Journal of Applied Psychology1984, Vol 69, No 2, 307-321

Copyright 1984 by theAmerican Psychological Association, lnc

Mediators, Moderators, and Tests for Mediation

Lawrence R. JamesGeorgia Institute of Technology

Jeanne M. BrettGraduate School of Management,

Northwestern University

The following points are developed. First, mediation relations are generally thoughtof in causal terms. Influences of an antecedent are transmitted to a consequencethrough an intervening mediator. Second, mediation relations may assume a numberof functional forms, including nonadditive, nonlinear, and nonrecursive formsSpecial attention is given to nonadditive forms, or moderated mediation, where itis shown that, although mediation and moderation are distinguishable processes,a particular variable may be both a mediator and a moderator within a single setof functional relations Third, current procedures for testing mediation relationsm industrial and organizational psychology need to be updated because these pro-cedures often involve a dubious interplay between exploratory (correlational) sta-tistical tests and causal inference It is suggested that no middle ground existsbetween exploratory and confirmatory (causal) analysis and that attempts to explainhow mediation processes occur require well-specified causal models. Given suchmodels, confirmatory analytic techniques furnish the more informative tests ofmediation.

Researchers in industrial and organizationalpsychology and organizational behavior areplacing increasing emphasis on studying me-diation models in which the influence of anantecedent is transmitted to a consequencethrough an intervening mediator. Cases inpoint include (a) job-perception studies inwhich the effects of work environments (an-tecedents) are transmitted to affective and be-havioral outcomes (consequences) by inter-vening job perceptions (mediators; cf. Brass,1981; Oldham & Hackman, 1981; Rousseau,1978a, 1978b; Sutton & Rousseau, 1979); (b)attrition studies in which the influences of en-vironmental events and individual attributes

Support for this project was provided under Officeof Naval Research Contracts N00014-80-C-0315 andN00014-83-K-0480, Office of Naval Research ProjectsNR170-904andNR475-026 Opinions expressed are thoseof the authors and are not to be construed as necessarilyreflecting the official view or endorsement of the Depart-ment of the Navy

The authors wish to thank Robert G Demaree, JeanneL Dugas, Sigrid B Gustafson, Allan P. Jones, Stanley AMulaik, and Gernt Wolf for their helpful suggestions andadvice

Requests for reprints should be sent to Lawrence RJames, School of Psychology, Georgia Institute of Tech-nology, Atlanta, Georgia 30332

are transmitted to attrition behaviors via in-tervening behavioral intentions to stay or leave(cf. Arnold & Feldman, 1982; Horn & Hulin,1981; Horn, Katerberg, & Hulin, 1979; Miller,Katerberg, & Hulin, 1979; Mobley, Hand,Baker, & Meghno, 1979; Mobley, Homer, &Hollingsworth, 1978); and (c) attribution re-search m leadership, where the effects of sub-ordinate performance on subsequent behaviorsby the leader toward a subordinate are trans-mitted by the leader's attributions of the causesof the subordinate's performance (cf. Ilgen,Mitchell, & Fredrickson, 1981; McFillen,1978; Mitchell & Kalb, 1981; Mitchell &Wood, 1980).

At the theoretical level, studies such as theseare typically based on causal models that as-sume complete mediation as well as additiveand linear causal relations. To illustrate theprinciples involved, a complete mediationmodel has the form x —• m —> y, where JC isthe antecedent, m is the mediator, and y is theconsequence. The antecedent x is expected toaffect the consequence y only indirectlythrough transmission of influence from x toy by the mediator m. The indirect transmissionof influence from x to y via m denotes thatall of the effect of x on y is transmitted by m.In causal terminology, this state of affairs is

307

308 LAWRENCE R. JAMES AND JEANNE M. BRETT

described as "the effect of x on y is completelymediated by m"; thus the term complete me-diation model Assuming linear and additivecausal relations, the complete mediation modelthus predicts that x has a direct effect on m,m has a direct effect on y, and x is not relateddirectly to y when m is held constant, if thesepredictions are empirically confirmed, thenone may infer that the complete mediationmodel has been corroborated and therefore isuseful for attempting to explain how x is re-lated to y through the intervening mediatorm (James, Mulaik, & Brett, 1982). Explanationis a matter of elucidating the processes bywhich m is a linear, additive function of x andy is a linear, additive function of m (Rozeboom,1956).

This article has two objectives, both ofwhich resulted from observations that manystudies that ostensibly derived from a linear,additive, complete mediation model departedfrom this theoretical base during empiricaloperationalizations of the model and/or ex-planations of the results of empirical tests ofthe model. The first objective is to discusscomplete mediation models that imply addi-tivity but take on a distinctly nonadditive flavorin empirical operationalizations, empiricaltests, and explanations of results. A case inpoint is the attribution model of leader be-havior proposed by Green and Mitchell (1979),which is: subordinate performance (x) —»leader's attributions of the causes of the sub-ordinate's performance (m) —* leader behaviortoward the subordinate (y). This model appearsto assume the x —• m —» y form, where at-tributions transmit, additively and linearly, in-fluence from subordinate performance toleader behaviors. Some attribution studies inleadership do indeed maintain an additive,linear, complete mediation form, althoughcauses of leaders' attributions other than sub-ordinate performance are typically includedin investigations (e.g., interdependence of su-pervisor and subordinate, see prior references).In other operationalizations, tests, and inter-pretations of the complete mediation model,the attributions are not treated as simple me-diators. Rather, they appear to assume the roleof moderators (Ilgen & Knowlton, 1980;Knowlton & Mitchell, 1980—see also Good-stadt & Kipnis, 1970; Kipnis & Cosentino,1969; Kipnis, Silverman, & Copeland, 1973).For example, empirical evidence indicates that

if poor subordinate performance is attributedto lack of effort, but not to lack of ability, thenthe leader is likely to increase close supervisionand decrease support. Conversely, if poor sub-ordinate performance is attributed to lack ofability (interpreted here as lack of training andexperience), but not to lack of effort, then theleader is likely to increase support but notclose supervision, at least not in the sense ofthe use of coercive power (e.g., reprimand thesubordinate).

