Introduction to Structural Equation Modeling with Latent Variables

In the section H2: Two-Factor Model with Parallel Tests for Lord Data, you fit a two-factor model with parallel tests for the Lord data by the PATH modeling language in PROC CALIS. Some paths and error variance are constrained under the PATH model. You can also specify this parallel tests model by the FACTOR modeling language, as shown in the following statements:

proc calis data=lord;
   factor
      F1  ===>  W  X    = 2 * beta1,
      F2  ===>  Y  Z    = 2 * beta2;
   pvar
      F1  = 1.0,
      F2  = 1.0,
      W X = 2 * theta1,
      Y Z = 2 * theta2;
   cov
      F1 F2;
run;

In this specification, you specify some parameters explicitly. You apply the parameter beta1 to the loadings of both W and X on F1. This means that F1 has the same amount of effect on W and X. Similarly, you apply the parameter beta2 to the loadings of Y and Z on F2. The constraints on the error variances for W, X, Y, and Z in this FACTOR model specification are done in the same way as in the PATH model specification in the section H2: Two-Factor Model with Parallel Tests for Lord Data.

The fit summary table for this parallel tests model is shown in Figure 17.34.

All the fit indices shown in Figure 17.34 for the FACTOR model match the corresponding PATH model results displayed in Figure 17.27. All the estimation results in Figure 17.35 for the FACTOR model are the same as those for the corresponding PATH model in Figure 17.28.