结构方程模型张伟雄

1RunningLISRELMeasurementModel

LISREL测量模型张伟雄博士香港中文大学工商管理学院副院长管理学系教授GordonW.Cheung,Ph.DProfessor,DepartmentofManagementAssociateDean,FacultyofBusinessAdministrationTheChineseUniversityofHongKong2MeasurementModel/

ConfirmatoryFactorAnalysisModel

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123ScalingofLatentVariable

设定因子的度量单位

Virtuallyalllatentvariableshaveambiguousscales,thescalechoiceislargelyarbitrary.Aconvenientchoiceistogivethesamescaleasinthesensethatiszeroandisone.Anotherchoiceistostandardizethelatentvariablessuchthat(将所有因子的方差固定为1)Bollen(1989).StructuralEquationswithLatentVariables.Pp.153.Wiley.4RunningLISRELProgramTitleline(标题)InputSpecification(输入设定)ModelSpecification(模型设定)OutputSpecification(输出设定)5InputSpecificationDANI=k[numberofindicators]NO=numberofcasesLA[labelsfortheobservedvariables]V1V2V3V4V5RAFI=filename[ofrawdata]CMFI=filename[ofcovariancematrix]KMFI=filename[ofcorrelationmatrix]SDFI=filename[ofstandarddeviations]MEFI=filename[ofobservedmeans]SE[SelectandSequence]54321/ 6ModelSpecification(I)MONY=2NX=3NE=1NK=2LY=FILX=FIBE=FIGA=FRPH=SY,FRPS=DI,FRTE=DI,FRTD=DI,FRTY=FITX=FITX=FIKA=FILKksilabelsLEetalabels7ModelSpecification(II)FRlistofparameterstobeestimatedFIlistofparameterstohavespecifiedvaluesVAnumericalvalueofFIparametersCOparametermatrixelement=expressionwithotherparametersIRlistofparametermatrixelements>number<numberEQparametervaluesconstrainedtobeequalSTstartingvalues8OutputSpecificationPathDiagramOUAD=OFFND=4MI9Exercise:CFAModel

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12Drawthediagram11InputSpecificationTitleline:ExerciseDANI=8NO=200LAV1V2V3V4V5V6V7V8CM1.65 0.45 1.14 0.35 0.30 1.01 0.51 0.49 0.43 1.58 0.07 0.20 0.20 0.23 0.75 0.17 0.14 0.17 0.27 0.23 0.65 0.41 0.20 0.07 0.21 0.11 0.25 0.85 0.22 0.23 0.26 0.36 0.24 0.25 0.16 0.7512ModelSpecification

MONX=8NK=2LX=FILKStaffCustomerVA1LX11LX52FRLX21LX31LX41FRLX62LX72LX82PDOUAD=OFFND=4MI13ReadingLISRELOutputCheckforunreasonableparameters(不正常参数)ModelfitParameterestimates(参数估值)MultiplecorrelationCFA1.ls814IdentificationDegreetowhichthereisasufficientnumberofequationsto“solvefor”eachoftheparameterstobeestimated.NumberofknownparametersNumberofestimatedparametersqDegreesofFreedom

(自由度)df=p–qCFA1.GIF15Goodness-of-Fit

拟合优度?Operatingmodel(formunknown)Populationdata

oPopulationCovarianceMatrixSpecifi-cation+parsimonyerrorSpecifi-cation+parsimonyerrorSpecifi-cation+parsimonyerroretc.etc.kk-1k+1###################################S

kSampleCovarianceMatrixFittedCovarianceMatrixSamplingErrorApproximatingModels

est

popPopulationDiscrepancyEstimatedDiscrepancy(OperationalizedasaGFI)POPULATIONSAMPLEspecifiesrelationshipsamong...

k^ApproximateCovarianceMatrixYSampledatamatrix16MinimumFitFunctionValues

拟合函数17Chi-SquareTestWheng=1:18Relativechi-square

2to1or3to1areindicativeofanacceptablefit(CarminesandMcIver,1981,p.80)19RootMeanSquareErrorofApproximationBrowne&Cudeck(1993)EstimatedRMSEA=pClose:p-valuefortestingthenullhypothesisthatthepopulationRMSEAisnogreaterthan.05:20ComparisonstoaBaselineModel(1)Bentler-Bonett(1980)normedfitindex(NFI)Bollen’s(1986)relativefitindex(RFI)21ComparisonstoaBaselineModel(2)Bollen’s(1989)incrementalfitindex(IFI)Tucker-LewisNon-normedfitindex(NNFI)22ComparisonstoaBaselineModel(3)McDonaldandMarsh’s(1990)relativenoncentralityindex(RNI)Bentler(1990)comparativefitindex(CFI)23OtherFitIndicesGoodnessoffitindex(GFI)AdjustedGoodnessoffitindex(AGFI)24FitIndicesforcomparisonacrossnon-nestedmodelsAkaike(1973)AkaikeInformationCriteria(AIC)Browne-Cudeck(1989)BCCBayesInformationCriterion(Schwarz,1978;Raftery,1993)25FitIndicesforcomparisonacrossnon-nestedmodelsBozdogan’s(1987)CAICECVI26Hoelter’sCriticalNThelargestsamplesizeforwhichonewouldnotrejectthehypothesisthatamodeliscorrectatalpha=.05.27RootMeanSquareResidual(RMR)Thesquarerootoftheaveragesquaredamountbywhichthesamplevariancesandcovariancesdifferfromtheirestimatesobtainedundertheassumptionyourmodeliscorrect.ThesmallertheRMRis,thebetter.28CFAExercise2(1)Thedatasetcontains204observationsof12continuousvariables.The12variablesareindicatorsofthelatentvariablesSelf-esteem,DepressionandImpulsiveness.The12variablesareobservedona5-pointLikertscale.ThedatasetislistedinthefileCFA2.PSF.29CFAExercise2(2)SELF1toSELF5areindicatorsofthelatentvariableSelf-esteem.DEPRES1toDEPRES4areindicatorsofthelatentvariableDepression.IMPULS1toIMPULS3areindicatorsofthelatentvariableImpulsiveness.PathDiagramCFA2.GIF30CFAExercise2:OutputProgramFileCFA2.ls831NestedModelsWhenoneormorefreeparametersofamodelareconstrained,themodelthusconstrainedissaidtobenestedintheonefromwhichitwasderived.Theconstrainedmodelusuallyhaveaworsefit.Doestheimprovementinfitprovidedbyamorecomprehensivemodelwarrantpreferringittoamoreparsimoniousmodelnestedinit?32LikelihoodRatioTestProblem:sensitivetosamplesizeSolution:

CFI

changesinCFIlessthan-.01Cheung&Rensvold(2002)StructuralEquationModeling,9,233-25533ModificationIndices

修正指数Calculatedforeachconstrainedrelationshippossibleinaspecifiedmodel.TheModificationIndex(MI)valueforaspecificconstrainedparameteri