These informative findings imply that thecomparative strengths of attributions to abilityand effort serve to moderate the relation be-tween subordinate performance and leaderbehavior. This stimulates the question: Are theattributions also mediators in the sense thatthey intervene between subordinate perfor-mance and leader behavior toward the sub-ordinate, as predicted by the Green andMitchell (1979) model? An answer to thisquestion is not easily furnished because it re-quires that we explore relations between theconcepts of mediator and moderator. In thebroader context, of concern are answers toquestions such as, "Must mediation relationsbe additive?" "May mediators also be mod-erators?" and "May moderators also assumethe role of mediators?" Exploration of the me-diator and moderator concepts and answersto these and related questions comprise thefirst objective of this article.

The second objective is to demonstrate whyinvestigators should devote more attention tothe assumptions for confirmatory (causal)analysis before conducting confirmatory testsof complete mediation models. Consider, forexample, the job perception and attritionstudies cited at the beginning of this article.Each of these studies proposed a verbal, andoften graphic, complete mediation model,which was then tested using analytic proce-dures typically associated with exploratory(i.e., correlational) analysis, such as hierar-chical regression and/or partial correlation.When methods such as hierarchical regressionand partial correlation are used to test com-plete mediation hypotheses, it follows that themethods have assumed the roles of confir-matory tests. It follows also that, like otherforms of confirmatory analysis (e.g., pathanalysis), these methods should only be em-ployed after conditions for confirmatory anal-ysis have been reasonably satisfied. The use of

MEDIATION 309

traditionally exploratory methods to test causalmodels does not absolve the researcher fromhaving to satisfy conditions for confirmatoryanalysis.

To set a fair stage for discussion, it shouldbe noted that prior tests of complete mediationmodels in the job perception and attrition lit-eratures represent initial attempts to advancefrom purely exploratory forms of analysis toconfirmatory tests of causal hypotheses. Fur-thermore, investigators typically devoted at-tention to some of the conditions for confir-matory analysis, such as justifying the pre-sumed causal ordering among variables. Ourconcern is that these initial and much neededattempts to advance from exploratory analysisto confirmatory analysis must now be regardedas incomplete in the context of recent accu-mulation of knowledge in industrial and or-ganizational psychology regarding all of theconditions that are prerequisite to meaningfulconfirmatory analysis (James et al., 1982).Moreover, whereas hierarchical regression andpartial correlation may indeed be used in theconfirmatory mode (Cohen & Cohen, 1983),these methods are limited in regard to boththe types of causal models for which they areapplicable and the information they provide(Griffin, 1977).

To illustrate concerns pertaining to condi-tions for confirmatory analysis, consider thatempirical support for the complete mediationmodel, job environment (e.g., job technol-ogy) —»job perceptions (e.g., job challenge) —*job satisfaction, is interpreted to mean that(a) job perceptions transmit causal influencesfrom the job environment to job satisfaction,and (b) individuals experiencing the same orsimilar type(s) of environments may differ interms of how they perceive the job and, there-fore, differ in how they respond affectively tothe job (see prior references). Interpretation"a" denotes that job perceptions covary sig-nificantly with between-job variation in suchthings as levels of technology and that co-variation in job perceptions is associated sig-nificantly with covariation in job satisfaction.The empirical data support this interpretation,which reflects an attempt to enhance expla-nation of the processes by which job environ-ments influence job satisfaction by identifyingan intervemng, perceptual mediators).

Interpretation "b" is not a legitimate causalinference because relevant causes of reliable

within-job variation in job perceptions (andjob satisfaction) are not included in the causalmodels or tested empirically. Clearly, if jobperceptions and job satisfaction vary reliablywithin levels of technology, then the interven-ing job perceptions are not just transmittinginfluences from job technology to job satis-faction. Rather, other causes of job perceptions(and job satisfaction), such as personal attri-butes and social influences, will likely have tobe invoked to explain the reliable within-jobvariation in job perceptions (see James &Jones, 1980; Kim, 1980; O'Reilly, Parlette, &Bloom, 1980; Schmitt, Coyle, White, & Raus-chenberger, 1978; Thomas & Griffin, 1983).When not included in a causal model, theseother causes are referred to as unmeasuredvariables Given stipulations to be discussedlater, failure to include one or more unmea-sured variables in the causal model results inbiased statistical results and erroneous causalinferences in regard to relations among vari-ables included explicitly in the causal model(cf. James, 1980).

Unmeasured variable problems are symp-tomatic of the incomplete transition from ex-ploratory modes of analysis to confirmatorymodes of analysis. In the presentation of Ob-jective 2, we will address these problems andother key conditions required for confirmatoryanalysis that must be considered in order toeffect a complete transition from exploratoryanalysis to confirmatory analysis. We will alsorecommend that hierarchical regression andpartial correlation should not be used in placeof confirmatory analytic procedures.

Objective 1: An Attempt to DistinguishBetween Mediators and Moderators

The first objective of this article is to definemediation and moderation and then to com-pare mediation with moderation. As part ofthis process, we shall see that contemporarydefinitions of mediation are somewhat mis-leading and that the distinction between me-diation and moderation can be blurred at boththe theoretical and operational levels of ex-planation.

