多層線性模型在追蹤研究中的應(yīng)用追蹤的多水平模型

1.追蹤數(shù)據(jù)的多水平分析2.HLM多水平分析操作3.SPSS多水平分析操作4.Mplus多水平分析操作當(dāng)前1頁，總共74頁。追蹤研究數(shù)據(jù)的多層分析當(dāng)對相同的觀測對象進(jìn)行重復(fù)測量時，可以將這些重復(fù)測量的數(shù)據(jù)本身看成是具有層次結(jié)構(gòu)特點的。如對生長發(fā)育期兒童身高和體重變化情況的追蹤調(diào)查等，可以將這些重復(fù)測量數(shù)據(jù)構(gòu)造出一個兩水平的層次結(jié)構(gòu)，其重復(fù)測量或測量點為水平1的單位，觀測個體為水平2的單位。

個體隨時間變化的問題，即個體的特征隨時間有什么樣的變化特點？個體之間變化差異的問題，即個體之間的變化是否存在差異？用什么特征可以預(yù)測或解釋個體之間變化的差異？當(dāng)前2頁，總共74頁。數(shù)據(jù)：香港三所小學(xué)264名學(xué)生，其中男生149名，女生115名。以每年測查一次的方式，對他們從三年級到六年級的自我概念進(jìn)行連續(xù)四次的測量，且在三年級第一次測試時對他們退縮行為進(jìn)行測量。測量：自我概念：采用SusanHarter（1982）的兒童自我能力感知量表對兒童不同領(lǐng)域能力的自我概念進(jìn)行測量。該量表包含與特殊領(lǐng)域相關(guān)聯(lián)的①認(rèn)知自我概念；②社交自我概念；③運(yùn)動自我概念三個方面，另外還包含與具體領(lǐng)域獨(dú)立的一般自我概念。量表共28個項目，其中每個分量表7個項目。兒童的退縮行為：采用兒童退縮行為量表對兒童的退縮行為進(jìn)行測量，該量表共由7個項目組成。當(dāng)前3頁，總共74頁。追蹤研究關(guān)心的問題三年級到六年級這一段時間，小學(xué)生自我概念發(fā)展有什么樣的特點，即線性增長（或下降），還是非線性的變化趨勢等（先增長后下降）；不同的學(xué)生在這一時期自我概念的發(fā)展是否存在個體之間的差異，如果存在差異，能否用一些變量來解釋或預(yù)測這些差異。

當(dāng)前4頁，總共74頁。隨機(jī)抽取60個學(xué)生自我概念的發(fā)展趨勢當(dāng)前5頁，總共74頁。隨機(jī)抽取的四個個體自我概念隨時間發(fā)展的特征當(dāng)前6頁，總共74頁。退縮行為高分組和低分組自我概念發(fā)展趨勢當(dāng)前7頁，總共74頁。追蹤研究中的兩水平模型水平1的模型，描述個體隨時間的發(fā)展；水平2模型，對個體間發(fā)展的差異進(jìn)行解釋。然后就關(guān)心的問題進(jìn)行分析和解釋。

當(dāng)前8頁，總共74頁。兩水平重復(fù)測量線性模型水平1（測量水平）水平2（個體水平）t表示不同次的測量，可以描述時間間隔，沒有必要等距（如0,1,1.5,2,....）。可說明個體間的差異當(dāng)前9頁，總共74頁。模型1：線性增長模型水平1模型當(dāng)前10頁，總共74頁。模型1：線性增長模型第二水平模型當(dāng)前11頁，總共74頁。當(dāng)前12頁，總共74頁。第二水平模型：預(yù)測變量第二水平預(yù)測變量模型可以用來自變量（如判斷性別差異、有無退縮行為）對自我觀念的變化有無趨勢及影響程度當(dāng)前13頁，總共74頁。當(dāng)前14頁，總共74頁。當(dāng)前15頁，總共74頁。當(dāng)前16頁，總共74頁。HLM軟件操作當(dāng)前17頁，總共74頁。HLM軟件操作當(dāng)前18頁，總共74頁。HLM軟件操作當(dāng)前19頁，總共74頁。HLM軟件操作當(dāng)前20頁，總共74頁。HLM軟件操作當(dāng)前21頁，總共74頁。HLM軟件操作當(dāng)前22頁，總共74頁。HLM軟件操作當(dāng)前23頁，總共74頁。HLM軟件操作當(dāng)前24頁，總共74頁。HLM軟件操作當(dāng)前25頁，總共74頁。當(dāng)前26頁，總共74頁。當(dāng)前27頁，總共74頁。當(dāng)前28頁，總共74頁。當(dāng)前29頁，總共74頁。模型定義：無條件線性增長模型當(dāng)前30頁，總共74頁。RUN

