结构方程模型第三讲知识讲解

结构方程模型及其应用第三讲LISREL及其应用WangShuJiaBusinessSchoolUniversityofShenzhen20一月20251STRUCTURALEQUATIONMODELING一个引例2STRUCTURALEQUATIONMODELINGConfirm.ls8locatedatc:/lisrel/project1/confirm.ls8ConfirmatoryfactoranalysisofhypotheticaldataforaclassexampleofhowtorunLISRELtoevaluateameasurementmodel.DAtaNInput=9NObservations=400MAtrix=CMLADepress1Frustrt1Stress1Depress2Frustrt2Depress2InteractLoveQualityKMSY1.00.61.00.50.61.00.70.40.31.00.30.40.40.51.00.40.30.30.50.61.00.40.30.40.30.30.31.00.50.30.30.30.40.30.41.00.40.40.30.30.20.30.40.51.03STRUCTURALEQUATIONMODELINGsd2.42.71.82.52.62.05.13.86.1MODELNY=6NX=3NE=2NK=1LY=FU,FILX=FU,FRCBE=FU,FIGA=FU,FRPH=SY,FRPS=DI,FR,TE=DI,FRCTD=DI,FRLKRel_QualLEStress_1Stress_2FREELY(1,1)LY(2,1)LY(3,1)LY(4,2)LY(5,2)FREELY(6,2)BE(2,1)OUtputSCEFVAMRPCPT4STRUCTURALEQUATIONMODELINGLonglines：Ifyourunoutofspaceonalineandwanttocontinuetothenextlineyoucanputa‘c’withatleastonespaceinfrontofitandthencontinue.Thisisthefirstline,itislongsocIcangotoasecondline.6STRUCTURALEQUATIONMODELING1.TitlelineUntilLISRELfindsalinestartingwithDA(forData),ittreatsalllinesasatitle.Forkeywordsonlythefirsttwolettersareread,soDAandDATAorDataarethesame.Confirm.ls8locatedatc:/lisrel/project1/confirm.ls8ConfirmatoryfactoranalysisofhypotheticaldataforaclassexampleofhowtorunLISRELtoevaluateameasurementmodel.7STRUCTURALEQUATIONMODELING2.DAtalineThislinebeginswithDAORData.NGroups=ThisindicatesthenumberofgroupsNInput=Numberofinputvariables(indicators).NObservations=Thesamplesize.MAtrix=CMforcovariancematrix,KMforcorrelations.8STRUCTURALEQUATIONMODELINGYoucanreadinacorrelationmatrixandstandarddeviations,butifyousayMA=CM,LISRELwillconvertyourmatrixintoacovariancematrix.e.g.DAtaNInput=9NObservations=400MAtrix=CM9STRUCTURALEQUATIONMODELING3.LAblesYoushouldlabelyourvariables.Herewearereferringtoindicatorsandnotlatentvariables.ThisisdonebyputtingLAononelineandlabelsonthefollowingline(s).Youarelimitedto8spacestotalperlabel.Youdonotneedlabels(LISRELwilluseVAR1,VAR2,etc.).Labelsmakereadingtheoutputmuchbetter.LADepress1Frustrt1Stress1Depress2Frustrt2Stress2InteractLoveQualityLA“DepI”“Frust1”“Stress1”“Dep2”“Frust2”“Stress2”InteractLoveQuality(Thequotesareusedifthereisaspaceinalabel.)10STRUCTURALEQUATIONMODELING4.EnteringDataYoucanenterrawdata,acovariancematrix,acorrelationmatrix,standarddeviations,andmeans.Herearethreeexamples:11STRUCTURALEQUATIONMODELING12STRUCTURALEQUATIONMODELINGIfthematrixislargeitmaybeusefultohavethematrixinanexternalfile.