Contemporary Definitions

The definition of mediator advanced byRozeboom (1956) for hypothetical constructsappears to be characteristic of the linear, ad-

310 LAWRENCE R JAMES AND JEANNE M BRETT

ditive, complete mediation models employedin many areas of psychology and the socialsciences. This definition is as follows: m is amediator of the probabilistic relation y =f(x)if m is a probabilistic function of x (i.e., m =f[x]) and y is a probabilistic function of m(i.e., y =/[/«]), where x, m, and y have differentontological content (i.e., represent differenthypothetical constructs or latent variables). Asdiscussed earlier, theoretical operationaliza-tions of mediation are usually based on causalmediation models, which in shorthand nota-tion assume the form x —> m—> y. In additionto the obvious point that a causal order mustbe assumed, the typical causal mediationmodel is based on the premises that (a) the/ s in m - f{x) and y = f(m) represent linear,additive, and recursive (i.e., unidirectional)functions, which in equation form for devia-tion scores are m = bx + e and y = bm + e,where b is a causal parameter and e is an erroror disturbance; (b) m transmits all of the in-fluence of an antecedent x to a consequencey, which implies that x and y are indirectlyrelated and that the relation between x and yvanishes if m is held constant; and (c) the in-clusion of m in the model serves to enhancethe explanatory power of the model becausem furnishes substantive explication of how theantecedent is related to the consequence,whereby "related" means how x "produces,""acts on," or otherwise influences y (cf Alwin& Hauser, 1975; Blalock, 1982; Cook &Campbell, 1979; Duncan, 1975; Heise, 1975;James et al, 1982; Kenny, 1979).

With respect to moderation, a variable z isa moderator if the relationship between two(or more) other variables, say x and y, is afunction of the level of z. This definition in-dicates an x by z interaction, or a nonadditiverelation, where y is regarded as a probabilisticfunction of x and z. Specifically, the proba-bilistic function is y = f(x, z), the function /being y — btx + b2z + byKZ + e for deviationscores and a model linear in the parameters.The bs in this function will be regardedas noncausal, statistical parameters for thepresent.

If we compare this definition to the Roze-boom (1956) definition for mediation, it wouldseem that a number of clear lines of demar-cation exist between the terms mediator andmoderator. In particular, the moderator modelis represented by a single, nonadditive, linear

function (although often tested by a hierar-chical process) in which it is desirable to haveminimal covariation between the moderatorand both the independent and dependent vari-ables (Abrahams & Alf, 1972). In comparison,mediation models must be represented by atleast two additive, linear functions m whichit is desirable to have high degrees of covari-ation between the mediator and both the an-tecedents) and consequence(s). Use of theterms independent and dependent in moderatormodels, and antecedent and consequence inmediator models, is purposeful and indicatesthat moderation carries with it no connotationof causality, although a causal relation maybe moderated (cf. Stolzenberg, 1979). Media-tion, on the other hand, implies at the mini-mum a causal order, and often additionalcausal implications are required to explainhow mediation occurred (these implicationsare considered later). Because of the causalovertones in mediation relations, a confir-matory analytic approach is employed belowto illustrate additional issues in moderationand mediation, although the basic statisticalarguments generalize to exploratory designs

Moderated Mediation

Things are not necessarily as straightforwardas the above definitional demarcations suggest,one reason being that mediation relations mayinvolve a moderator, m which case the me-diation relations cannot be additive. The issueshere will be presented by way of illustrationfor a self-attribution model based on simplifiedand overdramatized abstractions from Ban-dura (1977, 1978), Jones (1973), and Werner(1979). Suppose we conduct a study designedto test the propositions that (a) effort attri-butions mediate the relation between level ofpoor performance and degree of intended per-sistence for high-self-esteem individuals and(b) ability attributions mediate the relationbetween level of poor performance and degreeof intended persistence for low-self-esteem in-dividuals. The proposed causal models areshown in Figure 1, section a. Individuals arefirst given a self-esteem questionnaire and thenblocked (subgrouped) into high self-esteemsor low self-esteems, the criterion for blockingbeing whether an individual scores above orbelow a theoretical point on the self-esteemscale. Second, within the high- and low-self-

MEDIATION 311

esteem blocks, individuals are assigned ran-domly to five bogus performance-feedbackconditions (explained below). Third, individ-uals in all five conditions are asked to performthe same moderately difficult task, which re-quires mental effort and approximately 15minutes to complete. Fourth, following taskcompletion, individuals are given bogus per-formance feedback implying that they havefailed the task. Degree of failure is varied onan approximately interval scale (e.g., Condition1. 50% of the people did better than you .Condition 5- 90% of the people did better thanyou). Fifth, individuals are asked to make twoattributions, one regarding the degree to whichtheir performance was due to lack of effortand one regarding the degree to which theirperformance was due to lack of ability (e.g.,

0 = Effort [ability] had no effect on my per-formance . . 6 = My performance wasstrongly affected by a lack of effort [ability]).After completing the attribution items, indi-viduals are asked to report the extent to whichthey would now be willing to participate m asimilar task (e.g., 1 = Definitely not participate

. 3 = Ambivalent about participation . . .5 = Definitely participate). Scores on this scalerepresent degrees of "intended persistence."This is checked empirically by conducting asecond task, but we shall use the intended per-sistence indicator in order to stay m the para-metric realm and thereby not get bogged downin extraneous statistical issues. Finally, the ex-periment is ended by debriefing participants.

