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1、SEM结构方程模型第三讲 Still waters run deep.流静水深流静水深,人静心深人静心深 Where there is life,there is hope。有生命必有希望。有生命必有希望SEM一个引例一个引例PAGE2STRUCTURAL EQUATION MODELINGConfirm.ls8 located at c:/lisrel/project1/confirm.ls8 Confirmatory factor analysis of hypothetical data for a class example of how to run LISREL to evalua
2、te a measurement model.DAta NInput=9 NObservations=400 MAtrix=CMLADepress1 Frustrt1 Stress1 Depress2 Frustrt2 Depress2 Interact Love QualityKM SY1.00.6 1.00.5 0.6 1.00.7 0.4 0.3 1.00.3 0.4 0.4 0.5 1.00.4 0.3 0.3 0.5 0.6 1.00.4 0.3 0.4 0.3 0.3 0.3 1.00.5 0.3 0.3 0.3 0.4 0.3 0.4 1.00.4 0.4 0.3 0.3 0.2
3、 0.3 0.4 0.5 1.0PAGE3STRUCTURAL EQUATION MODELINGsd2.4 2.7 1.8 2.5 2.6 2.0 5.1 3.8 6.1MODEL NY=6 NX=3 NE=2 NK=1 LY=FU,FI LX=FU,FR CBE=FU,FI GA=FU,FR PH=SY,FR PS=DI,FR,TE=DI,FR CTD=DI,FRLKRel_QualLEStress_1 Stress_2FREE LY(1,1)LY(2,1)LY(3,1)LY(4,2)LY(5,2)FREE LY(6,2)BE(2,1)OUtput SC EF VA MR PC PTPAG
4、E4STRUCTURAL EQUATION MODELINGSEMLISREL的基本结构的基本结构Comments：Everything on a line that follows either“!”or“/*”is treated as a program comment:!This line is a comment or/*This line is a comment.PAGE5STRUCTURAL EQUATION MODELINGLong lines：If you run out of space on a line and want to continue to the next
5、 line you can put a c with at least one space in front of it and then continue.This is the first line,it is long so cI can go to a second line.PAGE6STRUCTURAL EQUATION MODELINGSEM1.Title lineUntil LISREL finds a line starting with DA(for Data),it treats all lines as a title.For key words only the fi
6、rst two letters are read,so DA and DATA or Data are the same.Confirm.ls8 located at c:/lisrel/project1/confirm.ls8Confirmatory factor analysis of hypothetical data for a class example of how to run LISREL to evaluate a measurement model.PAGE7STRUCTURAL EQUATION MODELINGSEM2.DAta lineThis line begins
7、 with DA OR Data.NGroups=This indicates the number of groupsNInput=Number of input variables(indicators).NObservations=The sample size.MAtrix=CM for covariance matrix,KM for correlations.PAGE8STRUCTURAL EQUATION MODELINGYou can read in a correlation matrix and standard deviations,but if you say MA=C
8、M,LISREL will convert your matrix into a covariance matrix.e.g.DAta NInput=9 NObservations=400 MAtrix=CMPAGE9STRUCTURAL EQUATION MODELINGSEM3.LAblesYou should label your variables.Here we are referring to indicators and not latent variables.This is done by putting LA on one line and labels on the fo
9、llowing line(s).You are limited to 8 spaces total per label.You do not need labels(LISREL will use VAR1,VAR2,etc.).Labels make reading the output much better.LADepress1 Frustrt1 Stress1 Depress2 Frustrt2 Stress2 Interact Love QualityLA“Dep I”“Frust 1”“Stress 1”“Dep 2”“Frust 2”“Stress 2”Interact Love
10、 Quality(The quotes are used if there is a space in a label.)PAGE10STRUCTURAL EQUATION MODELINGSEM4.Entering DataYou can enter raw data,a covariance matrix,a correlation matrix,standard deviations,and means.Here are three examples:PAGE11STRUCTURAL EQUATION MODELINGPAGE12STRUCTURAL EQUATION MODELINGI