Analysis當(dāng)前31頁，總共74頁。固定部分Finalestimationoffixedeffects(withrobuststandarderrors)----------------------------------------------------------------------------StandardApprox.FixedEffectCoefficientErrorT-ratiod.f.P-value----------------------------------------------------------------------------ForINTRCPT1,P0INTRCPT2,B002.8160840.021325132.0542630.000ForTIMEslope,P1INTRCPT2,B10-0.0840120.011601-7.2422630.000----------------------------------------------------------------------------當(dāng)前32頁，總共74頁。隨機(jī)部分Finalestimationofvariancecomponents:-----------------------------------------------------------------------------RandomEffectStandardVariancedfChi-squareP-value

DeviationComponent-----------------------------------------------------------------------------INTRCPT1,R00.229300.05258263466.535480.000TIMEslope,

R10.127480.01625263483.192100.000level-1,

E0.311530.09705-----------------------------------------------------------------------------當(dāng)前33頁，總共74頁。當(dāng)前34頁，總共74頁。----------------------------------------------------------------------------StandardApprox.FixedEffectCoefficientErrorT-ratiod.f.P-value----------------------------------------------------------------------------ForINTRCPT1,P0INTRCPT2,B002.814

0.03094.8732610.000GENDER,B010.004

0.0410.0992610.922WITHDRAW,B02-0.104

0.020-5.3132610.000ForTIMEslope,P1INTRCPT2,B10-0.117

0.016-7.4222610.000GENDER,B110.058

0.0222.5922610.010WITHDRAW,B120.032

0.0122.7662610.007----------------------------------------------------------------------------當(dāng)前35頁，總共74頁。Finalestimationofvariancecomponents:-----------------------------------------------------------------------------RandomEffectStandardVariancedfChi-squareP-valueDeviationComponent-----------------------------------------------------------------------------INTRCPT1,R00.2060.042261424.170.000TIMEslope,R10.1220.015261460.290.000level-1,E

0.3120.097-----------------------------------------------------------------------------當(dāng)前36頁，總共74頁。非線性變化趨勢當(dāng)前37頁，總共74頁。固定部分Finalestimationoffixedeffects(withrobuststandarderrors)----------------------------------------------------------------------------StandardApprox.FixedEffectCoefficientErrorT-ratiod.f.P-value----------------------------------------------------------------------------ForINTRCPT1,P0

INTRCPT2,B002.8520.023125.8572630.000ForTIMEslope,P1

INTRCPT2,B10-0.1920.032-6.0192630.000ForTIME2slope,P2INTRCPT2,B200.0360.0103.7182630.000----------------------------------------------------------------------------當(dāng)前38頁，總共74頁。隨機(jī)部分Finalestimationofvariancecomponents:-----------------------------------------------------------------------------RandomEffectStandardVariancedfChi-squareP-valueDeviationComponent-----------------------------------------------------------------------------INTRCPT1,R00.2270.051263422.840.000TIMEslope,R1

0.229

0.052

263

326.340.005TIME2slope,R20.0530.003263295.600.081level-1,E

0.2980.089-----------------------------------------------------------------------------當(dāng)前39頁，總共74頁。當(dāng)前40頁，總共74頁。用SPSSMixedModel定義多水平模型一個個體一行記錄，多個變量，含有一個描述個體編號的變量

MultipleVariableDataStructure（MV）

一次觀測一行記錄，含有一個個體編號和測量次數(shù)或時間的變量

MultipleRecordDataStructure（MR）

當(dāng)前41頁，總共74頁。MultipleVariableDataStructure當(dāng)前42頁，總共74頁。MultipleRecordDataStructure當(dāng)前43頁，總共74頁。具有一般嵌套結(jié)構(gòu)特點的多層數(shù)據(jù)－－學(xué)生嵌套于學(xué)校GETFILE='C:\HLM_EXAMPLE\EX1.SAV'.MIXEDMATHACHBYSECTORWITHMEANSESCSES/METHOD=REML/PRINT=SOLUTIONTESTCOV/FIXED=MEANSESSECTORCSESMEANSES*CSESSECTORCSES[SSTYPE(3)]/RANDOM=INTERCEPTCSES[SUBJECT(SCHOOL)]COVTYPE(UN).當(dāng)前44頁，總共74頁。句法（Syntax）－－解釋1GETFILE='C:\HLM_EXAMPLE\EX1.SAV'.2MIXEDMATHACHBYSECTORWITHMEANSESCSES3/METHOD=REML4/PRINT=SOLUTIONTESTCOV5/FIXED=MEANSESSECTORCSESMEANSES*CSESSECTORCSES[SSTYPE(3)]6/RANDOM=INTERCEPTCSES[SUBJECT(SCHOOL)]COVTYPE(UN).

