Launch Amos Graphics. The complete data containing missing values is saved as the SPSS file values_full.sav in the C:\temp\CFA folder. To load the data, choose File → Data Files. After the Data Files dialog box opens, click on File Name. Navigate to the CFA directory and choose the correct file.

Click Open, Then Okay.

Begin drawing the path diagram by clicking on the Add Unobserved Variable button and drawing an oval to represent a latent variable. Move the cursor just below the oval and click once to create a second oval of the same size.

Click on the Draw a latent variable button or add an indicator to a latent variable button . Click three times inside each oval to add a total of six indicators and their respective error terms. By default, Amos sets the metric of each error term by constraining the path parameters to one. The factor loading of the first indicator for each latent variable is also set to one. If you are not happy with where Amos added the indicators, it is possible to rotate each latent variable by choosing the Rotate the Indicators of a Latent Variable button and clicking each factor until you are satisfied with the appearance. Finally, add a covariance between the two common factors by choosing the Draw Covariance button and drawing the two-headed arrow. Your screen should now look like the following:

To label the latent variables, right-click in one of the ovals and choose Object Properties. When the Object Properties dialog box opens, choose the Text tab. Name one variable ECONOMIC and the other MORALS.

Do the same to name the error terms d1 through d6.

To name the observed variables, choose View → Variables in Dataset. Click and drag the names of each variable to the appropriate box in the path diagram. If the names do not fit you can resize the box after clicking on the Change the Shape of Objects button . The path diagram should look something like the following:

Earlier analysis suggested that GOVTRESP was not strongly tapping purely economic values, and modification indices suggested an improved model fit by adding a path connecting it to the MORALS factor (see the previous section). In the path diagram, add an arrow from the MORALS latent variable to the GOVTRESP indicator.

When missing values are present it is necessary to request that Amos estimate means and intercepts (required for FIML estimation), which is not the default. Choose View → Analysis Properties, click the Estimation tab in the Analysis Properties dialog box, and select Estimate means and intercepts.

Next click on the Output tab. Minimization History is checked by default. Also place checks next to Standardized Estimates and Squared Multiple Correlations.

To estimate the model, go to Analyze → Calculate Estimates. To see the results in the path diagram, click on the View the Output Path Diagram button.

The unstandardized estimates are displayed by default. Choose instead to display the standardized estimates.

If the results are hard to read it is possible to move elements of the diagram by displaying the input path diagram, choosing the Move Objects button and changing the position of parts of the drawing. The standardized output can then be viewed again by requesting the output path diagram.

Amos now displays the standardized factor loadings, the squared multiple correlation coefficient for each observed variable, and a χ² statistic of model fit. Note that, for some models with many parameters and missing data, Amos (and all SEM software) may require a large number of iterations to estimate a χ² statistic. For this simple model, however, there is no problem. To see more detail about the results, go to View → Text Output. A selected portion of the output is the following:

The overall model fit appears quite good. The χ² test yields a statistic 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. Additionally, the RMSEA is only .007, offering further evidence that the model fits the data well.

Under the Regression Weights heading, the unstandardized loadings appear along with standard errors, a critical ratio, and p-values. The critical ratio and p-values can be used to ascertain statistical significance. A critical ratio greater than 1.96 or a p-value smaller than .05 signifies significance. Three asterisks (***) indicate that the p-value is smaller than .001. 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 strength of loadings. The GOVTRESP has low standardized loadings on both factors (.156 for ECONOMIC and .161 for MORALS), suggesting that it is an unreliable indicator of both economic and moral values. However, the other indicators have moderate to strong standardized loadings. For PRIVTOWN the loading is .615, for COMPETE it is .691, for HOMOSEX it is .637, for ABORTION it is .783, and for EUTHANAS it is .667.

The squared multiple correlations provide information about 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 (.379), HOMOSEX (.406), EUTHANAS (.445), COMPETE (.478), and ABORTION (.614). Finally, the correlation between the two common factors is -.018, and the covariance estimate of -.051 is not statistically distinguishable from zero (p<.823).