To demonstrate principles, realizing thatdichotomous blocking on a continuous self-

Block

HighSelf-Esteem

LowSelf-Esteem

PerformanceFeedback

PerformanceFeedback

Mediation Relation

Effort*" Attributions

Ability*" Attributions ^

IntendedPersistence

IntendedPersistence

-HSE

-LSE

-LSE

-HSE

% 3 1PF

3PF

(b)

5H

IP 32

I

-HSE

-LSE

*. 3

E

51

IP 31I

-HSE

-LSE

a. 3A

M 5 b

(d) (e)

Figure 1 Mediation relations for performance feedback (PF), effort (E) and ability (A) attributions, andintended persistence (IP), moderated by self-esteem (HSE = high self-esteem, LSE = low self-esteem)

312 LAWRENCE R. JAMES AND JEANNE M BRETT

esteem variable is questionable and that therelations to be presented are overdramatic, letus suppose that the results of our study cor-respond to a priori predictions and are asshown in Figure 1, sections b through e. Thesefigures portray regression slopes associatedwith relations among raw or deviation scoreson the variables. For high self-esteem individ-uals, Figure 1, sections b and c, suggests atendency to attribute increasing degrees offailure to a steadily increasing lack of effort,but not to ability. Specifically, scores on effortattributions vary from 2 to 6 and are associatedwith performance feedback (see Figure 1, sec-tion b), whereas scores on ability attributionsvary randomly between 0 and 1 and are notassociated with performance feedback (seeFigure 1, section c). The explanation for theseresults is that high-self-esteem individuals haveconfidence in their abilities and thus are proneto attribute unexpected failure to an unstablecause such as lack of effort. Continuing withhigh-self-esteem individuals, Figure 1, sectiond, indicates that the higher the perceived lackof effort, the more likely the intended persis-tence to participate on a second task The ra-tionale here is that comparatively stronger ef-fort attributions reflect a greater imbalancebetween a positive self-concept and perfor-mance feedback, and therefore a stronger forceto correct the imbalance by performing suc-cessfully on the second task. Finally, inasmuchas performance was essentially not attributedto ability, ability attributions are unrelated tointended persistence for high-self-esteem in-dividuals (see Figure 1, section e).

In regard to low-self-esteem individuals,Figure 1, sections b and c, shows that ability,but not effort, attributions are a positive func-tion of performance feedback. That is, thehigher the failure, the stronger the attributionto lack of ability, for which scores vary from2 to 6 (see Figure 1, section c), but scores oneffort attributions assume random values be-tween 0 and 1 and are unrelated to degree offailure (see Figure 1, section b). Figure 1, sec-tion e, demonstrates that intended persistenceis an inverse function of ability attributions(i.e., the stronger the attribution to lack ofability, the lower the intention to participatein the second task). Effort attributions are notrelated to intended persistence (see Figure 1,section d) because performance feedback was

essentially not attributed to effort. The ratio-nale for these relations is that (a) implied fail-ure is consistent with low-self-esteem individ-uals' lack of self-confidence, thereby resultingin the performance feedback —» ability attri-bution relation and (b) intent to persist, whichis never high, decreases as attributions to lackof ability increase because individuals perceivean increasing likelihood of failure and, as aform of defense, withdraw to protect an al-ready vulnerable self-concept (cf. Jones, 1973).

Now let us play the game of find the mod-erators) and the mediators). Application ofthe Rozeboom (1956) definition for mediationindicates that self-esteem is not a mediatorbecause self-esteem is not a direct or indirectfunction of performance feedback. That is, ifx = performance feedback and m — self-es-teem, then self-esteem fails to satisfy the firstcriterion for mediation because m i=f(x). Thisis clearly the case because self-esteem wasmeasured before the experiment. Rather, self-esteem is a moderator, which is evident inFigure 1 because relations between the ante-cedent performance-feedback conditions andthe attributions, and between the attributionsand intended persistence, are contingent onthe level of self-esteem.

In contrast, the attributions appear to bemediators. The attributions have ontologicalcontent that differs from performance feed-back and intended persistence (and self-es-teem). There is an explicit causal order inwhich the attributions occur after performancefeedback and prior to intended persistence,and, contingent on the level of self-esteem, theattributions are effects of performance feed-back and causes of intended persistence. Thissuggests that inclusion of the attributions inthe model helps to explain how performancefeedback influences intended persistence in thesense that the attributions specify the processesby which the influences of performance feed-back are transmitted to intended persistence.Finally, the attributions are complete media-tors of the relation between performance feed-back and intended persistence, contingent onthe level of self-esteem, which is to say thatperformance feedback affects intended persis-tence only indirectly through the attributions.

The fact that the mediation relations arecontingent on the level of self-esteem suggeststhe need to amend Rozeboom's (1956) defi-

MEDIATION 313

nition of mediation to include moderation.This is easily accomplished by mapping theRozeboom (1956) functional relations into therelations and accompanying functional equa-tions implied by Figure 1, only here we willinclude the nonadditive relations required bythe self-esteem moderator. The term functionalequation refers to a quantitative statement ofthe presumed structure of causal relationsamong a set of variables in a self-containedsystem, whereby self-contained is meant thatall relevant causes of an effect or endogenousvariable are included m the equation for thatvariable (James et al., 1982; Simon, 1952,1953, 1977). For the Rozeboom function m =

J{x), we have E = f(PF, SE) and A = f(PF,SE), where E = effort attribution, PF = per-formance feedback, SE = self-esteem, and A =ability attribution The "/" in the functionsfor E and A represents a nonadditive, althoughlinear, relation, as seen by the inclusion ofinteraction terms in the following functionalequations for E and A (the variables in theseequations and all remaining equations are as-sumed to be in deviation form).

E = bE,PFPF + bEtSESE

+ bE,{PFXsE{PF X SE) + e (1)

A = bA,PFPF + bA<SESE

XSE) (2)

The "6s" in Equations 1 and 2 represent causalor structural parameters. For example, bEiPFin Equation 1 is denned as the unique amountof change in E brought about by a unit ofchange in PF. Given reasonable satisfactionof the assumptions or conditions for confir-matory analysis, which are discussed in Ob-jective 2, the structural parameters may beestimated by unstandardized, ordinary leastsquares (OLS) regression weights. In this sense,the statistical estimating equations for Equa-tions 1 and 2 may be thought of as simplemultiple regression equations. Inspection ofFigure 1, Sections b and c, indicates that es-timates of the structural parameters repre-senting the interactions (i.e., bExPFxsE) andbAAPFxSE)) will be significant. In other words,the relation between E and PF is moderatedby SE, as is the relation between A and PF.(A point worthy of brief mention is that errorsof estimate as well as slope coefficients vary

as a function of SE blocks in Figure 1, Sectionb through Section e. Technically, heteroge-neous errors of estimate would preclude testsof slope—Gulliksen & Wilks, 1950).

