中文教授基于lisrelsem note4

1MeasurementEquivalence/Invariance

測(cè)量等同張偉雄博士香港中文大學(xué)工商管理學(xué)院副院長(zhǎng)管理學(xué)系教授GordonW.Cheung,Ph.DProfessor,DepartmentofManagementAssociateDean,FacultyofBusinessAdministrationTheChineseUniversityofHongKong2WhatisMeasurementEquivalence/Invariance(ME/I)ME/I(測(cè)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(指標(biāo)截距)(TX)LatentMeans(因子均值)(KA)8BasicTypesofME/IConfiguralEquivalence(形態(tài)相同)MetricEquivalence(因子負(fù)荷等同)ScalarEquivalence(指標(biāo)截距等同)UniquenessEquivalence(誤差方差等同)ConstructVarianceEquivalence(因子方差等同)ConstructRelationsEquivalence(因子關(guān)系等同)LatentMeanEquivalence(因子均值等同)9ConfiguralEquivalence

形態(tài)相同Bothgroupsassociatethesamesubsetsofitemswiththesameconstructs(thecognitivedomainsarethesame)LX=PSTX=PSKA=FR10MetricEquivalence

因子負(fù)荷等同Overall,thestrengthoftherelationshipsbetweenitemsandtheirunderlyingconstructsarethesameacrossgroups.(Theconstructsaremanifestedinthesameway)LX=INTX=PSKA=FR11ScalarEquivalence

指標(biāo)截距等同Thecross-culturaldifferencesindicatedbytheitemsarethesameacrossitems.Alternatively:allitemsindicatethesamecross-culturaldifferences.LX=INTX=INKA=FR

12UniquenessEquivalence

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

13ConstructVarianceEquivalence

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

因子協(xié)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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FactorialFactorialInvarianceFailsTest2:InvarianceExistsMultiple

Invarianceof

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invarianceexistsConstructTest3:Constructinvariance

foreachconstructinmodel

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TestsTest4:Factor-ratiotestComparemeansMorestringentOther(allargumentsand

oflatentmeasurementsubstantivereferentsineachconstruct)variablese