香港中文大学 基于lisrel的SEM讲义Note4

1MeasurementEquivalence/Invariance测量等同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,FacultyofBusinessAdministrationTheChineseUniversityofHongKong2WhatisMeasurementEquivalence/Invariance(ME/I)ME/I(测量等同)isageneraltermthatcanbeappliedtothecomparisonofthevariouscomponentsofmeasurementmodels,andcansometimesbeextendedtostructuralmodelsandmeanstructures3ApplicationofME/ICross-culturalcomparisonsComparisonsofpeoplewithdifferentlevelsofacademicachievementComparisonacrossgendersComparisonofexperimentalversuscontrolgroupsComparisonoftheselfratingofperformanceversusratingbysupervisors4MeasurementModel1X1X2X3X41234413121112X5X6X7X8567882726252125ModelwithMeanStructuresRelationshipsbetweentheobservedvariablesandthelatentconstruct:(1)Thecovariancematrixofxis:(2)Themeanvalueofis:(3)ijijiixxxjijiixE6ScalingofLatentVariable••Virtuallyalllatentvariableshaveambiguousscales,thescalechoiceislargelyarbitrary.•Aconvenientchoiceistogivethesamescaleasinthesensethatiszeroandisone.•ShouldNOTstandardizethelatentvariablesbysettingbecausemeanofstandardizedvariableiszero.1111X1Bollen(1989).StructuralEquationswithLatentVariables.Pp.153.Wiley.111jijiixE72AdditionalVectors•Intercepts(指标截距)(TX)•LatentMeans(因子均值)(KA)8BasicTypesofME/IConfiguralEquivalence(形态相同)MetricEquivalence(因子负荷等同)ScalarEquivalence(指标截距等同)UniquenessEquivalence(误差方差等同)ConstructVarianceEquivalence(因子方差等同)ConstructRelationsEquivalence(因子关系等同)LatentMeanEquivalence(因子均值等同)9ConfiguralEquivalence形态相同Bothgroupsassociatethesamesubsetsofitemswiththesameconstructs(thecognitivedomainsarethesame)LX=PSTX=PSKA=FR)2()1(formform10MetricEquivalence因子负荷等同Overall,thestrengthoftherelationshipsbetweenitemsandtheirunderlyingconstructsarethesameacrossgroups.(Theconstructsaremanifestedinthesameway)LX=INTX=PSKA=FR)2()1(11ScalarEquivalence指标截距等同Thecross-culturaldifferencesindicatedbytheitemsarethesameacrossitems.Alternatively:allitemsindicatethesamecross-culturaldifferences.LX=INTX=INKA=FR)2()1(ii12UniquenessEquivalence误差方差等同Itemshavethesameinternalconsistencyforbothgroups.Alternatively:forbothgroups,itemshavethesamequalityasmeasuresoftheunderlyingconstruct.LX=INTD=IN)2()1(13ConstructVarianceEquivalence因子方差等同Therangeofresponsesgiventoeachitemisthesameacrossgroups.Alternatively:thevariability/rangeofdiversitywithrespecttotheconstructsarethesameacrossgroups.LX=INPH=FREQPH111PH11EQPH122PH22)2()1(iiii14ConstructCovarianceEquivalence因子协方差等同Therelationshipsamongconstructs(e.g.,covariance)arethesameacrossgroups.LX=INPH=FREQPH121PH21)2()1(ijij15LatentMeanEquivalence因子均值等同Themeanlevelofeachconstructisthesameacrossgroups.LX=INTX=INKA=IN)2()1(jj16LikelihoodRatioTestProblem:sensitivetosamplesizeSolution:CFI–changesinCFIlessthan-.01–Cheung&Rensvold(2002)StructuralEquationModeling,9,233-255222nedunconstraidconstrainenedunconstraidconstrainedfdfdf17MeasurementEquivalenceExample1•Hau,K.,WenZ.,&Cheng,Z.(2004).StructuralEquationModelandItsApplications.pp.92.Beijing:EducationalSciencePublishingHouse.•Maleandfemalesstudents’confidenceinLearningChinese,MathematicsandEnglish,eachmeasuredwith3tests•SampleSize:Male(600),Female(700)18•Model0aforMalestudentsMG1_MM.ls8•Model0bforFemalestudentsMG1_MF.ls8•Model1forConfiguralEquivalenceMG1_CONF.ls8Modelχ2dfRMSEANNFICFISRMR0a49.5724.0423.9688.9792.02900b44.9324.0347.9759.9840.0275194.5048.0384.9725.9816.027519•Model2forMetricEquivalenceMG1_FMI.ls8•Model3forFactorVarianceEquivalenceMG1_FVAR.ls8•Model4forFactorCovarianceEquivalenceMG1_FCVAR.ls8Modelχ2dfΔχ2ΔdfpRMSEANNFICFISRMR2107.185412.686.048.0389.9720.9790.03063108.61571.433.699.0373.9743.9796.03194107.5757.393.942.0369.9748.9800.031220•Model5forUniquenessEquivalenceMG1_TD.ls8•Model5aforidentifyingitemwithnon-equivalentuniquenessMG1_TD1.ls8Modelχ2dfΔχ2ΔdfpRMSEANNFICFISRMR5129.086321.909.009.0394.9702.9739.03065a107.9455.761.383.0385.9726.9791.03045b108.71551.531.216.0387.9722.9788.03055c120.435513.251.000.0418.9662.9742.03055d107.9155.731.393.0384.9727.9791.03035e108.1155.931.335.0385.9726.9790.03095f108.78551.601.206.0388.9722.9788.03045g108.86551.681.195.0388.9722.9787.03085h107.2355.051.823.0383.9730.9794.03065i108.61551.431.232.0388.9723.9788.030421•Model6forScalarEquivalenceMG1_SI.ls8•Model7ato7cforLatentMeanEquivalenceMG1_LMI.ls8Modelχ2dfΔχ2ΔdfpRMSEANNFICFISRMR6108.27601.096.982.0351.9771.9809.03057a108.4061.131.718.0345.9779.9813.03057b114.38616.111.013.0366.9751.9789.03057c113.78615.511.019.0364.9754.9792.0305MaleFemaleMeans.d.Means.d.Chinese2.0048.90722.0239.8901Math3.2049.58073.1040.5367English2.6684.49632.7515.493622MeasurementEquivalenceExample2•Myersetal.(2000).AcademicInsights:AnapplicationofMultiple-GroupCausalModelsinAssessingCross-CulturalMeasurementEquivalence,JournalofInternationalMarketing,8,108-121.•Attitudetowardthead(5items);Attitudetowardthebrand(5items);Buyerintent(3items)•KoreanSample(180);USSample(180)•PathDiagramMG2_K.GIF23MeasurementModel•Model0aforKoreanSampleM