The salient point here is that moderationmay be functionally involved in the first-stageof a mediation relation, but the moderator isnot a mediator. Specifically, variation in per-formance feedback affects only an attribution,but the explanation of the effects of perfor-mance feedback on ability and effort attri-butions is contingent on the level of self-es-teem. Moderation carries over into the secondstage of mediation in this model, because therelations between intended persistence andboth effort and ability attributions are contin-gent on the level of self-esteem (see Figure 1,Sections d and e). Rozeboom's second func-tional relation for mediated relations, y -f(m),stated separately for A and E, is IP =f(A, SE)and IP =/ (£ , SE), where IP = intended per-sistence, and the functions again representnonadditive relations In equation form, thefunctions are as follows:

XSE) + e (3)

IP = b]PJ£ + bIP^ESE

IP = bIP,AA +

+ bIPMxSE)(AXSE) + e (4)

Like Equations 1 and 2, OLS estimates ofthe structural parameters representing the in-teractions would be significant This suggeststhat the attributions transmit the influence ofperformance feedback to intended persistenceand enhance the explanatory power of themodel by specifying the processes throughwhich feedback acts on intentions. However,such transmission and enhancement is con-tingent on the level of self-esteem, and althoughself-esteem transmits nothing from feedbackto intentions, and thus cannot be a mediator,it contributes directly to the explanatory powerof the model. It might also be noted that asingle equation for IP could be developed.Analyses would demonstrate that the equationwith the best fit to the data would involve thefirst-order interactions bjPi(ExsE)(E X SE) andbIPXAXSE){A X SE). Interactions involving(A X E) and (AX EX SE) would be redundantwith the first-order interactions using SE asthe moderator.

314 LAWRENCE R JAMES AND JEANNE M BRETT

A final test of the model would consist ofascertaining whether all of the influence ofperformance feedback (PF) on IP is trans-mitted by the mediating attribution variables.The many options available for this test, typ-ically referred to as a "goodness of fit test" ora "test of logical consistency," include anomitted parameter test (Duncan, 1975; Jameset al., 1982; Namboodiri, Carter, & Blalock,1975), a disturbance term regression test(James & Jones, 1980), and hierarchical OLSin the confirmatory mode. Given high cor-relations between PF and E in the high-self-esteem block, and between PF and A in thelow-self-esteem block, use of the omitted pa-rameter test would likely be subject to mul-ticollinearity. Thus, the latter two procedureswould be the prime candidates for the good-ness-of-fit test To illustrate the use of hier-archical OLS in the confirmatory mode, theregressions indicated by Equations 3 and 4would be conducted and i?2s estimated. Theseare referred to as R2

3 and R24 to indicate es-

timates based on Equations 3 and 4, respec-tively. Next, .PF and (PF X SE) would be addedto Equation 3 as independent variables, anda new R2 computed, which is designated R2

3+.A nonsignificant difference between R2

3 andR2

3+ would imply that, within the self-esteemblocks, PF is not directly related to IP whenE is held constant. The key inference wouldbe that E completely mediates the effects ofPF on IP for high-self-esteem individuals. Asimilar process would be conducted for Equa-tion 4, namely PF and (PF X SE) would beadded to Equation 4 and J?2

4+ computed. Anonsignificant difference between R2

A and i?24+

would confirm the prediction that A com-pletely mediates the influences of PF on IPfor low-self-esteem individuals. Should R2

3+ >R\, and/or i?2

4+ > R24, then at least one of

the predictions based on the causal model hasbeen disconfirmed. The resulting inferencewould be that at least one of the mediators isnot a complete mediator, which is to say thatPF has a direct effect on IP in the high-self-esteem block and/or the low-self-esteem block.

In sum, moderators and mediators have dif-ferent roles, even though they may occurjointly in the same model. If one is willing toadopt the formal definition of mediator forhypothetical constructs advanced by Roze-boom (1956), then specific criteria must be

satisfied before a variable may be designateda mediator. It is particularly important to rec-ognize that m = f(x) and y = f(m) not onlyassume an explicit causal order but also implyactive causal processes in which m transmitsthe effects of x to y and, as part of this trans-mission process, enhances explanation becauseit specifies the processes by which x acts onor produces y. On the other hand, there is norequirement that mediation relations be ad-ditive. Nonadditive relations require the ad-dition of a moderator for either the m =f(x)or y =f(m) relations, or both (as shown here).In this condition, the moderator is added tothe function (e.g., IP = f[A, SE]) and "/" isspecified as nonadditive. The term moderatedmediation is suggested for such models to de-note that mediation relations are contingenton the level of a moderator.

Roles of Variables in Mediationand Moderation

It follows from the discussion above thatmediators are distinguished from moderatorsby the operational roles played by variables infunctional relations and equations. A seem-ingly logical deduction is that a particularvariable can be unambiguously classified aseither a mediator or a moderator In some,and perhaps most, cases this is true. In othercases it is false because a particular variablemay assume the roles of both mediator andmoderator in the same model, and even in thesame functional relation and equation. To seehow this could occur, suppose we conduct thesame experiment as described above, only thistime we randomly assign individuals to thefive performance-feedback conditions withoutmeasurement or blocking on self-esteem. As-suming that high-self-esteem individuals areas likely as low-self-esteem individuals to berandomly placed m each performance-feed-back condition, we would find that each at-tribution variable serves as both a mediatorand a moderator.