11、f the matrix is large it may be useful to have the matrix in an external file.KM SY FI=c:projectmydata.datRA FI=c:projectmydata.datEX(free format)EX(fixed format)PAGE13STRUCTURAL EQUATION MODELINGSEM5.Selecting/Rearranging VariablesLISREL allows you to select variables and rearrange them.This is ver
12、y useful if you are going to run different models on the same data.Once you enter the data,you can select/arrange variables however you want.SEDepress1 Frustrt1 Stress1 Interact Love Per Qual/orSE1 2 3 7 8 9/PAGE14STRUCTURAL EQUATION MODELINGSEM6.MOdelThe MOdel line is the most complex line in the L
13、ISREL program.This describes all of the matrices.This is done by specifying the numbers that determine their dimensions and then telling LISREL about the matrix(free,fixed,symmetrical,full,etc.).The description of the matrix,e.g.,fixed at some value such as 0 or 1,is selected to describe most of the
14、 parameters.Latter,you will tell LISREL those elements that are different(e.g.,free meaning you want LISREL to estimate them).PAGE15STRUCTURAL EQUATION MODELINGFirst,you need to write the eight matrices that fit your figure.For our example,the matrices are:PAGE16STRUCTURAL EQUATION MODELINGPAGE17STR
15、UCTURAL EQUATION MODELINGPAGE18STRUCTURAL EQUATION MODELINGSUMMARY*Cant be changed on Model line but elements can be free.PAGE19STRUCTURAL EQUATION MODELINGEXAMPLEMODEL NY=6 NX=3 NE=2 NK=1 LY=FU,FI LX=FU,FR CBE=FU,FI GA=FU,FR PH=SY,FR PS=DI,FR,TE=DI,FR CTD=DI,FRORMODEL NY=6 NX=3 NE=2 NK=1 LX=FU,FR B
16、E=FU,FI CPS=DI,FRPAGE20STRUCTURAL EQUATION MODELINGSEM7.LK and LE linesThese lines provide labels for the latent variables.LKRel_QualLEStress_1 Stress_2PAGE21STRUCTURAL EQUATION MODELINGSEMThese lines free parameters that should be free but were misspecified as fixed in the MODEL line and they fix p
17、arameters that were misspecified as free in the MODEL line.At the end of the FR and FI lines,Lisrel should be able to reproduce the eight matrices you wrote to describe the figure.In our example we dont have to change LX at all since it is already full and free.We have to free the lambdas in LY,and
18、the beta in BE.We do not have to change anything from free to fixed.FREE LY(1,1)LY(2,1)LY(3,1)LY(4,2)LY(5,2)LY(6,2)FREE BE(2,1)8.FRee and FIxed linesPAGE22STRUCTURAL EQUATION MODELINGSEM9.OUputSS-Prints standardized structural model(beta,gamma,psi)SC-Prints standardized output where everything is st
19、andardizedEF-Prints total and indirect effects,their standard errors,and their t-values(z-scores).MR-Prints variances and covariances of latent variables with each other and with indicators.This also gives you the residual analysis and Q-plot FS-Prints factor scores regression.PAGE23STRUCTURAL EQUAT
20、ION MODELINGPT-This prints some technical output such as the value ofthe fitting function for each iteration.PC-Prints correlations of parameter estimates.This can be very long.If you have 200 parameter estimates,this matrix will have 40,000 elements.This can be a useful way of diagnosing identifica
