香港中文大学 基于lisrel的SEM讲义 Note1

1StructuralEquationModeling结构方程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,FacultyofBusinessAdministrationTheChineseUniversityofHongKong2ClassicalTrueScoreModel•X=T+E▪X=Observedscore▪T=TrueScore▪E=MeasurementError3PropertiesofTrueandErrorScores•Meanoftheerrorscoresforapopulationiszero()•Correlation(相关系数)betweentrueanderrorscoresforapopulationiszero()•Correlationbetweenerrorscoresiszero()0E00.TE021EE4Construct(LatentVariable)潜变量•Conceptthattheresearchercandefineinconceptualtermsbutnormallycannotbedirectlymeasuredormeasuredwithouterror•Approximatelymeasuredbyindicators(指标)Hair,etal(1995).MultivariateDataAnalysiswithReadings.Pp.618PrenticeHall.5Babbie(1992).ThePracticeofSocialResearch.Pp.121.WadsworthPublishing6Babbie(1992).ThePracticeofSocialResearch.Pp.121.WadsworthPublishing7Babbie(1992).ThePracticeofSocialResearch.Pp.121.WadsworthPublishing8Babbie(1992).ThePracticeofSocialResearch.Pp.121.WadsworthPublishing9CriteriaforMeasurementQuality•Reliability(信度)referstothelikelihoodthatagivenmeasurementprocedurewillyieldthesamedescriptionofagivenphenomenon•Validity(效度)referstotheextenttowhichaspecificmeasurementprovidesdatathatrelatetocommonlyacceptedmeaningsofaparticularconcept.Facevalidity,criterion-related(predictive)validity,contentvalidity,andconstructvalidity10OperationalizationChoices•VariationsbetweentheExtremes•RangeofVariation•LevelsofMeasurement–NominalMeasures(定类)–OrdinalMeasures(定序)–IntervalMeasures(定距)–RatioMeasures(定比)•SingleorMultipleIndicators(单一指标或多项指标)11Dimension•Aspecifiableaspectorfacetofaconcept•Forexample:JobSatisfaction–Satisfactionwithsupervisor–Satisfactionwithco-workers–Satisfactionwithenvironment–Satisfactionwithpay–Satisfactionwithjobcontent12LISRELisGreektoMe!Hayduk(1987).StructuralEquationModelingwithLISREL.pp.88.JohnsHopkins.13UppercaseLowercaseNameUppercaseLowercaseNameΑαalphaΝνnuΒβbetaΞξxiΓγgammaΟοomicronΔδdeltaΠπpiΕεepsilonΡρrhoΖζzetaΣσsigmaΗηetaΤτtauΘθthetaΥυupsilonΙιiotaΦφphiΚκkappaΧχchiΛλlambdaΨψpsiΜμmuΩωomegaHayduk(1987).StructuralEquationModelingwithLISREL.pp.89.JohnsHopkins.14WhatisSEM•Simultaneousregressionequations(回归方程)•Modelinglatentvariables(潜变量/因子)fromobservedvariables(指标/题目)•Estimateparameters(参数)ofthemeasurementmodel(测量模型)&structuralmodel(结构模型)•Comparisonbetweenimpliedcovariancematrix(隐含协方差矩阵)&observedcovariancematrix(样本协方差矩阵)15WhatisSEM?Operatingmodel(formunknown)PopulationdataSoPopulationCovarianceMatrixSpecifi-cation+parsimonyerrorSpecifi-cation+parsimonyerrorSpecifi-cation+parsimonyerroretc.etc.kk-1k+1###################################SSkSampleCovarianceMatrixFittedCovarianceMatrixSamplingErrorApproximatingModelsDestDpopPopulationDiscrepancyEstimatedDiscrepancy(OperationalizedasaGFI)POPULATIONSAMPLEspecifiesrelationshipsamong...Sk^ApproximateCovarianceMatrixYSampledatamatrix16ImpliedCovarianceMatrix隐含协方差矩阵where=covariancematrixofForMeasurementModelS1111IIIIxSxxBollen(1989).StructuralEquationswithLatentVariables.Pp.86&236.Wiley.17BasicSEMModels•MeasurementModel(测量模型)•PathModel(结构模型)•FullModel(全模型)•ModelwithMeanStructures(均值结构模型)18MeasurementModel测量模型1X1X2X3X41234413121112X5X6X7X85678827262521219PathModel结构模型X1X2X3Y1Y2Y3111213233231213221320FullModel全模型1X1X2X3X41234413121111y1y2y3y41234413121112y5y6y7y856788272625211212121MatricesoftheX-Modelxx4321214232211143210000xxxx22xobservedindicatorsofξΛxfactorloadingsrelatingxtoξξlatentexogenousvariables(外源变值)δmeasurementerrorsforx23Variance/Covariancesamongtheexogenousvariables自变因子方差/协方差矩阵22211124MatricesoftheY-Model4321214232211143210000yyyyyy25yobservedindicatorsofηΛyfactorloadingsrelatingytoηηlatentendogenousvariables(内生变值)εmeasurementerrorsfory26MatricesoftheStructuralModel212121112121210000027ΒcoefficientsrelatingηtoηΓcoefficientsrelatingξtoηζresidualsinequations28Residualsinthepredictionoftheendogenousvariables结构方程残差的协方差矩阵22211129BenefitsofSEM•Accommodatingmultipleinterrelateddependencerelationships•Incorporatingvariablesthatwedonotmeasuredirectly(潜变量/因子)•Specifyingmeasurementerror(测量误差)•ImprovingstatisticalestimationHair,etal(1995).MultivariateDataAnalysiswithReadings.Pp.622PrenticeHall.30AdverseEffectsofMeasurementError=observedcorrelationbetweenXandY=correlationbetweenthetruescoresofXandYyyxxxyxyrrrr*xyr*xyr31StepsinStructuralEquationModeling•Step1:Developingatheoreticallybasedmodel(基于理论提出一个或多个基本模型)•Step2:Constructingapathdiagramofcausalrelationships•Step3:ConvertingthepathdiagramintoasetofstructuralequationsandspecifyingthemeasurementmodelHair,etal(1995).MultivariateDataAnalysiswithReadings.Pp.626PrenticeHall.32StepsinStructuralEquationModeling•Step4:Estimatingtheproposedmodel•Step5:Evaluatinggoodness-of-fit(拟合程度)criteria•Step6:Interpretingandmodi