Illustrations of the relations are presentedin Figure 2. Figure 2, sections b and c, showsthat ability attributions moderate the regres-sions of effort attributions on performancefeedback and intended persistence on effortattributions. The rationale here is the same asthat for self-esteem, only here high-self-esteem

MEDIATION 315

A=0,1

A>2

E=0,1

I a S H 5

PFI a 3 4 S

PF

5

IP 3

aI

o | » 3 M 5 fc

E

5M

IP 3

I

ES2

I i 3 H 5 fc

A

Cc) (<i)

Figure 2 Functional components of mediation relations with ability (A) and effort (E) attributions servingas both mediators and moderators (PF = performance feedback, IP = intended persistence)

individuals are represented by scores of 0 or1 on the ability attribution scale, and low-self-esteem individuals are represented by scoresequal to or greater than 2 on the ability at-tribution scale. The salient points are that ef-fort attributions are mediators, whereas abilityattributions are moderators. Consistent withthese points is the observation that an attemptto fit a linear, additive, mediation model tothe relations involving effort attributions,namely E = f(PF) and IP = f(E), would failbecause the errors of estimate are heterosce-dastic in both relations. This is easily seen, forexample, in Figure 2, section a, where thecluster of points in the bivanate scatterplotwould be roughly triangular if moderation byability was disregarded.

We can now reverse the process, so to speak,and regard effort attributions as the moderatorand ability attributions as the mediator. Asseen in Figure 2, section b, the regression ofability attributions on performance feedbackis "significant" for individuals with scores of0 and 1 on the effort attribution scale (low-self-esteem individuals), and "nonsignificant"for individuals with scores equal to or greaterthan 2 on the effort attribution scale (high-self-esteem individuals). The moderation by

effort attributions carries over to the regressionof intended persistence on ability attributions(see Figure 1, section d).

Algebraic expression may help to clarify thepoints above. Mapping the Rozeboom (1956)relation rh = f(x), amended for moderation,into the relations above furnishes the followingfunctional equations:

E = bE,PFPF + bE,AA

bE,iPFXA)(PF XA)

A = bA,PFPF + bA,EE

bMPFxE)(PF XE)

(5)

(6)

Figure 2, sections a and b, denotes thatOLS estimates of terms representing the in-teractions will be significant, thus indicatingthat both A and E assume the functional roleof moderator in one of the equations. Yet,each attribution satisfies the first criterion formoderated mediation in the equation m whichit serves as an endogenous (dependent) vari-able.

Joint roles as a mediator and as a moderatorare even more apparent when Rozeboom'ssecond criterion for a mediation relation, y =f(m) amended for moderation, is mapped into

316 LAWRENCE R. JAMES AND JEANNE M. BRETT

our example. The equation is the same foreither^ or £ as a mediator and/or moderator,and is as follows:

IP = + biP,A

(7)

Given that the estimate of bIPt(ExA) is signifi-cant, Equation 7 may be interpreted as (a) theeffects of E on IP are contingent on the valueof A (see Figure 2, section c), or as (b) theeffects of A on IP are contingent on the levelof E (see Figure 2, section d). Combining thefirst interpretation of Equation 7 with Equa-tion 5 gives us £ as a mediator and A as amoderator. Combining the second interpre-tation of Equation 7 with Equation 6 gives usA as a mediator and E as a moderator

In conclusion, it may be impossible to clas-sify a particular variable as either a mediatoror a moderator because this variable may playboth roles in a set of simultaneous equationsdesigned to represent a causal model or system(i.e., Equations 5, 6, and 7 represent a set ofsimultaneous, functional equations for onecausal system—cf. Simon, 1977). This neednot be confusing if one remembers that it isthe role or roles that a variable plays that de-termine whether it is a moderator, a mediator,or both. Thus, applying the definitions for me-diation, moderation, and moderated mediationto the operational role(s) played by a variablein each functional relation and equation overthe set of relations and equations in a causalsystem furnishes the basis for ascertainingwhether the variable is a mediator, a moder-ator, or both a mediator and a moderator.

Other Amendments to the FunctionalDefinition of Mediation

In addition to moderation, it is necessaryto extend the Rozeboom (1956) functional def-inition of mediation to other types of func-tional relations. First, there is the question ofnonlinearity in the variables. For example, mmay be a linear, additive function of x, but ymay be an additive, nonlinear function of m.The mediation relation takes a form such asfn = f(x), y = /(AM2), which may be testedempirically by applying hierarchical OLS pro-cedures to operationalized functional equa-tions (Stolzenberg, 1979). Second, mediation

functions may involve nonrecursive relations,such as x —* m <=> y, where "<=»" denotes re-ciprocal causation. The mediation relation inthis case would be m = f(x, y), y = f(m),although additional exogenous causes of m andy would have to be added before empiricaltests are possible (cf. James & Singh, 1978)Examples of tests for mediation m nonrecur-sive designs are presented in James and Jones(1980) and Maruyama and McGarvey (1980)Cyclical recursive designs involving feedbackloops are another possibility, such as x —>m —>y —• x, where m = f(x), y = f(m), and x =f(y). The last term represents a feedback loop,with a specified time interval, from y to x.Empirical tests of cyclical recursive designsrequire a time-series analysis in which eachvariable is measured at a distinct time periodthat reflects the (causal) interval required forcause-effect relations to stabilize (cf. Heise,1975; James et al., 1982; Strotz & Wold, 1971).