21、tion problems and multicolinearity.When two parameter estimates are highly correlated,say r .8,then LISREL is having trouble estimating them.ND=x This gives you x decimal places,the default is 2.AD=off This turns off an admissibility check.LISREL stops at 20 iterations if it thinks a matrix is probl
22、ematic.You should turn this off if you fix any of the error variances in TE or TD to zero.OUtput SC EF VA MR PC PTPAGE24STRUCTURAL EQUATION MODELINGConfirm.ls8 located at c:/lisrel/project1/confirm.ls8 Confirmatory factor analysis of hypothetical data for a class example of how to run LISREL to eval
23、uate a measurement model.DAta NInput=9 NObservations=400 MAtrix=CMLADepress1 Frustrt1 Stress1 Depress2 Frustrt2 Depress2 Interact Love QualityKM SY1.00.6 1.00.5 0.6 1.00.7 0.4 0.3 1.00.3 0.4 0.4 0.5 1.00.4 0.3 0.3 0.5 0.6 1.00.4 0.3 0.4 0.3 0.3 0.3 1.00.5 0.3 0.3 0.3 0.4 0.3 0.4 1.00.4 0.4 0.3 0.3 0
24、.2 0.3 0.4 0.5 1.0PAGE25STRUCTURAL EQUATION MODELINGsd2.4 2.7 1.8 2.5 2.6 2.0 5.1 3.8 6.1MODEL NY=6 NX=3 NE=2 NK=1 LY=FU,FI LX=FU,FR CBE=FU,FI GA=FU,FR PH=SY,FR PS=DI,FR,TE=DI,FR CTD=DI,FRLKRel_QualLEStress_1 Stress_2FREE LY(1,1)LY(2,1)LY(3,1)LY(4,2)LY(5,2)FREE LY(6,2)BE(2,1)OUtput SC EF VA MR PC PT
25、PAGE26STRUCTURAL EQUATION MODELINGSEMEXAMPLE-Longitudinal ModelsPAGE27STRUCTURAL EQUATION MODELINGIn this model,Q7(Quantitative ability at grade 7)and V7(Verbal Ability at grade 7)are latent exogenous variables and we assume they are correlated.测量模型测量模型 结构模型结构模型 PAGE28STRUCTURAL EQUATION MODELINGWe
26、need to do all eight matrices.This includes(a)LAMBDA-X(loadings for Xi),(b)THETA-DELTA(errors for Xi),(c)LAMBDA-Y(loadings for Yi),(d)THETA-EPSILON(errors for Yi),and(e)PHI(covariance of exogenous KSI variables).for the measurement model,(f)BETA(endogenous ETAs endogenous ETAs),(g)GAMMA(exogenous KS
27、Isendogenous ETAs),and(h)PSI(for ZETAunexplained variance,residuals)PAGE29STRUCTURAL EQUATION MODELINGSEMPAGE30STRUCTURAL EQUATION MODELINGSEMPAGE31STRUCTURAL EQUATION MODELINGSEMProgramSEM2_longitudinal.ls8Verbal and Quantitative Ability In Grades 7 and 9.Model:GA=DI,PS=DI and TD and TE uncorrelate
28、dDA NI=12 NO=383LAMATH7 SCI7 SS7 READ7 SCATV7 SCATQ7 MATH9 SCI9 SS9 READ9 SCATV9 SCATQ9PAGE32STRUCTURAL EQUATION MODELINGSEMKM sy1.6498 1.6809.7362 1.6959.7025.7570 1.6868.7120.7844.8287 1.7053.5971.6433.6088.6096 1.7364.6085.6528.6574.6533.6953 1.6419.7339.7434.6794.6995.5606.6686 1.6719.6905.7462.
29、7239.7227.5994.7055.7391 1.6400.6346.7178.7724.7512.5693.6644.6934.6927 1.6837.7155.7557.7909.8830.5998.6911.7355.7400.7879 1.6511.5164.5445.5445.5621.7145.7521.5774.6065.5903.5918 1PAGE33STRUCTURAL EQUATION MODELINGSD11.4008 9.2213 13.0459 14.6407 11.6230 12.420411.6608 11.4428 13.3248 12.1527 11.7
30、089 14.5348SEMATH9 SCATQ9 SCI9 SS9 READ9 SCATV9 MATH7 SCATQ7 SCI7 SS7READ7 SCATV7MO NX=6 NY=6 NK=2 NE=2LEQ9 V9LKQ7 V7FI GA 1 2 GA 2 1FR LY 1 1 LY 3 1 LY 4 1 LY 3 2 LY 4 2 ly 5 2FR LX 1 1 LX 3 1 LX 4 1 LX 3 2 LX 4 2 lx 5 2Value 1.0 ly 2 1 ly 6 2 lx 2 1 lx 6 2Path DiagramOU sc MI ad=offPAGE34STRUCTURAL EQUATION MODELINGAny Questions?PAGE35STRUCTURAL EQUATION MODELING