关于部分中介与完全中介作用与课堂定义相同.docx

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DavidA.Kenny

January10,2008

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MEDIATION

WhatisMediation?

Baron&KennySteps

MeasuringMediationortheIndirectEffect

DesignIssues

SpecificationError

Extensions

LinkstoOtherSites

References

WhatIsMediation?

   ConsideravariableXthatisassumedtoaffectanothervariableY. ThevariableXiscalledtheinitialvariableandthevariablethatitcausesorYiscalledtheoutcome. Indiagrammaticform,theunmediatedmodelis图片显示不出来

TheeffectofXonYmaybemediatedbyaprocessormediatingvariableM,andthevariableXmaystillaffectY. Pathciscalledthetotaleffect. Themediatedmodelis图片显示不出来

（Thesetwodiagramsareessentialtotheunderstandingofthispage. Pleasestudythemcarefully!

） Pathc'iscalledthedirecteffect. Themediatorhasbeencalledaninterveningorprocessvariable. CompletemediationisthecaseinwhichvariableXnolongeraffectsYafterMhasbeencontrolledandsopathc'iszero.PartialmediationisthecaseinwhichthepathfromXtoYisreducedinabsolutesizebutisstilldifferentfromzerowhenthemediatoriscontrolled.

   Notethatamediationalmodelisacausalmodel. Forexample,themediatorispresumedtocausetheoutcomeandnotviceversa. Ifthepresumedmodelisnotcorrect,theresultsfromthemediationalanalysisareoflittlevalue. Mediationisnotdefinedstatistically;ratherstatisticscanbeusedtoevaluateapresumedmediationalmodel. Thereadershouldconsultthesectionbelowon SpecificationError.

   Thereisalonghistoryinthestudyofmediation（Hyman,1955;MacCorquodale&Meehl,1948）. Currentlymediationisaverypopulartopic. （Thispageaveragesover100differentvisitorsaday.） Thereareseveralreasonsfortheintenseinterestinthistopic. Onereasonfortestingmediationistryingtounderstandthemechanismthroughwhichtheinitialvariableaffectstheoutcome. Mediation（andmoderation）analysisareakeypartofwhathasbeencalledprocessanalysis. Moreoverwhenmostcausalorstructuralmodelsareexamined,themediationalpartofthemodelisthemostinteresting.

BaronandKennySteps

   Ifthemediationalmodel（seeabove）iscorrectlyspecified,thepaths（c,a,b,andc'）canbeestimatedbymultipleregression,sometimescallordinaryleastsquaresorOLS. Asdiscussedlater,othermethodsofestimation（e.g.,logisticregressionandstructuralequalmodeling）canbeused. Regardlessofwhichdataanalyticmethod（thegeneralassumptiononthispageisthatitismultipleregression）isused,thestepsnecessaryfortestingmediationarethesame. Thissectiondescribestheanalysesrequiredfortestingmediationalhypotheses[previouslypresentedbyBaronandKenny（1986）andJuddandKenny（1981）].

   BaronandKenny（1986）andJuddandKenny（1981）havediscussedfourstepsinestablishingmediation:

Step1:

 Showthattheinitialvariableiscorrelatedwiththeoutcome. UseYasthecriterionvariableinaregressionequationandXasapredictor（estimateandtestpathc）.Thisstepestablishesthatthereisaneffectthatmaybemediated.

Step2:

Showthattheinitialvariableiscorrelatedwiththemediator. UseMasthecriterionvariableintheregressionequationandXasapredictor（estimateandtestpatha）. Thisstepessentiallyinvolvestreatingthemediatorasifitwereanoutcomevariable.

Step3:

 Showthatthemediatoraffectstheoutcomevariable. UseYasthecriterionvariableinaregressionequationandXandMaspredictors（estimateandtestpathb）. Itisnotsufficientjusttocorrelatethemediatorwiththeoutcome;themediatorandtheoutcomemaybecorrelatedbecausetheyarebothcausedbytheinitialvariableX. Thus,theinitialvariablemustbecontrolledinestablishingtheeffectofthemediatorontheoutcome.

Step4:

 ToestablishthatMcompletelymediatestheX-Yrelationship,theeffectofXonYcontrollingforM（pathc'）shouldbezero（seediscussiononsignificancetesting）. TheeffectsinbothSteps3and4areestimatedinthesameequation.

Ifallfourofthesestepsaremet,thenthedataareconsistentwiththehypothesisthatvariableMcompletelymediatestheX-Yrelationship,andifthefirstthreestepsaremetbuttheStep4isnot,thenpartialmediationisindicated. Meetingthesestepsdoesnot,however,conclusivelyestablishthatmediationhasoccurredbecausethereareother（perhapslessplausible）modelsthatareconsistentwiththedata. SomeofthesemodelsareconsideredlaterintheSpecificationErrorsection.

