中文教授基于lisrelsem 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

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125ModelwithMeanStructuresRelationshipsbetweentheobservedvariablesandthelatentconstruct: (1)Thecovariancematrixofxis: (2)Themeanvalueofis: (3)6ScalingofLatentVariable

Virtuallyalllatentvariableshaveambiguousscales,thescalechoiceislargelyarbitrary.Aconvenientchoiceistogivethesamescaleasinthesensethatiszeroandisone.ShouldNOTstandardizethelatentvariablesbysettingbecausemeanofstandardizedvariableiszero.Bollen(1989).StructuralEquationswithLatentVariables.Pp.153.Wiley.72AdditionalVectorsIntercepts(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=FR10MetricEquivalence

因子负荷等同Overall,thestrengthoftherelationshipsbetweenitemsandtheirunderlyingconstructsarethesameacrossgroups.(Theconstructsaremanifestedinthesameway)LX=INTX=PSKA=FR11ScalarEquivalence

指标截距等同Thecross-culturaldifferencesindicatedbytheitemsarethesameacrossitems.Alternatively:allitemsindicatethesamecross-culturaldifferences.LX=INTX=INKA=FR

12UniquenessEquivalence

误差方差等同Itemshavethesameinternalconsistencyforbothgroups.Alternatively:forbothgroups,itemshavethesamequalityasmeasuresoftheunderlyingconstruct.LX=INTD=IN

13ConstructVarianceEquivalence

因子方差等同Therangeofresponsesgiventoeachitemisthesameacrossgroups.Alternatively:thevariability/rangeofdiversitywithrespecttotheconstructsarethesameacrossgroups.LX=INPH=FREQPH111PH11EQPH122PH2214ConstructCovarianceEquivalence

因子协方差等同Therelationshipsamongconstructs(e.g.,covariance)arethesameacrossgroups.LX=INPH=FREQPH121PH2115LatentMeanEquivalence

因子均值等同Themeanlevelofeachconstructisthesameacrossgroups.LX=INTX=INKA=IN16LikelihoodRatioTestProblem:sensitivetosamplesizeSolution:CFI

changesinCFIlessthan-.01Cheung&Rensvold(2002)StructuralEquationModeling,9,233-25517MeasurementEquivalenceExample1Hau,K.,WenZ.,&Cheng,Z.(2004).StructuralEquationModelandItsApplications.pp.92.Beijing:EducationalSciencePublishingHouse.Maleandfemalesstudents’confidenceinLearningChinese,MathematicsandEnglish,eachmeasuredwith3testsSampleSize:Male(600),Female(700)18Model0aforMalestudentsMG1_MM.ls8Model0bforFemalestudentsMG1_MF.ls8Model1forConfiguralEquivalenceMG1_CONF.ls8Modelχ2dfRMSEANNFICFISRMR0a49.5724.0423.9688.9792.02900b44.9324.0347.9759.9840.0275194.5048.0384.9725.9816.027519Model2forMetricEquivalenceMG1_FMI.ls8Model3forFactorVarianceEquivalenceMG1_FVAR.ls8Model4forFactorCovarianceEquivalenceMG1_FCVAR.ls8Modelχ2dfΔχ2ΔdfpRMSEANNFICFISRMR2107.185412.686.048.0389.9720.9790.03063108.61571.433.699.0373.9743.9796.03194107.5757.393.942.0369.9748.9800.031220Model5forUniquenessEquivalenceMG1_TD.ls8Model5aforidentifyingitemwithnon-equivalentuniquenessMG1_TD1.ls8Modelχ2dfΔχ2ΔdfpRMSEANNFICFISRMR5129.086321.909.009.0394.9702.9739.03065a107.9455.761.383.0385.9726.9791.03045b108.71551.531.216.0387.9722.9788.03055c120.435513.251.000.0418.9662.9742.03055d107.9155.731.393.0384.9727.9791.03035e108.1155.931.335.0385.9726.9790.03095f108.78551.601.206.0388.9722.9788.03045g108.86551.681.195.0388.9722.9787.03085h107.2355.051.823.0383.9730.9794.03065i108.61551.431.232.0388.9723.9788.030421Model6forScalarEquivalenceMG1_SI.ls8Model7ato7cforLatentMeanEquivalenceMG1_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.Chinese2.0048.90722.0239.8901Math3.2049.58073.1040.5367English2.6684.49632.7515.493622MeasurementEquivalenceExample2Myersetal.(2000).AcademicInsights:AnapplicationofMultiple-GroupCausalModelsinAssessingCross-CulturalMeasurementEquivalence,JournalofInternationalMarketing,8,108-121.Attitudetowardthead(5items);Attitudetowardthebrand(5items);Buyerintent(3items)KoreanSample(180);USSample(180)PathDiagramMG2_K.GIF23MeasurementModelModel0aforKoreanSampleMG2_K2.ls8Model0bforUSSampleMG2_US2.ls8Model1forConfiguralEquivalenceMG2_CONF2.ls8Modelχ2dfRMSEANNFICFISRMR0a108.3762.0672.9873.9899.04350b148.6462.0879.9776.9822.03411257.01124.0782.9823.9860.034124Model2forMetricEquivalenceMG2_FMI2.ls8Model3forFactorVarianceEquivalenceMG2_FVAR.ls8Model4forUniquenessEquivalenceMG2_TD.ls8Modelχ2dfΔχ2ΔdfpRMSEANNFICFISRMR2280.0913423.0810.010.0783.9821.9846.03993290.3413710.253.017.0790.9816.9838.08674434.41147154.3213.000.0996.9678.9697.04364e300.8013520.711.000.0807.9798.9825.04104f294.2813514.191.000.0798.9806.9832.03934g293.3313513.241.000.0793.9807.9833.04064i315.0113534.921.000.0876.9781.9810.04074k307.5513527.461.000.0847.9790.9818.040225FullStructuralModelModel5a(FullModelforKoreanSample)MG2_K.ls8Model5b(FullModelforUSSample)MG2_US.ls8Model5cforMetricEquivalenceMG2_FMI.ls8Model6aforGamma(1,1)EquivalenceMG2_GAMMA.ls8