1打開數(shù)據(jù)文件；

2因變量為MATHACH，自變量為SECTOR，MEANSESCSES，分類自變量寫在BY的后面，連續(xù)自變量寫在WITH的后面；3用限制性極大似然估計法，在MixedModel中估計方法有REML和ML兩種，REML是缺省的設(shè)置；SOLUTION定義打印輸出固定部分參數(shù)估計和檢驗結(jié)果，TESTCOV要求打印輸出隨機(jī)部分協(xié)方差矩陣的估計和檢驗結(jié)果；FIXED后面定義模型中的預(yù)測變量；Random后的變量用來定義允許第二層有差異的隨機(jī)變量，SUBJECT后的SCHOOL為更高的組變量，COVTYPE用來定義協(xié)方差矩陣的類型當(dāng)前45頁，總共74頁。MIXEDMODEL應(yīng)用舉例：模型1－－無條件模型GETFILE='C:\HLM_EXAMPLE\EX1.SAV'.MIXEDMATHACH/METHOD=REML/PRINT=SOLUTIONTESTCOV/FIXED=|SSTYPE(3)/RANDOM=INTERCEPT|SUBJECT(SCHOOL)COVTYPE(UN).當(dāng)前46頁，總共74頁。應(yīng)用舉例：模型1——無條件模型參數(shù)估計結(jié)果當(dāng)前47頁，總共74頁。應(yīng)用舉例：模型2－－條件模型（水平2預(yù)測變量）MIXEDMATHACHwithmeanses/METHOD=REML/PRINT=SOLUTIONTESTCOV/FIXED=MEANSES|SSTYPE(3)/RANDOM=INTERCEPT|SUBJECT(SCHOOL)COVTYPE(UN).當(dāng)前48頁，總共74頁。應(yīng)用舉例：模型2－－條件模型（水平2預(yù)測變量）結(jié)果當(dāng)前49頁，總共74頁。應(yīng)用舉例：模型3－－條件模型（水平1預(yù)測變量中心化）MIXEDMATHACHwithcses/METHOD=REML/PRINT=SOLUTIONTESTCOV/FIXED=CSES|SSTYPE(3)/RANDOM=INTERCEPTcses|SUBJECT(SCHOOL)COVTYPE(UN).當(dāng)前50頁，總共74頁。應(yīng)用舉例：模型3－－條件模型（水平1預(yù)測變量中心化）結(jié)果當(dāng)前51頁，總共74頁。應(yīng)用舉例：模型4－－同時含有水平1和水平2的預(yù)測變量MIXEDMATHACHBYSECTORWITHMEANSESCSES/METHOD=REML/PRINT=SOLUTIONTESTCOV/FIXED=MEANSESSECTORCSESMEANSES*CSESSECTOR*CSES|SSTYPE(3)/RANDOM=INTERCEPTCSES|SUBJECT(SCHOOL)COVTYPE(UN).當(dāng)前52頁，總共74頁。應(yīng)用舉例：模型4－－同時含有水平1和水平2的預(yù)測變量結(jié)果當(dāng)前53頁，總共74頁。用SPSSMIXEDMODEL分析追蹤研究的數(shù)據(jù)GETFILE='C:\HLM_EXAMPLE\OPPOSITES_PP.SAV'.mixedoppwithtimeccog/print=solution/method=reml/fixed=intercepttimeccogtime*ccog/repeatedwave|subject(id)covtype(un).當(dāng)前54頁，總共74頁。Mplus操作：兩水平模型組內(nèi)變量：X對Y的影響一般多水平模型下，x是組內(nèi)變量追蹤模型下，x是時間變量或隨時間變化的變量組間變量：W對Y的影響XM（協(xié)變量）對Y的影響一般多水平模型下，w是組間變量追蹤模型下，w是個體變量或不隨時間變化的變量當(dāng)前55頁，總共74頁。Mplus操作：兩水平模型輸入程序TITLE:thisisanexampleofatwo-levelregressionanalysisfora continuousdependentvariablewitharandominterceptandan observedcovariateDATA:FILE=ex9.1a.dat;VARIABLE:NAMES=yxwxmclus;WITHIN=x;BETWEEN=wxm;CLUSTER=clus;CENTERING=GRANDMEAN(x);ANALYSIS:TYPE=TWOLEVEL;MODEL:%WITHIN%yONx;%BETWEEN%yONwxm;當(dāng)前56頁，總共74頁。Mplus操作：兩水平模型輸出結(jié)果SUMMARYOFANALYSISNumberofgroups1Numberofobservations1000Numberofdependentvariables1Numberofindependentvariables3Numberofcontinuouslatentvariables0ObserveddependentvariablesContinuousYObservedindependentvariablesXWXMVariableswithspecialfunctionsClustervariableCLUSWithinvariablesXBetweenvariablesWXMCentering(GRANDMEAN)X當(dāng)前57頁，總共74頁。Mplus操作：兩水平模型輸出結(jié)果SUMMARYOFDATANumberofclusters110Averageclustersize9.091EstimatedIntraclassCorrelationsfortheYVariablesIntraclassVariableCorrelationY0.570當(dāng)前58頁，總共74頁。