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Structural Equation Modeling Using LISREL

Structural Equation Modeling Using LISREL

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This page describes how to fit a full structural equation model in LISREL. Details on the model, and a link to download the data, can be found here. Estimation was done using the free student version of LISREL, which can be downloaded here.

The previous page on confirmatory factor analysis showed how to read in the raw data from an SPSS file (click here to review).

The LISREL or SIMPLIS syntax used to estimate the model can be created by drawing a path diagram. To do this, go to File → New and scroll down to choose Path Diagram.

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When prompted, name the path diagram Full SEM. An empty drawing area opens.

To establish the variable names for the model, go to Setup → Title and Comments.

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The Title and Comments dialog box opens. Enter the title Full SEM.

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Click Next. A new dialog box titled Group Names opens.

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Because the purpose is not to compare different groups, this can be left blank. Click Next.

The Labels dialog box opens, which is used to identify the names of the variables in the model.

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To specify the observed variables from the raw data file, click on Add/Read Variables. A new box opens. Change the Read from file option to PRELIS System File, then browse to find the PRELIS file that was created from the PASW file.

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Click OK. The names of the variables from the data file will appear in the Observed Variables column. To name the latent variables, click Add Latent Variables. The first latent variable will be named Intelligence.

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The full SEM will also contain a latent variable for humor, so click Add Latent Variables a second time to create an additional variable named Humor.

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Click OK. A final dialog box opens to describe the data.

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Because LISREL will be reading from a raw data file, it is not necessary to include any information about the number of observations. Click OK one more time.

The drawing pad appears again. In the model, humor is treated as endogenous (that is, it is caused by intelligence). Thus, it is necessary to identify humor as an Eta variable by clicking in the box next to the variable name on the left side of the screen. In addition, it is necessary to define the observed variables which correspond to humor as Y variables in the same manner.

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Drag the variables onto the drawing pad. (Note: If you get error messages, change the Models: drop-down menu to Basic Model.) Then draw arrows from Intelligence to its indicators, Humor to its indicators, and from Intelligence to Humor. If Humor is not declared to be endogenous (an Eta variable), LISREL will not let you draw the path.

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The model is not identified unless additional assumptions are introduced. By default, LISREL will assume that the variances for the two latent variables equal one. In this example, the model will be identified by assuming the variance of Intelligence is one, but the scale for Humor will be set by constraining one of the factor loadings. This can be done by clicking on the loading for Simpsons and changing it to one. LISREL won’t recognize this change, however, until the user then right-clicks on the constraint and chooses Fix.

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To build the SIMPLIS syntax that will estimate the model, go to Setup → Build SIMPLIS Syntax. LISREL’s syntax editor opens and displays the SIMPLIS syntax.

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Click the Run LISREL button to run the model.

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An output file is created (.OUT extension) which contains the model estimates, standard errors, and a number of model fit indices. In addition, the results now display in the path diagram. It is possible to toggle between different types of estimates using the Estimates pull down menu.

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The results look like the following:

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More information on fit indices and the specific model parameters can be found in the model’s output file (.OUT extension) written to the working directory. The output for this model looks like the following:

                                DATE:  2/11/2010
                                  TIME: 13:18


                                L I S R E L  8.80

                                       BY

                         Karl G. Joreskog & Dag Sorbom



                    This program is published exclusively by
                    Scientific Software International, Inc.
                       7383 N. Lincoln Avenue, Suite 100
                        Lincolnwood, IL 60712, U.S.A. 
            Phone: (800)247-6113, (847)675-0720, Fax: (847)675-2140
        Copyright by Scientific Software International, Inc., 1981-2006 
          Use of this program is subject to the terms specified in the
                        Universal Copyright Convention.
                          Website: www.ssicentral.com

 The following lines were read from file D:My DocumentsSEMfullsem.SPJ:

 Full SEM
 Raw Data from file 'D:My DocumentsSEMINTELLIGENCE.psf'
 Latent Variables  humor intelligence
 Relationships
 SIMPSONS = 1.00*humor
 FAMILYGU = humor
 AMERDAD = humor
 READING = intelligence
 WRITING = intelligence
 MATH = intelligence
 ANALYTIC = intelligence
 humor = intelligence
 Path Diagram
 End of Problem

 Sample Size =   100

 Full SEM                                                                       

         Covariance Matrix       

            SIMPSONS   FAMILYGU    AMERDAD    READING    WRITING       MATH   
            --------   --------   --------   --------   --------   --------
 SIMPSONS       0.69
 FAMILYGU       0.58       0.85
  AMERDAD       0.63       0.64       0.84
  READING       0.21       0.24       0.19       1.12
  WRITING       0.14       0.18       0.15       0.82       0.93
     MATH       0.28       0.27       0.29       0.84       0.77       1.00
 ANALYTIC       0.23       0.24       0.21       0.82       0.71       0.80

