In the section H2: TwoFactor Model with Parallel Tests for Lord Data, you fit a twofactor 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: TwoFactor Model with Parallel Tests for Lord Data.
The fit summary table for this parallel tests model is shown in Figure 17.31.
Figure 17.31: Fit Summary of the Confirmatory Factor Model with Parallel Tests for Lord Data
Fit Summary  

ChiSquare  1.9335 
ChiSquare DF  5 
Pr > ChiSquare  0.8583 
Standardized RMR (SRMR)  0.0076 
Adjusted GFI (AGFI)  0.9970 
RMSEA Estimate  0.0000 
Bentler Comparative Fit Index  1.0000 
All the fit indices shown in Figure 17.31 for the FACTOR model match the corresponding PATH model results displayed in Figure 17.24. All the estimation results in Figure 17.32 for the FACTOR model are the same as those for the corresponding PATH model in Figure 17.25.
Figure 17.32: Estimation Results of the Confirmatory Factor Model with Parallel Tests for Lord Data
Factor Loading Matrix: Estimate/StdErr/tvalue  

F1  F2  
W 



X 



Y 



Z 


Factor Covariance Matrix: Estimate/StdErr/tvalue  

F1  F2  
F1 



F2 


Error Variances  

Variable  Parameter  Estimate  Standard Error 
t Value 
W  theta1  28.55545  1.58641  18.00000 
X  theta1  28.55545  1.58641  18.00000 
Y  theta2  23.73200  1.31844  18.00000 
Z  theta2  23.73200  1.31844  18.00000 