Finally, prior discussion has focused oncomplete mediation, where the antecedent xaffects the consequence y only indirectlythrough the mediator m. The possibility ofpartial mediation also exists. A partial me-diation model is usually displayed in one ofthe following two equivalent forms, given thatrelations are recursive'

m m\I

In these models, x has both a direct effect ony and an indirect effect on y, the latter beingtransmitted by m. This indicates that only partof the total effect of x on y is due to mediationby m (cf. Duncan, 1970, 1975; Heise, 1975;Kenny, 1979). The mediation function has theform rh = J\x), y = f(x, m). Analytic proce-dures for partial mediation models are over-viewed in Alwin and Hauser (1975).

Summary

There are many types of causal mediationrelations and models. Yet, all have the commonattribute that the mediator transmits influencefrom an antecedent to a consequence. Thetransmission need not involve all of the influ-ence of the antecedent on the consequence,nor need the mediation relation be additive,

MEDIATION 317

linear, or recursive. Indeed, many possiblecombinations exist. Nevertheless, each com-bination specifies a particular operational rolefor each variable, and mediators are thosevariables whose operational role involvestransmission of influence. With mediators thusdescribed, let us now turn to the question ofspecification errors in causal mediation modelsand tests of causal mediation models.

Objective 2: Identifying Specification Errorsin Causal Mediation Models

A confirmatory test of a causal mediationmodel is designed to ascertain whether themodel is useful for explaining how variablesincluded explicitly in the model occurred andare related (cf. James et al., 1982). Confir-matory tests should only be conducted on"well-specified" causal models, by which it ismeant that the assumptions or conditions forconfirmatory analysis have been reasonablysatisfied. Specification error is the general termused in confirmatory analysis to indicate thatone or more conditions for confirmatory anal-ysis has (have) not been reasonably satisfied.In the presentation below, we have selectivelyfocused attention on specification errors con-sidered to be of major salience in confirmatorytests of complete mediation models. The dis-cussion is presented in the form of summarystatements, with accompanying references be-cause space considerations preclude furnishinga thorough review here. Brief mention is madeof additional concerns in concluding remarks,with emphasis placed on the need to adoptanalytic methods specifically designed forconfirmatory analysis.

To preface our remarks, allow us to reiterateseveral points made in the introductory com-ments to this article. The specification errorsdiscussed below are symptomatic of an in-complete transition from exploratory analysisto confirmatory analysis in areas such as jobperception and attrition research. The speci-fication errors became apparent only afterknowledge accumulated concerning all of theconditions that are prerequisite to meaningfulconfirmatory analysis. In a sense, therefore, itis unfair to criticize prior research on completemediation models inasmuch as researchersemployed what at the time was considered avalid paradigm for causal analysis. On the

other hand, a complete transition fromexploratory analysis to confirmatory analysiswill not be effected until the specification errorsare recognized and subsequently addressed infuture research. Thus, we will point out thespecification errors in prior research, but weshall do so at a general level and in the interestof identifying the principles involved ratherthan raising ad hominem arguments in regardto specific studies.

Examples of important specification errorsin causal, or structural, models based on com-plete mediation relations of the form x —* m —»y include the following: (a) misspecification ofcausal order (e.g, the true model is m —* x —>y or x —> y —»m); (b) misspecification of causaldirection (e.g., the true model is x —> m <=> y);(c) lack of self-containment, or an unmeasuredvariables problem, which is illustrated below;(d) the assumed additive, linear relations arenonadditive, nonlinear, or both; and (e) themodel is unstable (i.e., nonstationary), whichdenotes that the variables and relations in themodel are subject to severe random fluctua-tions or shocks (cf. James et al., 1982). It isonly after (a) the model can be regarded asnot being subject to one or more of these majorspecification errors and (b) after the model isshown by confirmatory analysis to have a goodempirical fit with data that (c) it is justifiedto consider the results of the confirmatoryanalysis as useful for attempting to explainhow a mediation process occurred (i.e., tomake causal inferences), or to employ a termsuch as causal effect or its various euphemisms,such as "determine," "indirect effect," "influ-ence," and "transmit."

Now consider that many mediation studiesin the industrial and organizational literatureand the organizational behavior literature be-gin with verbal, and often graphic, causalmodels in which considerable attention is givento causal order and explication of mediationprocesses. Causal relations are typically re-cursive throughout the model, although thisappears to be more a matter of conveniencethan a well-thought-out, defensible case forunidirectional causation. Attention may ormay not be given to additivity, linearity, andstability. However, attention is almost nevergiven to the possibility of misspecification dueto a "serious" unmeasured variables problem.By a serious unmeasured variables problem

318 LAWRENCE R. JAMES AND JEANNE M. BRETT

is meant that a stable variable exists that (a)has a unique, nonmmor, direct influence onan effect (either m or y, or both); (b) is relatedat least moderately to a measured cause of theeffect (e.g., is related to x in the functionalequation for m); and (c) is unmeasured—thatis, is not mcluded explicitly in the causal modeland the confirmatory analysis (James, 1980;James et al., 1982). This is unfortunate becausea serious unmeasured variables problem pre-cludes confirmatory analysis and the use ofcausal inference to attempt to explain media-tion processes (cf. Billings & Wroten, 1978;Darlington, 1968; Duncan, 1970, 1975; Jameset al., 1982; linn & Werts, 1969; Simon, 1952,1953, 1977). In particular, confirmatory an-alytic techniques such as path analysis andstructural equation analysis should not beused. If they are used, then, as shown in manyof the references above, estimates of causalparameters and the ensuing causal inferenceswill be biased.