Notethatthestepsarestatedintermsofzeroandnonzerocoefficients,notintermsofstatisticalsignificance,astheywereinBaronandKenny（1986）. Becausetriviallysmallcoefficientscanbestatisticallysignificantwithlargesamplesizesandverylargecoefficientscanbenonsignificantwithsmallsamplesizes,thestepsshouldnotbedefinedintermsofstatisticalsignificance. Statisticalsignificanceisinformative,butotherinformationshouldbepartofstatisticaldecisionmaking. Forinstance,considerthecaseinwhichaislarge,biszero,andsoc=c'. Itisverypossiblethatthestatisticaltestofc'isnotsignificant（duetothecollinearityofXandM）whereascissignificant.Itwouldthenappearthatthereiscompletemediationwheniffactthereisnomediationatall.

   Following,Kenny,Kashy,andBolger（1998）,onemightaskwhetherallofthestepshavetobemetfortheretobemediation. Certainly,Step4doesnothavetobemetunlesstheexpectationisforcompletemediation. Intheopinionofmostthoughnotallanalysts,Step1isnotrequired. However,notethatapathfromtheinitialvariabletotheoutcomeisimpliedifSteps2and3aremet. Ifc'wereoppositeinsigntoabsomethingthatMacKinnon,Fairchild,andFritz（2007）refertoas"inconsistentmediation,"thenitcouldbethecasethatStep1wouldnotbemet,butthereisstillmediation.Inthiscasethemediatoractslikeasuppressorvariable. MostanalystsbelievethattheessentialstepsinestablishingmediationareSteps2and3.

   JamesandBrett（1984）havearguedthatStep3shouldbemodifiedbynotcontrollingfortheinitialvariable. Theirrationaleisthatifthereiscompletemediation,therewouldbenoneedtocontrolfortheinitialvariable. However,becausecompletemediationdoesnotalwaysoccur,itwouldseemsensibletocontrolforXinStep3.

MeasuringMediationortheIndirectEffect

   Theamountofmediation,whichiscalledtheindirecteffect,isdefinedasthereductionoftheeffectoftheinitialvariableontheoutcomeorc-c'. ThisdifferenceincoefficientsistheoreticallyexactlythesameastheproductoftheeffectofXonMtimestheeffectofMonYorab;thusitholdsthatab≈c-c'. Thetwoareexactlyequalwhena）multipleregression（orstructuralequationmodelingwithoutlatentvariables）isused,b）therearenomissingdata,c）andthesamecovariatesareintheequation. However,thetwoareonlyapproximatelyequalformultilevelmodels,logisticanalysisandstructuralequationmodelwithlatentvariables. Forsuchmodels,itisprobablyinadvisabletocomputecfromStep1,butrathercshouldbeinferredtobec'+abandnotdirectlycomputed. NotethattheamountofreductionintheeffectofXonYisnotequivalenttoeitherthechangeinvarianceexplainedorthechangeinaninferentialstatisticsuchasForapvalue. ItispossiblefortheFfromtheinitialvariabletotheoutcometodecreasedramaticallyevenwhenthemediatorhasnoeffectontheoutcome!

 Itisalsonotequivalenttoachangeinpartialcorrelations.

   IfStep2（thetestofa）andStep3（thetestofb）aremet,itfollowsthattherenecessarilyisareductionintheeffectofXonY. Onewaytotestthenullhypothesisthatab=0istotestthatbothaandbarezero（Steps2and3）. Ifsuchastrategywereusedandonewanteda.05probabilityofthecombinedtestthata=0andb=0,thenalphaforthetestsofaandbshouldloweredto.0253sothattheTypeIerrorprotectionrateiscorrect.

   Muchmorecommonly,asingletestisusedandishighlyrecommended（MacKinnon,Lockwood,Hoffman,West,&Sheets,2002）. ThetestwasfirstproposedbySobel（1982）. Itrequiresthestandarderrorofaorsa（whichequalsa/tawheretaisthettestofcoefficienta）andthestandarderrorofborsb. TheSobeltestprovidesthestandarderrorofabcanbeshowntoequalapproximatelythesquarerootof

b2sa2+a2sb2

Otherstandarderrorshavebeenproposed,buttheSobeltestisbyfarthemostcommonlyreported. ThetestoftheindirecteffectisgivenbydividingabbythesquarerootoftheabovevarianceandtreatingtheratioasaZtest（i.e.,largerthan1.96inabsolutevalueissignificantatthe.05level）. KristopherJ.PreacherandGeoffreyJ.Leonardellihaveanexcellentwebpagethatcanhelpyoucalculatethesetest（gototheSobeltest）. Measuresandtestsofindirecteffectsarealsoavailablewithinmanystructuralequationmodelingprograms.TheseprogramsappeartousetheSobelformula.

   ThederivationoftheSobelstandarderrorpresumesthataandbareindependent,somethingthatistruewhenthetestsarefrommultipleregressionbutnottruewhenothertestsareused（e.g.,logisticregression,structuralequationmodeling,andmultilevelmodeling）. Insuchcases,theresearcherideallyprovidesevidenceforapproximatei