Model6bforGamma(1,2)EquivalenceModelχ2dfΔχ2ΔdfpRMSEANNFICFISRMR5a108.3762.0672.9873.9899.04355b148.6462.0879.9776.9822.03415c280.0913423.0810.010.0783.9821.9846.03996a281.131351.041.308.0779.9822.9846.04266b280.18135.091.764.0777.9823.9847.040326MeasurementEquivalenceExample3WorkOrientationfromISSPSamplesfromUSA(823)andWestGermany(591)SatisfactionwithJobContext,JobContent,andWorkEnvironment.EachMeasuredwith4items27Model0aforUSsampleMG3_USA.ls8Model0bforWestGermanysampleMG3_WG.ls8Model1forConfiguralEquivalenceMG3_CONF.ls8Modelχ2dfRMSEANNFICFISRMR0a259.6851.0701.9253.9423.05600b137.3251.0541.9557.9658.04181397.00102.0639.9378.9519.049128Model2:MetricEquivalenceMG3_FMI.ls8Model2a:MetricEquivalenceforContextMG3_FMI1.ls8Model2b:MetricEquivalenceforContentMG3_FMI2.ls8Model2c:MetricEquivalenceforEnvironmentMG3_FMI3.ls8Modelχ2dfΔχ2ΔdfpRMSEANNFICFISRMR2465.6411168.649.000.0670.9313.9422.05672a398.251051.253.741.0627.9399.9522.04232b422.7210525.723.000.0650.9349.9482.04802c438.5510541.553.000.0674.9317.9457.051429IdentifyingNon-invariantItemsStandardizationProblemFactor-RatioTestList-and-DeleteMethodCheung&Rensvold(1999)JournalofManagement,25,1-27.30Factor-RatioTest31List-and-DeleteMethod(4items)123412123131241413423234243432Model2b1toModel2b6:PartialMetricEquivalenceforContentModel2b1:LX(6,2)InvariantMG3_FMI2a.ls8Modelχ2dfΔχ2ΔdfpRMSEANNFICFISRMR2b1409.0810312.081.000.0647.9361.9501.04482b2403.971036.971.008.0642.9372.9510.04322b3400.781033.781.052.0636.9378.9515.04332b4397.19103.191.663.0635.9386.9521.04202b5417.2010320.201.000.0651.9344.9488.04752b6410.6310313.631.000.0646.9358.9499.045933List-and-DeleteMethodRemoveallcombinationswith[5,6](2b1);[5,7](2b2);[6,8](2b5);[7,8](2b6)567856567575685857867678687834Model2c1toModel2c6:PartialMetricEquivalenceforEnvironmentModel2c1:LX(9,3)InvariantMG3_FMI3a.ls8Modelχ2dfΔχ2ΔdfpRMSEANNFICFISRMR2c1432.1010335.101.000.0673.9313.9464.04952c2426.7010329.701.000.0670.9324.9473.04852c3408.7610311.761.000.0649.9362.9502.04382c4397.37103.371.543.0635.9385.9520.04202c5408.3610311.361.000.0649.9362.9502.04462c6406.011039.011.003.0645.9367.9506.044035List-and-DeleteMethodRemoveallcombinationswith[9,10](2c1);[9,11](2c2);[9,12](2c3);[10,12](2c5);[11,12](2c6)9101112910910119119101291291112

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1011121012111236Test0:EqualityofCovarianceMatricesTest1:Invarianceof

FactorForms

FactorialFactorialInvarianceFailsTest2:InvarianceExistsMultiple

Invarianceof

OptionsiffactorialConstructs

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invarianceexistsConstructTest3:Constructinvariance

foreachconstructinmodel

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TestsTest4:Factor-ratiotestComparemeansMorestringentOther(allargumentsand

oflatentmeasurementsubstantivereferentsineachconstruct)variablese