It is also the case that procedures typicallyassociated with exploratory forms of analysis,namely hierarchical OLS or partial correlation,should not be employed in a confirmatorymode to test causal hypotheses or to serve asa basis for causal inference in the presence ofa serious unmeasured variables problem. Onthe other hand, a serious unmeasured variablesproblem does not preclude the use of hier-archical OLS or partial correlation in an ex-ploratory mode as long as the results of thehierarchical or partial correlation analysis areinterpreted in correlational terms with nocausal overtones. For example, an empiricaltest of a model of the form m =/(x), y =f(m),where the / s represent covariation and notcausal relations, may be based on a hierarchicalOLS and may show that R2^^ is not signif-icantly greater than R2

y. m. This indicates thatinclusion of x adds nothing to the predictionofy over that already furnished by m. It mayalso be shown that R2

y.mx is significantlygreater than R2

y.x, which denotes that m addsuniquely to the prediction of y in relation tox. Such results support a correlational formof mediation and an interpretation such as"the covariation between x and y vanishes ifm is controlled." The results cannot be inter-preted causally, such as m transmits causalinfluence from x to y or serves to explain howx and y are related, unless it can be assumed

that the mediation relations are not subject toa serious unmeasured variables problem. Ofcourse, use of correlational forms of mediationdefeats the main purpose for developing andtesting mediation models (i.e., explanation)and is the reason that most mediation modelsare presented in the causal mode (Rozeboom,1956).

Unfortunately, it is often the case in fieldstudies that causal mediation models with ob-vious misspecifications (i.e., unmeasuredvariables, unanalyzed reciprocal causation)have been subjected to goodness-of-fit tests us-ing hierarchical OLS and/or partial correla-tion. In the context of present knowledge, thesetests should be regarded as exploratory testsof correlational mediation hypotheses. Instead,these tests have been interpreted as confir-matory tests of causal hypotheses and used tomake causal inferences. In effect, we have anunwarranted intertwining of confirmatory andexploratory procedures, which is evidenced bysuch things as the use of beta weights fromthe hierarchical OLS analyses as implicit pathcoefficients (i.e., the weights are interpreted interms of importance and utility—cf. Darling-ton, 1968), the use of partial correlations thattend to zero (by controlling on a mediator) asevidence that an antecedent had no "directeffect" on a consequence, and the use of asignificant increment in R2

y.xm in relation toR2

y x to support a causal inference that the"influence" of x on y is transmitted throughthe mediator m. Remember also the examplepresented in the introduction to this article,where unmeasured variables would have to beinvoked to attempt to explain within-job vari-ation in job perceptions and job satisfaction.

In sum, the models, analyses, and resultsof many tests of mediation in the industrialand organizational literature and the organi-zational behavior literature do not furnish suf-ficient evidence for the causal interpretationsoffered in Discussion sections. It is recom-mended, therefore, that investigators begin todevote attention to all of the conditions forconfirmatory analysis before conducting con-firmatory tests on causal models and using theresults of these tests to support causal infer-ences. A review of the conditions for confir-matory analysis and causal inference is pre-sented in James et al. (1982). If one or moremajor sources of specification error is consid-

MEDIATION 319

ered viable, then use procedures such as hi-erarchical OLS or partial correlation in theexploratory mode and limit discussion to cor-relational interpretations. On the other hand,if all sources of misspecification are considered,and no major misspecification is consideredlikely, then confirmatory analytic techniquessuch as path analysis and structural equationanalysis should be used. This is because suchtechniques furnish (a) a means to test causalhypotheses that cannot be addressed by cor-relational techniques, such as reciprocal cau-sation; (b) estimates of causal parameters; and(c) a basis for estimating "indirect effects," amajor concern in mediation analysis (cf. Grif-fin, 1977). To illustrate the last point, if amodel of the form x —> m —» y is confirmed,then the path coefficient linking x to m (Pmx)may be multiplied by the path coefficient link-ing m t o j ' (pvm) or PmxPym. This product re-flects the magnitude of the indirect effect ofx on y. There is no analogue of this procedurein hierarchical OLS or partial correlation. Onthe other hand, we are not suggesting that hi-erarchical OLS and partial correlation haveno place in confirmatory analysis. Thesemethods have limited applications in the con-firmatory mode (Cohen & Cohen, 1983), anexample being the prior use of hierarchicalOLS to test a portion of the causal hypothesesassociated with a nonadditive, complete me-diation model (see Figure 1). The point wewish to emphasize is that hierarchical OLSand partial correlation should not be used inplace of confirmatory analytic methods.

Concluding Remarks

The following points were developed. First,mediation is generally thought of in terms ofcausal mediation, which connotes transmis-sion of influences from antecedents to con-sequences and an attempt to explain how an-tecedents produce consequences. Second, me-diation relations may assume any number offunctional forms, including nonadditive, non-linear, and nonrecursive forms. Third, confir-matory analytic techniques furnish the mostinformative tests of mediation. Fourth, thereis no middle ground between exploratory(correlational) and confirmatory analysis. At-tempts to explain how mediation processesoccur by causal inference require well-specified

causal models and empirically demonstratedgoodness of fit between models and data.Specification errors, such as a serious unmea-sured variables problem or misspecified causaldirection, preclude confirmatory analysis andcausal inference. Fifth, and finally, if causalmodels are well-specified, then confirmatoryanalytic techniques applicable to the model(s)of concern should be employed to furnish allrelevant information (e.g., estimates of causalparameters, estimates of indirect effects, testsof nonadditivity, etc.).

A full treatment of mediation requires con-sideration of issues not addressed here. Theseissues include (a) the use of the interveningvariable form of mediator in experimentalanalysis (MacCorquodale & Meehl, 1948;Rozeboom, 1956) and exploratory factoranalysis (Royce, 1963); (b) the use of "me-diating mechanisms" to develop theoreticalrationales for causal hypotheses, whereby me-diating mechanism means a hypothetical me-diator that is not tested empirically (James etal., 1982), and (c) micromediational processes,which consist of mediating relations at a finerlevel of explanation than that of the model inquestion (e.g., at the level of receptor, neural,or muscular mediating processes—Cook &Campbell, 1979). Although important, theseissues require a somewhat more esoteric pre-sentation than the "applied" orientation ofthis article.

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