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1、DataProblemsinSEMIncompleteData/CategoricalDataTheimpactofincompletedata(andofanyprocedurefordealingwithincompletedata)dependssomewhatonthepatternofincompleteness:MissingCompletelyAtRandom(MCAR)ThemissingandobserveddistributionsofYareidentical:Y1Y2112233445566P(Y
2、inc
3、omplete)=P(Y
4、complete)i.e.,themissingvaluesareliterallyasimplerandomsampleexcisedfromanotherwisecompletedatasetSoitfollowsthatthecompletecases(ifany)arearandomsamplingfromamongtheentiredataset,i.e.,thesamemodelappliestoboththecompletecasesandthetotaldataset.MissingAt
5、Random(MAR)Y1Y2X11322123354465515668ForvariableY,themissingandobserveddistributionsareidentical,conditionalonsomeothersetofvariables:P(Y
6、incomplete,X)=P(Y
7、complete)ButthemissingnessmechanismisnottiedtothevalueofYitself.Onthepositiveside,thevaluesofothervariablesmayal
8、lowtheresearchertostatisticallyreconstructthemissingvaluesofY.EndersrecommendsusingauxiliaryvariablestocapitalizeonMAR.SimplyexcludingthemissingcasesmaytruncateoraltertheassessedrelationshipbetweenYandtheothervariables.However,theestimatedmeanandvarianceofYinthecompl
9、etecaseswillbeanunbiasedestimateofacompletesample.NonignorableMissingnessY1Y2312213445566–themissingandobservedvaluesofYarenotthesame,underanyconditions:P(Y
10、incomplete)≠P(Y
11、complete)Thereasonthatagivenvalueismissingmayhavetodowiththevalueitself.Inotherwords,anymodelf
12、orthevaluesofYbasedonlyontheobservedvalueswillbewrong.AnyestimateofstatisticsforY,orfortherelationshipsbetweenYandothervariables,maybebiased.Theresearchercannotbesureofobtainingcorrectestimates,regardlessoftechniqueused.Resolvingthesequestionsrequiresnewdatacollectio
13、n.ProceduresfordealingwithincompletedatainSEM:1.Forgetaboutit—treatmissingvalueplaceholdersasiftheywererealnumbers.Y1Y2312213495969Notrecommended,butprobablyhappensregularly.Consequences(underanymissingnesscondition):BiasedparameterestimatesForLikertdata,oftenincreas
14、eserrorvarianceIll-conditionedcovariancematrices2.Listwisedeletion—discardentirecaseifitisincomplete.UnderMCARParameterestimatesare
