Chi-square differences & covariation ...
Message/Author
 Anonymous posted on Thursday, May 19, 2005 - 4:35 pm
All of the variables in the model are dichotomous and the model is being run using the theta parameterization.

I have two questions concerning the models below. First, the models are nested, however, when running the models, the number of df given when using the difftest option is not equal to the difference between df in the H0 and H1 models. In the model with the Dep and Anx latent factors, there are 30 df, and in the model with the CF latent factor, there are 27 df; yet in the difftest there are 5 df.

Second, does the program account for the covariance between z1-z4, or does that need to be specified. If that does need to be specified, being that z1-z4 are dichotomous variables, is the covariation between these factors done by:
q1 BY z1* z2 (c);
q2 BY z1* z3 (d);
etc. for all pairs.

The syntax for the models are below:

The 2-factor model:

MODEL: Dep BY x1* x2 x3 x4 (a);
Anx BY y1* y2 y3 y4 (b);
Dep Anx ON z1 z2 z3 z4;
Dep@1;
Anx@1;
er1 BY x1@1; x1@0;
er2 BY x2@1; x2@0;
er3 BY x3@1; x3@0;
er4 BY x4@1; x4@0;
er4@1;
er5 BY y1@1; y1@0;
er6 BY y2@1; y2@0;
er7 BY y3@1; y3@0;
er8 BY y4@1; y4@0;
er8@1;
er2 ON er1;
er3 ON er2;
er4 ON er3;
er6 ON er5;
er7 ON er6;
er8 ON er7;
er1 WITH er5;
er2 WITH er6;
er3 with er7;
er4 with er8;
er1 WITH Anx@0;
er1 WITH Dep@0;
er5 WITH Anx@0;
er5 WITH Dep@0;
er8 WITH Dep@0;
er8 WITH Anx@0;
er4 WITH Dep@0;
er4 WITH Anx@0;
Anx WITH Dep;

The One-factor model:

MODEL: CF BY x1* x2 x3 x4 (a);
y1* y2 y3 y4 (b);
CF ON z1 z2 z3 z4;
CF@1
er1 BY x1@1; x1@0;
er2 BY x2@1; x2@0;
er3 BY x3@1; x3@0;
er4 BY x4@1; x4@0;
er4@1;
er5 BY y1@1; y1@0;
er6 BY y2@1; y2@0;
er7 BY y3@1; y3@0;
er8 BY y4@1; y4@0;
er8@1;
er2 ON er1;
er3 ON er2;
er4 ON er3;
er6 ON er5;
er7 ON er6;
er8 ON er7;
er1 WITH er5;
er2 WITH er6;
er3 with er7;
er4 with er8;
er1 WITH Anx@0;
er1 WITH Dep@0;
er5 WITH Anx@0;
er5 WITH Dep@0;
er8 WITH Dep@0;
er8 WITH Anx@0;
er4 WITH Dep@0;
er4 WITH Anx@0;
Anx WITH Dep;

I apologize for the length of this message and I thank you very much for your time.
 Linda K. Muthen posted on Friday, May 20, 2005 - 7:21 am
I suspect that you are using the WLSMV estimator. The degrees of freedom for WLSMV are not computed in the regular way. See formula 110 in the Technical Appendices which are on the website. This is why you don't see an agreement in the difference between the two degrees of freedom.

Yes, the program does account for the covariances among z1-z4. You should not include them in the model. The CATEGORICAL option is only for dependent variables so z1-z4 should not be specified as categorical.
 Anonymous posted on Friday, May 20, 2005 - 8:11 am
Thanks for the quick and concise reply!