Mplus操作：兩水平模型輸出結(jié)果TESTSOFMODELFITChi-SquareTestofModelFitValue0.000*DegreesofFreedom0P-Value0.0000ScalingCorrectionFactor1.000forMLR*Thechi-squarevalueforMLM,MLMV,MLR,ULSMV,WLSMandWLSMVcannotbeusedforchi-squaredifferencetestingintheregularway.MLM,MLRandWLSMchi-squaredifferencetestingisdescribedontheMpluswebsite.MLMV,WLSMV,andULSMVdifferencetestingisdoneusingtheDIFFTESToption.當(dāng)前59頁，總共74頁。Mplus操作：兩水平模型Chi-SquareTestofModelFitfortheBaselineModelValue491.881DegreesofFreedom3P-Value0.0000CFI/TLICFI1.000TLI1.000LoglikelihoodH0Value-1525.938H0ScalingCorrectionFactor0.940forMLRH1Value-1525.938H1ScalingCorrectionFactor0.940forMLR當(dāng)前60頁，總共74頁。Mplus操作：兩水平模型InformationCriteriaNumberofFreeParameters6Akaike(AIC)3063.876Bayesian(BIC)3093.322Sample-SizeAdjustedBIC3074.266(n*=(n+2)/24)RMSEA(RootMeanSquareErrorOfApproximation)Estimate0.000SRMR(StandardizedRootMeanSquareResidual)ValueforWithin0.000ValueforBetween0.000當(dāng)前61頁，總共74頁。Mplus操作：兩水平模型MODELRESULTSTwo-TailedEstimateS.E.Est./S.E.P-ValueWithinLevelYONX0.7240.03322.1180.000ResidualVariancesY1.0220.04125.1170.000BetweenLevelYONW0.5700.1085.3050.000XM0.9760.1606.1070.000InterceptsY1.9910.08024.8040.000ResidualVariancesY0.5710.0886.4860.000當(dāng)前62頁，總共74頁。Mplus操作：兩水平模型STDYXStandardizationTwo-TailedEstimateS.E.Est./S.E.P-ValueWithinLevelYONX0.5770.02029.0590.000ResidualVariancesY0.6670.02329.1160.000BetweenLevelYONW0.4280.0755.7320.000XM0.4880.0766.4470.000InterceptsY1.3970.09414.7900.000ResidualVariancesY0.2810.0456.1990.000當(dāng)前63頁，總共74頁。Mplus操作：兩水平隨機(jī)系數(shù)模型輸出結(jié)果TITLE:thisisanexampleofatwo-levelregressionanalysisforacontinuousdependentvariableDATA:FILEISex9.1.dat;VARIABLE:NAMESAREyxwclus;WITHIN=x;BETWEEN=w;CLUSTER=clus;CENTERING=GRANDMEAN(x);ANALYSIS:TYPE=TWOLEVELRANDOM;MODEL:%WITHIN%s|yONx;%BETWEEN%ysONw;當(dāng)前64頁，總共74頁。Mplus操作：兩水平模型輸出結(jié)果SUMMARYOFANALYSISNumberofgroups1Numberofobservations1000Numberofdependentvariables1Numberofindependentvariables2Numberofcontinuouslatentvariables1ObserveddependentvariablesContinuousYObservedindependentvariablesXWVariableswithspecialfunctionsClustervariableCLUSWithinvariablesXBetweenvariablesWCentering(GRANDMEAN)X當(dāng)前65頁，總共74頁。Mplus操作：兩水平模型輸出結(jié)果TESTSOFMODELFITLoglikelihoodH0Value-1582.207H0ScalingCorrectionFactor0.912forMLRInformationCriteriaNumberofFreeParameters7Akaike(AIC)3178.413Bayesian(BIC)3212.768Sample-SizeAdjustedBIC3190.535(n*=(n+2)/24)當(dāng)前66頁，總共74頁。Mplus操作：兩水平模型輸出結(jié)果MODELRESULTS