         Covariance Matrix       

            ANALYTIC   
            --------
 ANALYTIC       0.95
 


 Full SEM                                                                       

 Number of Iterations =  5

 LISREL Estimates (Maximum Likelihood)                           

         Measurement Equations

 
 SIMPSONS = 1.00*humor, Errorvar.= 0.12  , Rý = 0.83
 Standerr                         (0.032)           
 Z-values                          3.66             
 P-values                          0.000  
 
 FAMILYGU = 1.02*humor, Errorvar.= 0.26  , Rý = 0.69
 Standerr  (0.091)                (0.047)           
 Z-values   11.21                  5.60             
 P-values   0.000                  0.000  
 
  AMERDAD = 1.10*humor, Errorvar.= 0.15  , Rý = 0.82
 Standerr  (0.086)                (0.039)           
 Z-values   12.81                  3.85             
 P-values   0.000                  0.000  
 
 
  READING = 0.94*intellig, Errorvar.= 0.23  , Rý = 0.80
 Standerr  (0.084)                   (0.044)           
 Z-values   11.24                     5.24             
 P-values   0.000                     0.000  
 
  WRITING = 0.84*intellig, Errorvar.= 0.22  , Rý = 0.76
 Standerr  (0.078)                   (0.040)           
 Z-values   10.85                     5.57             
 P-values   0.000                     0.000  
 
     MATH = 0.91*intellig, Errorvar.= 0.16  , Rý = 0.84
 Standerr  (0.078)                   (0.035)           
 Z-values   11.74                     4.66             
 P-values   0.000                     0.000  
 
 ANALYTIC = 0.86*intellig, Errorvar.= 0.20  , Rý = 0.79
 Standerr  (0.078)                   (0.038)           
 Z-values   11.13                     5.35             
 P-values   0.000                     0.000  
 

         Structural Equations

 
    humor = 0.24*intellig, Errorvar.= 0.51  , Rý = 0.10
 Standerr  (0.080)                   (0.091)           
 Z-values   3.01                      5.63             
 P-values   0.003                     0.000  
 

         Correlation Matrix of Independent Variables 

            intellig   
            --------
                1.00
 

         Covariance Matrix of Latent Variables   

               humor   intellig   
            --------   --------
    humor       0.57
 intellig       0.24       1.00


                           Goodness of Fit Statistics

                             Degrees of Freedom = 13
                Minimum Fit Function Chi-Square = 13.68 (P = 0.40)
        Normal Theory Weighted Least Squares Chi-Square = 13.93 (P = 0.38)
                 Estimated Non-centrality Parameter (NCP) = 0.93
              90 Percent Confidence Interval for NCP = (0.0 ; 14.21)
 
                        Minimum Fit Function Value = 0.14
               Population Discrepancy Function Value (F0) = 0.0094
               90 Percent Confidence Interval for F0 = (0.0 ; 0.14)
             Root Mean Square Error of Approximation (RMSEA) = 0.027
             90 Percent Confidence Interval for RMSEA = (0.0 ; 0.11)
               P-Value for Test of Close Fit (RMSEA < 0.05) = 0.60
 
                  Expected Cross-Validation Index (ECVI) = 0.44
             90 Percent Confidence Interval for ECVI = (0.43 ; 0.58)
                         ECVI for Saturated Model = 0.57
                        ECVI for Independence Model = 6.53
 
      Chi-Square for Independence Model with 21 Degrees of Freedom = 632.67
                            Independence AIC = 646.67
                                Model AIC = 43.93
                              Saturated AIC = 56.00
                            Independence CAIC = 671.90
                                Model CAIC = 98.00
                             Saturated CAIC = 156.94
 
                          Normed Fit Index (NFI) = 0.98
                        Non-Normed Fit Index (NNFI) = 1.00
                     Parsimony Normed Fit Index (PNFI) = 0.61
                        Comparative Fit Index (CFI) = 1.00
                        Incremental Fit Index (IFI) = 1.00
                         Relative Fit Index (RFI) = 0.96
 
                             Critical N (CN) = 197.84
 
 
                     Root Mean Square Residual (RMR) = 0.030
                             Standardized RMR = 0.034
                        Goodness of Fit Index (GFI) = 0.96
                   Adjusted Goodness of Fit Index (AGFI) = 0.92
                  Parsimony Goodness of Fit Index (PGFI) = 0.45

                           Time used:    0.016 Seconds

                          

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