KMSYFI=c:\project\mydata.dat RAFI=c:\project\mydata.datEX(freeformat)EX(fixedformat)13STRUCTURALEQUATIONMODELING5.Selecting/RearrangingVariablesLISRELallowsyoutoselectvariablesandrearrangethem.Thisisveryusefulifyouaregoingtorundifferentmodelsonthesamedata.Onceyouenterthedata,youcanselect/arrangevariableshoweveryouwant.SE‘Depress1’‘Frustrt1’‘Stress1’‘Interact’‘Love’‘PerQual’/orSE123789/14STRUCTURALEQUATIONMODELING6.MOdelTheMOdellineisthemostcomplexlineintheLISRELprogram.Thisdescribesallofthematrices.ThisisdonebyspecifyingthenumbersthatdeterminetheirdimensionsandthentellingLISRELaboutthematrix(free,fixed,symmetrical,full,etc.).Thedescriptionofthematrix,e.g.,fixedatsomevaluesuchas0or1,isselectedtodescribemostoftheparameters.Latter,youwilltellLISRELthoseelementsthataredifferent(e.g.,freemeaningyouwantLISRELtoestimatethem).15STRUCTURALEQUATIONMODELINGFirst,youneedtowritetheeightmatricesthatfityourfigure.Forourexample,thematricesare:16STRUCTURALEQUATIONMODELING17STRUCTURALEQUATIONMODELING18STRUCTURALEQUATIONMODELINGSUMMARY*Can’tbechangedonModellinebutelementscanbefree.19STRUCTURALEQUATIONMODELINGEXAMPLEMODELNY=6NX=3NE=2NK=1LY=FU,FILX=FU,FRCBE=FU,FIGA=FU,FRPH=SY,FRPS=DI,FR,TE=DI,FRCTD=DI,FRORMODELNY=6NX=3NE=2NK=1LX=FU,FRBE=FU,FICPS=DI,FR20STRUCTURALEQUATIONMODELING7.LKandLElinesTheselinesprovidelabelsforthelatentvariables.LKRel_QualLEStress_1Stress_221STRUCTURALEQUATIONMODELINGTheselinesfreeparametersthatshouldbefreebutweremisspecifiedasfixedintheMODELlineandtheyfixparametersthatweremisspecifiedasfreeintheMODELline.AttheendoftheFRandFIlines,Lisrelshouldbeabletoreproducetheeightmatricesyouwrotetodescribethefigure.Inourexamplewedon’thavetochangeLXatallsinceitisalreadyfullandfree.WehavetofreethelambdasinLY,andthebetainBE.Wedonothavetochangeanythingfromfreetofixed.FREELY(1,1)LY(2,1)LY(3,1)LY(4,2)LY(5,2)LY(6,2)FREEBE(2,1)8.FReeandFIxedlines22STRUCTURALEQUATIONMODELING9.OUputSS-Printsstandardizedstructuralmodel(beta,gamma,psi)SC-PrintsstandardizedoutputwhereeverythingisstandardizedEF-Printstotalandindirecteffects,theirstandarderrors,andtheirt-values(z-scores).MR-Printsvariancesandcovariancesoflatentvariableswitheachotherandwithindicators.ThisalsogivesyoutheresidualanalysisandQ-plotFS-Printsfactorscoresregression.23STRUCTURALEQUATIONMODELINGPT-Thisprintssometechnicaloutputsuchasthevalueofthefittingfunctionforeachiteration.PC-Printscorrelationsofparameterestimates.Thiscanbeverylong.Ifyouhave200parameterestimates,thismatrixwillhave40,000elements.Thiscanbeausefulwayofdiagnosingidentificationproblemsandmulticolinearity.Whentwoparameterestimatesarehighlycorrelated,sayr>.8,thenLISRELishavingtroubleestimatingthem.ND=xThisgivesyouxdecimalplaces,thedefaultis2.AD=offThisturnsoffanadmissibilitycheck.LISRELstopsat20iterationsifitthinksamatrixisproblematic.YoushouldturnthisoffifyoufixanyoftheerrorvariancesinTEorTDtozero.OUtputSCEFVAMRPCPT24STRUCTURALEQUATIONMODELINGConfirm.ls8locatedatc:/lisrel/project1/confirm.ls8ConfirmatoryfactoranalysisofhypotheticaldataforaclassexampleofhowtorunLISRELtoevaluateameasurementmodel.DAtaNInput=9NObservations=400MAtrix=CMLADepress1Frustrt1Stress1Depress2Frustrt2Depress2InteractLoveQualityKMSY1.00.61.00.50.61.00.70.40.31.00.30.40.40.51.00.40.30.30.50.61.00.40.30.40.30.30.31.00.50.30.30.30.40.30.41.00.40.40.30.30.20.30.40.51.025STRUCTURALEQUATIONMODELINGsd2.42.71.82.52.62.05.13.86.1MODELNY=6NX=3NE=2NK=1LY=FU,FILX=FU,FRCBE=FU,FIGA=FU,FRPH=SY,FRPS=DI,FR,TE=DI,FRCTD=DI,FRLKRel_QualLEStress_1Stress_2FREELY(1,1)LY(2,1)LY(3,1)LY(4,2)LY(5,2)FREELY(6,2)BE(2,1)OUtputSCEFVAMRPCPT26STRUCTURALEQUATIONMODELINGEXAMPLE--LongitudinalModels27STRUCTURALEQUATIONMODELINGInthismodel,Q7(Quantitativeabilityatgrade7)andV7(VerbalAbilityatgrade7)arelatentexogenousvariablesandweassumetheyarecorrelated.测量模型

结构模型

28STRUCTURALEQUATIONMODELINGWeneedtodoalleightmatrices.Thisincludes(a)LAMBDA-X(loadingsforXi),(b)THETA-DELTA(errorsforXi),(c)LAMBDA-Y(loadingsforYi),(d)THETA-EPSILON(errorsforYi),and(e)PHI(covarianceofexogenousKSIvariables).forthemeasurementmodel,

(f)BETA(endogenousETAsàendogenousETAs),(g)GAMMA(exogenousKSIsàendogenousETAs),and(h)PSI(forZETA—unexplainedvariance,residuals)29STRUCTURALEQUATIONMODELING30STRUCTURALEQUATIONMODELING31STRUCTURALEQUATIONMODELINGProgramSEM2_longitudinal.ls8VerbalandQuantitativeAbilityInGrades7and9.Model:GA=DI,PS=DIandTDandTEuncorrelatedDANI=12NO=383LAMATH7SCI7SS7READ7SCATV7SCATQ7MATH9SCI9SS9READ9SCATV9SCATQ932STRUCTURALEQUATIONMODELINGKM