关于部分中介与完全中介作用与课堂定义相同Word下载.docx
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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
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