Highlight each variable name by clicking on PRIVTOWN, holding down the shift button, and clicking on EUTHANAS. Click on Missing Values
to bring up the Missing Values
box. Click on the Missing Values
radio button, enter -999999.0 in the first empty field, and check the Apply to all
Click OK, then OK again. Save the data so that the changes take effect.
The next step is to draw the path diagram. Go to File → New, choose Path Diagram, and click OK. You will be prompted to save the path diagram. Name it values_full and click Save. An empty window opens where the path diagram will be drawn.
The next step is to name the observed and latent variables and tell LISREL to call the raw data from the PRELIS file. Go to Setup → Title and Comments to open a dialog box to label the analysis. Enter “Confirmatory Factor Analysis with Missing Data” in the Title field.
Click Next. This opens the Group Names dialog box, which is used when comparing models across different clusters of observations. Because this example is concerned with only a single sample, click Next to bring up the Labels box.
To read in the names of the observed variables, click on the Add/Read Variables button. Make sure the Read from file radio button is chosen along with the PRELIS System File option. Browse to the C:\temp\CFA directory to choose the values_full.psf file.
Click OK. The next step is to name the latent variables. Click on the Add Latent Variables button and add the name ECONOMIC. Click again to add MORALS.
Choose Next. A final box appears to specify the location of the data file to be analyzed. Make sure Raw Data is entered in the Statistics from field and that PRELIS System Data is chosen in the File type field. The PRELIS system file contains information about the number of observations and missing data codes, so no further changes need to be made.
To begin drawing the path diagram, first drag each of the variable names from the left-hand side of the screen to the drawing area.
Next, draw single-headed arrows pointing from ECONOMIC to PRIVTOWN, GOVTRESP, and COMPETE. Draw additional arrows pointing from MORALS to HOMOSEX, ABORTION, EUTHANAS, and GOVTRESP. Unlike with Amos, it is not necessary to draw unique factors corresponding to measurement error in the observed indicators; LISREL includes these by default. Finally, add a two-headed arrow to represent the covariance between ECONOMIC and MORALS. The path diagram should now look like the following:
The last step is to set the metric of the two common factors by constraining factor loadings to equal one. Double-click the 0.00 on the path from ECONOMIC to PRIVTOWN and change the loading to 1.00. Right-click and choose Fix to constrain the loading to one.
Do the same for the path between MORALS and HOMOSEX.
Before estimating the model, it is necessary to build from the path diagram the syntax LISREL uses to estimate the model. Choose Setup → Build SIMPLIS syntax
. This opens the syntax editor along with the commands required to estimate the model drawn in the path diagram. If we had not previously told PRELIS which codes were missing it would be necessary to add the line MISSING VALUE CODE = -999999. To begin the estimation, click on the Run LISREL
The unstandardized estimates are immediately displayed in the path diagram along with two measures of overall fit: χ2 and RMSEA. To view the standardized results, choose Standardized Solution from the Estimates pull-down menu.
The path diagram will now look like this:
More detailed information can be obtained by looking at the output text file generated after estimation. This file is given the same name as the path diagram plus an .out extension and stored in the working directory. The file values_full.out looks like the following:
The overall model fit appears quite good. The χ2 test yields a value of 7.402 (df=7), which has a corresponding p-value of .388. This p-value is too high to reject the null of a good fit. In addition, the RMSEA is only .007, offering further evidence that the model fits the data well.
Under the Measurement Equations heading, the unstandardized loadings appear along with standard errors, t-values, estimates of error variance, and squared multiple correlation coefficients (R2). A standard error at least twice the size of the estimate can be considered evidence of significance. In this case all of the unconstrained estimates are significant. The unstandardized weights are highly sensitive to model constraints, whereas the standardized regression weights provide more intuitive information about the loadings. Standardized solutions are not printed by default in the output but can be recovered from the path diagram. The GOVTRESP has low standardized loadings on both factors (.16 for ECONOMIC and .16 for MORALS), suggesting that it is a weak indicator of both economic and moral values. However, the other indicators have moderate to strong standardized loadings. For PRIVTOWN the loading is .62, for COMPETE it is .69, for HOMOSEX it is .64, for ABORTION it is .78, and for EUTHANAS it is .67.
The squared multiple correlations provide information on how much variance the factors account for in the observed variables. Despite receiving a path from both latent variables, GOVTRESP has a very low R2 of only .049. The remaining R2 statistics are, in order of increasing magnitude, PRIVTOWN (.38), HOMOSEX (.41), EUTHANAS (.45), COMPETE (.48), and ABORTION (.61). Finally, the correlation between the two common factors is a very small -.02 (according to the path diagram), and the covariance estimate of -.05 is not statistically distinguishable from zero (Standard Error = .12).