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Example 16
Comparison of Sörbom’s Method with the Method of Example 9
Sörbom’s alternative to analysis of covariance is more difficult to apply than the
method of Example 9. On the other hand, Sörbom’s method is superior to the method
of Example 9 because it is more general. That is, you can duplicate the method of
Example 9 by using Sörbom’s method with suitable parameter constraints.
We end this example with three additional models called X, Y, and Z. Comparisons
among these new models will allow us to duplicate the results of Example 9. However,
we will also find evidence that the method used in Example 9 was inappropriate. The
purpose of this fairly complicated exercise is to call attention to the limitations of the
approach in Example 9 and to show that some of the assumptions of that method can
be tested and relaxed in Sörbom’s approach.
Model X
First, consider a new model (Model X) that requires that the variances and covariances
of the observed variables be the same for the control and experimental conditions. The
means of the observed variables may differ between the two populations. Model X
does not specify any linear dependencies among the variables. Model X is not, by
itself, very interesting; however, Models Y and Z (coming up) are interesting, and we
will want to know how well they fit the data, compared to Model X.
Modeling in Amos Graphics
Because there are no intercepts or means to estimate, make sure that there is not a check
mark next to
Estimate means and intercepts on the Estimation tab of the Analysis
Properties dialog box.