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1、结构方程模型及其应用第三讲LISREL 及其应用,Wang Shu JiaBusiness School University of Shenzhen2023年10月17日星期二,PAGE2,STRUCTURAL EQUATION MODELING,一个引例,Confirm.ls8 located at c:/lisrel/project1/confirm.ls8 Confirmatory factor analysis of hypothetical data for a class example of how to run LISREL to evaluate a measurement
2、 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 0.3 0.4 0.5 1.0
3、,sd2.4 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,PAGE5,STRUCTURAL EQUATION MODELING,LISREL的基本结构,Com
4、ments：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.,Long lines：If you run out of space on a line and want to continue to the next line you can put a c with at least one space in front of it and then continue.This
5、is the first line,it is long so cI can go to a second line.,PAGE7,STRUCTURAL EQUATION MODELING,1.Title line,Until LISREL finds a line starting with DA(for Data),it treats all lines as a title.For key words only the first two letters are read,so DA and DATA or Data are the same.Confirm.ls8 located at
6、 c:/lisrel/project1/confirm.ls8Confirmatory factor analysis of hypothetical data for a class example of how to run LISREL to evaluate a measurement model.,PAGE8,STRUCTURAL EQUATION MODELING,2.DAta line,This line begins with DA OR Data.NGroups=This indicates the number of groupsNInput=Number of input
7、 variables(indicators).NObservations=The sample size.MAtrix=CM for covariance matrix,KM for correlations.,You can read in a correlation matrix and standard deviations,but if you say MA=CM,LISREL will convert your matrix into a covariance matrix.e.g.DAta NInput=9 NObservations=400 MAtrix=CM,PAGE10,ST
8、RUCTURAL EQUATION MODELING,3.LAbles,You 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 following line(s).You are limited to 8 spaces total per label.You do not need labels(LISREL will use VAR1,VAR2,etc
9、.).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 Quality(The quotes are used if there is a space in a label.),PAGE11,STRUCTURAL EQUATION MODELING,4.Entering Dat
10、a,You can enter raw data,a covariance matrix,a correlation matrix,standard deviations,and means.Here are three examples:,If 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.dat,EX(free format),EX(fixed format),PAGE14,STRUCT
11、URAL EQUATION MODELING,5.Selecting/Rearranging Variables,LISREL allows you to select variables and rearrange them.This is very 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 Intera
12、ct Love Per Qual/orSE1 2 3 7 8 9/,PAGE15,STRUCTURAL EQUATION MODELING,6.MOdel,The MOdel line is the most complex line in the LISREL 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,sy
13、mmetrical,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 parameters.Latter,you will tell LISREL those elements that are different(e.g.,free meaning you want LISREL to estimate them).,First,you need to write the eight matrices that
14、 fit your figure.For our example,the matrices are:,SUMMARY,*Cant be changed on Model line but elements can be free.,EXAMPLEMODEL 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 BE=FU,FI CPS=DI,FR,PAGE21,STRUCTURAL EQUA
15、TION MODELING,7.LK and LE lines,These lines provide labels for the latent variables.LKRel_QualLEStress_1 Stress_2,PAGE22,STRUCTURAL EQUATION MODELING,These lines free parameters that should be free but were misspecified as fixed in the MODEL line and they fix parameters that were misspecified as fre
16、e 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 the beta in BE.We do not have to change
17、 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 lines,PAGE23,STRUCTURAL EQUATION MODELING,9.OUput,SS-Prints standardized structural model(beta,gamma,psi)SC-Prints standardized output where everything is standardizedEF-Prints total and indirec
18、t 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.,PT-This prints some technical output such as the value oft
19、he 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 identification problems and multicolinearity.When two parameter estimates are hi
20、ghly 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 problematic.You should turn this off if you fix any of the error variances i
21、n TE or TD to zero.OUtput SC EF VA MR PC PT,Confirm.ls8 located at c:/lisrel/project1/confirm.ls8 Confirmatory factor analysis of hypothetical data for a class example of how to run LISREL to evaluate a measurement model.DAta NInput=9 NObservations=400 MAtrix=CMLADepress1 Frustrt1 Stress1 Depress2 F
22、rustrt2 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 0.3 0.4 0.5 1.0,sd2.4 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=
23、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,PAGE27,STRUCTURAL EQUATION MODELING,EXAMPLE-Longitudinal Models,In this model,Q7(Quantitative ability at grade 7)and V7(Verbal Ability a
24、t grade 7)are latent exogenous variables and we assume they are correlated.,测量模型,结构模型,We 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)
25、.for the measurement model,(f)BETA(endogenous ETAs endogenous ETAs),(g)GAMMA(exogenous KSIsendogenous ETAs),and(h)PSI(for ZETAunexplained variance,residuals),PAGE30,STRUCTURAL EQUATION MODELING,PAGE31,STRUCTURAL EQUATION MODELING,PAGE32,STRUCTURAL EQUATION MODELING,Program,SEM2_longitudinal.ls8Verba
26、l and Quantitative Ability In Grades 7 and 9.Model:GA=DI,PS=DI and TD and TE uncorrelatedDA NI=12 NO=383LAMATH7 SCI7 SS7 READ7 SCATV7 SCATQ7 MATH9 SCI9 SS9 READ9 SCATV9 SCATQ9,PAGE33,STRUCTURAL EQUATION MODELING,KM sy1.6498 1.6809.7362 1.6959.7025.7570 1.6868.7120.7844.8287 1.7053.5971.6433.6088.609
27、6 1.7364.6085.6528.6574.6533.6953 1.6419.7339.7434.6794.6995.5606.6686 1.6719.6905.7462.7239.7227.5994.7055.7391 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 1,SD11.4008 9.2213 13.0459 14.6
28、407 11.6230 12.420411.6608 11.4428 13.3248 12.1527 11.7089 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=off,Any Questions?,
