第八讲中介效应及其检验msci

第八讲中介效应及其检验中介变McKinnonDP.2008.Introductiontostatisticalmediation andFrancisGroup:NewYork.博 样博 中介效应路径模型和回归方博 检验中介效应的回归方博 中介效Totaleffect=Directeffect+IndirectTotaleffect,Directeffect,Indirecteffect(Mediatedeffect),总效应,直接效应,间接效应（中介效应）,博 博 完全中介vs.部分中步条完全中部分中(1)以X预测预测效果存预测效果存(2)以X预测预测效果存预测效果存(3)同时以X与M预测XMYXMYXMYXMY完全中介(Complete 部分中介(p8rtial博 中介效应的检验方Barron&Kenny博 Barron&Kenny模中介效果的检公平知(X,自变量 (M,中介变量 (Y,因变量BasedonBaron&Kenny(1986);Alsosee博 BarronandKenny,博 Step1:RelationofXtoXXYY=i1+cX+博 Step2:RelationofXtoXYM=i2+aX+博 Step3:RelationofXandMto XXYY=i3+c’X+bM+博 样博 第三步：检验中介变量对因变量的影响（控制自变量MeasuringItholdsthat:c=c’+ab,a)multipleregression(orstructuralequationmodelingwithoutlatentvariables)isused,b)therearenomissingdata,c)thesamecovariatesareinthe博 IssueswithBaron&KenneyTheysaytotaleffectcfromY=i1+cX+ε1mustbestatisticallysignificantbeforeproceedingWhatifcandabareoppositeinAnnoyanceofmultiplestepsandhandStatisticalsignificanceofthe博 SobelSobel博 AExampleofSobel博 SobelTheSobeltestworkswellonlyinlargeWemendusingthistestonlyiftheuserhasnoaccesstorawdata.Ifyouhavetherawdata,bootstrap offersamuchbetteralternativethatimposesnodistributionalPreacherK,HayesA.2004.SPSSandSASproceduresforestimatingindirecteffectsinsimplemediationmodels.BehaviorResearchMethods,Instruments,& 6(4):717- DistributionoftheThemediatedeffectistheproductoftwocoefficientsaandb.Thedistributionoftheproducthasanormaldistributiononlyinspecialcases.Atlowvaluesofaandb,thedistributionhasexcesskurtosisandskewness,e.g.whenaandbarebothzero,kurtosisis6.Itisnotsurprisingthattheconfidencelimitsareinaccurateifthedistributionisassumedtobenormal.Onesolutionistousethedistributionoftheproductinstatisticaltestsandconfidencelimits.博 博 CriticalValuesforDistributionoftheBecausethedistributionoftheproductisnotnormal,therearedifferentcriticalvaluesforthedistribution foreachvalueofa/saandb/sb.Thecriticalvaluesare-1.96and+1.96forthe95%confidenceintervalfromthenormaldistribution.Therearedifferentupperandlowercriticalvaluesforthedistributionoftheproduct.Confidencelimitsandsignificancetestsaremoreaccurateusingthecriticalvaluesfromthedistributionoftheproduct(MacKinnonetal.2004).博 ResamplingAnothergoodoptionfordatathatdonothaveanormaldistributionisresamplingmethods(MacKinnonetal.2004).BootstrapmethodformediatedeffectswasdescribedbyBollen&Stine(1991),Lockwood&MacKinnon(1998),MacKinnonetal.,(2004)andShrout&Bolger(2002)Purposeistousethedataitselftoformadistributionofastatistic(Manly,1997).Doesnotmakeasmanyassumptionsandcanhandlenon-normaldistributions.Thevalueofastatisticintheobservedsampleiscomparedtothedistributionofthestatisticformedbyresamplingfromthedataalargenumberoftimes.博 usescomputerintensiveresamplingtomakeinferencesratherthanmakingassumptionsaboutthepopulation.Inotherwords,bootstrap treatsagivensampleasthepopulation.博 Bootstrapthesamplingdistributionofabandderiveaconfidenceintervalwiththeempiricallyderivedbootstrappedsamplingdistribution.Thebootstrap isplishedbytakingalargenumberofsamplesofsizen(wherenistheoriginalsamplesize)fromthedata,samplingwith cement,andcomputingtheindirecteffect,ab,ineachsample.博 博 Assumeforillustrationthat1,000bootstrapsampleshavebeentaken.Thepointestimateofabissimplythemeanabcomputedoverthe1,000samples.Thesdofthe1000valuesistheSE.Toderivethe1-αconfidenceSORTtheelementsofthevectorof1,000estimatesoffromlowtoThelowerlimitoftheconfidenceintervalisthe(α/2)1000value,andtheupperlimitisthe(1-α/2)1000‘thvalueinthesortedsample.博 Theconfidenceintervalcanandoftenisasymmetric(inaccordancewiththeskewnessofthesamplingdistributionofab)If0isoutsidetheCI,thenullhypothesisofnomediationisrejectedattheαlevelofsignificance.博 Thestepsofabootstrap博 Thestepsofabootstrap博 BootstrapTestforEstimatethemediatedeffectintheMakeanewdatasetbysamplingNsubjectsdata cementandestimatingthemediatedeffectineachofalargenumber(e.g.2000)ofbootstrapsamples.Determinesignificancelevelbylocatingthemediatedeffectfortheobservedsampleinthedistributionofthebootstrapsample.Find2.5%and97.5%valuesforconfidenceinterval.Bias-correctedbootstrapmakesacorrectionforthedifferencebetweentheobservedandaveragebootstrappedmediated博 AdvantagesofTheadvantageofbootstrap methodsisitsgreatsimplicity.Itisstraightforwardtoapplythebootstraptoderiveestimatesofstandarderrorsandconfidenceintervalsforcomplexestimatorsofcomplexparameters. isingthemostpopularmethodoftestingmediationbecauseitdoesnotrequirethenormalityassumptiontobemet,andbecauseitcanbeeffectivelyutilizedwithsmallersamplesizes.博 MinorDrawbacksofMoretimeconsumingfortheBootstrapyieldsslightlydifferentCI’seachtimeyouapplythismethodtothesamedata.博 StatisticalMediationTestsTestsdiffersubstantiallyinTypeIerrorandstatisticalpower.Requirementforsignificanttotaleffect,c,andrequirementthatc’isnon-significantreducesaccuracyofcausalstepsmethods.Assumptionthatthemediatedeffectdividedbyitsstandarderrorhasanormaldistributionisincorrectforsomevalues.Besttestsarebasedonthedistributionoftheproductandresamplingmethods.博 小Baron&Kenny方法现在很少用，主流期 律都是用系数乘积项检验法(productsofcoefficients)，即H0:ab=0。其中，a是从自变量X博 Woodetal.,Forallapproaches,theassumptionofcausalityisimplicitinthedefinitionofmediation.Amediatorisdefinedasanex natorymechanismthroughwhichonevariab