第三讲 结构方程建模及其分析步骤

第三讲结构方程建模与分析的步骤主讲：张林（博士）一、结构方程模型的一般结构测量模型:（验证性因子分析）Ｘ=Λｘξ+δＹ=Λγη+εＸ、Ｙ分别是外源和内源指标;η、ξ分别是内源和外源变量;δ、ε分别是Ｘ、Ｙ的测量误差;Λｘ是Ｘ指标与外源潜变量ξ的关系;Λγ是Ｙ指标与内源潜变量η的关系。结构模型:η=βη+Γξ+ζβ是内源潜变量之间的关系；Γ是外源潜变量对内源潜变量的影响；ζ是模型中未能解释的部分。Pathdiagram–notationSEMx32x42x53x6321xx11y32y42y21y11123121211122223x1x2x3x4x5x6y1y2y3y4123412345621213231MeasurementmodelStructuralmodel二、结构方程模型的基本步骤1模型构想2模型指定3模型识别4模型拟合5模型评价•1模型构想模型构想：结构方程模型的出发点是为观察变量间假设的因果关系建立起具体的因果模型,也就是可以用路径图明确指定变量间的因果联系。但模型的建立必须以正确的理论为基础,否则无法正确解释变量关系。•2模型指定模型指定我们可以用线性方程系统表示出理论模型,主要依据以下假设:一是线性模型可以体现观察数据特征的假设;二是观察指标与潜变量关系的假设;三是潜变量或观察指标作用方向及属性的假设。•3模型识别模型识别识别所指定的模型是建立ＳＥＭ模型的重要阶段,如果假设的模型本身不能识别,则无法得到系统各个自由参数的唯一估计值。模型识别的一个必要但非充分的条件是,模型的自由参数不能多于观察数据的方差和协方差总数。•4模型拟合模型拟合就是把观察数据与统计模型相拟合,并用一定的拟合指标对其拟合程度加以判断。•5模型评价模型评价模型评价是在已有的证据和理论范围内,考察所提出的模型是否能最充分地对观察数据作出解释。因此,它远比仅确定模型与数据的拟合程度更为复杂。StructuralEquationModelingEvangeliaDemerouti,PhDUtrechtUniversityAthens,18.05.2004UseofSEMTotestwhethertheoreticalhypothesisaboutcausalrelationshipsfittoempiricaldata.Ithasaconfirmatorycharacter(i.e.,researcherdeterminestherelationshipsbetweenthevariables)Ittestsrelationshipsbetweenobservedaswellasunobserved,latentvariablesItcombinesregression,factoranalysisandanalysisofvariance.StepsintheutilizationofSEM1.Developmentofhypothesis2.Constructionofpathdiagram3.Specificationofmodelstructure4.Identificationofmodelstructure5.Parameterestimation6.Evaluationoftheresults7.Modificationofthemodel1.HypothesisHowaretheconstructsrelatedtoeachotherIndependent(latent)variables:exogenous()Dependent(latent)variables:endogenous()SpecifythestructuralmodelTimepressurePerformancex1y1y1=a+bx1observed,arehypothetical,abstractconstructsthatdonotexistinrealityandwhicharemeasured/operationalizedthroughmeasurementvariables/indicatorsJobdemandsPerformanceTimepressureCognitivedemandsNumbersalesNumbersteadycustomers111=a+b1latent2.ConstructionofpathdiagramSpecifythemeasurementmodel(=theempiricalindicatorsofthelatentconstructs)PainttherelationshipsusingtheconnotationofSEMPathdiagram–notationSEMx32x42x53x6321xx11y32y42y21y11123121211122223x1x2x3x4x5x6y1y2y3y4123412345621213231MeasurementmodelStructuralmodel3.SpecificationofmodelstructureMathematicalspecificationofthehypothesesusingmatricesofequitiesRules1.errorsshouldbeuncorrelatedwiththelatentconstructs(otherwisethereisanothervariablewhichsystematicallyinfluencesthemodelvariable,i.e.,incompletemodel)2.errorsshouldbeuncorrelatedwitheachother(otherwisethereisasystematicerrorthatinfluenceallindependentvariables,i.e.,methodfactor)4.IdentificationofmodelstructureCheckwhetherthematricescanbesolved,I.e.,whetherthereisenoughinformationfromtheempiricaldatatodeterminetheunknownparametersIfn=numberofindicators/observedvariabless=n(n+1)/2correlationcoefficientsornumberofequitiesIft=numberofunknownparametersthents(i.e.,df0)5.ParameterestimationThemodeltheoreticalcorrelationmatrix(sigma)hasthecorrelationcoefficientswhichweexpectwithinthedatasampleifthemodelisrightandthesampleisrepresentingthepopulationTheempiricalcorrelationmatrixhasthe(Pearsonproduct-moment)correlationcoefficients(rxy)whichindicateinhowfartherelationbetweentwovariablesxandyresemblesastraightline(ifonevariableincreases,theotherdoesalso)IterativeestimationsofthecorrelationcoefficientsintriestominimizethedifferencesbetweenandSTheoryEmpiricaldataThediscrepancybetweenandSexpresseswhethertheoreticalmodelisacceptable5.Parameterestimation:MeasurementmodelFactoranalysisexplainsthecorrelationamongitemsbyassuminganunderlyingfactorTherespectiveregressioncoefficientiscalledlambda()/loadingEgotisticbusinessgoalsd1Qebgi1d2Qebgc1Latentvariableksi1x1x2Factorloading=Indicatestheextenttowhichtheratingsofitemsdependonthelatentvariable11215.Parameterestimation:Structuralmodelpathcoefficient=regressionweight=standardizedregressioncoefficientThepathcoefficientfortheindependentonthedependentvariablesisindicatinginhowfarisexplainedbyEgotisticbusinessgoalsd1Qebgi1d2Qebgc1e1Qepgi1e2Qepgc1AltruisticbusinessgoalsLatentvariableksi1Latentvariableeta1Independent(1)Dependent(1)x1x2y1y26.Evaluationoftheresults:TotalmodelThemostcommonlyusedmodelfitstatisticsistheChiSquare(2)testforassociation2calculatesthedegreeofindependencebetweentwovariables(i.e.thetheoreticallyexpectedvaluesvs.theempiricaldata)Thelargerthediscrepancy(independence),thesooner2becomessignificantBecausewearedealingwithameasureofmisfit,thep-valuefor2shouldbelargerthan.05todecidethatthetheoreticalmodelfitsthedataHowever,therearemanymeasuresofmodelfit(seenextslides),eachwiththeirownassumptionsandlimitations6.Evaluationoftheresults:ModelpartsPlausibilityofparameterestimationt-valuefortheestimatedparametersshowingwhethertheyaredifferentfrom0;t1.96,p.05Chisquaredifferencetest7.Modificationofthemodelsimplifythemodel(i.e.,deletenon-significantparametersorparameterswithlargestandarderror)Expandthemodel(i.e.,includenewpathsusingthemodificationindexes,m5.00)MediationMediationWeseethatXa