Introduction to Structural Equation Modeling with Latent Variables


Specifying the Parallel Tests Model (H2) by the FACTOR Modeling Language: Lord Data

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.

Figure 17.34: Fit Summary of the Confirmatory Factor Model with Parallel Tests for Lord Data

Fit Summary
Chi-Square 1.9335
Chi-Square DF 5
Pr > Chi-Square 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 17.34 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.

Figure 17.35: Estimation Results of the Confirmatory Factor Model with Parallel Tests for Lord Data

Factor Loading Matrix: Estimate/StdErr/t-value/p-value
  F1 F2
W
7.6010
0.2684
28.3158
<.0001
[beta1]
0
 
 
 
 
X
7.6010
0.2684
28.3158
<.0001
[beta1]
0
 
 
 
 
Y
0
 
 
 
 
8.5919
0.2797
30.7215
<.0001
[beta2]
Z
0
 
 
 
 
8.5919
0.2797
30.7215
<.0001
[beta2]

Factor Covariance Matrix: Estimate/StdErr/t-value/p-value
  F1 F2
F1
1.0000
 
 
 
 
0.8986
0.0187
48.1801
<.0001
[_Parm1]
F2
0.8986
0.0187
48.1801
<.0001
[_Parm1]
1.0000
 
 
 
 

Error Variances
Variable Parameter Estimate Standard
Error
t Value Pr > |t|
W theta1 28.55545 1.58641 18.0000 <.0001
X theta1 28.55545 1.58641 18.0000 <.0001
Y theta2 23.73200 1.31844 18.0000 <.0001
Z theta2 23.73200 1.31844 18.0000 <.0001