currently being advanced along these lines (e.g., Judd et al., 2001; Kenny,

Korchmaros, & Bolger, 2003). In summary, multi-level designs expand the scope of mediational

inferences to incorporate relationships that reside within levels of analysis, traverse levels of analysis,and unfold over time.

Conclusion

Our goal for this paper was to revisit issues related to the validity of mediational inferences in

organizational behavior. We sought to emphasize the inextricable ties between theory, design,

measurement, and analysis related to such inferences. We also argued that indirect effects, partial

mediation, and full mediation represent slightly different forms of intervening effects. We submittedthat researchers should specify which they anticipate a priori, as each relies on slightly different types

of statistical evidence. Our hope is that this paper provides a framework for future investigations. We

also believe that this approach should provide a foundation upon which to expand and incorporate

moderated relationships, more complex multiple mediation applications, and multi-level designs.

Acknowledgements

We thank Gilad Chen, Jodi Goodman, Kris Preacher, Jack Veiga, and Zeki Simsek for their helpfulcomments on an earlier version of this paper.

Author biographies

John E. Mathieu ([email protected]) is a Professor and Cizik Chair of Management

at the University of Connecticut. He received his PhD in Industrial/Organizational Psychology from

Old Dominion University. He is a member of the Academy of Management and a Fellow of the Society

of Industrial Organizational Psychology, and the American Psychological Association. His currentresearch interests include models of team and multi-team processes, and cross-level models of

organizational behavior.

Scott R. Taylor ([email protected]) is a PhD candidate in organizational behavior at

the University of Connecticut. He received his MBA from the University of Virginia. He is a student

member of the Academy of Management and Society of Industrial Organizational Psychology. His

current research interests include team leadership and influence, multi-level models of organizational

behavior, and multi-team systems.





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