Parameterization
Message/Author
 Eric Teman posted on Tuesday, January 24, 2012 - 4:28 pm
I am running a Monte Carlo simulation study. I created a population model and then created equivalent parameterizations (a CFA and full structural model). When running the simulation, all fit indexes and standardized parameter estimates are identical across parameterizations, as would be expected. However, the unstandardized factor loadings are a bit different across parameterizations. Why would this occur?
 Eric Teman posted on Wednesday, January 25, 2012 - 9:59 am
Let me clarify my previous inquiry with an example. Let's say I have a population CFA. I am sampling from that with a CFA model and a full structural model.

My CFA model:
F1 BY x1-x4*;
F2 BY x5-x8*;
F3 BY x9-x12*;
F1@1;
F2@1;
F3@1;

My SEM model (should be identical to CFA, just parameterized as SEM):
F1 BY x1-x4*;
F2 BY x5-x8*;
F3 BY x9-x12*;
F3 ON F1 F2;
F2 ON F1;
F1@1;
F2@.84;
F3@.77143;

When I do this, everything is identical in output (i.e., standardized factor loadings, fit, etc.), but the UNstandardized factor loadings differ slightly. Is this supposed to occur, or have I misspecified something?

Thanks,
Eric
 Bengt O. Muthen posted on Wednesday, January 25, 2012 - 10:15 am
Check in TECH4 that you get the same factor covariance matrix in the two cases.
 Eric Teman posted on Wednesday, January 25, 2012 - 6:11 pm
The covariance matrices from CFA to SEM different slightly. How can I make these exact for CFA and SEM parameterizations of the same model?

If you look at my two examples above, I am fixing the latent variables in the SEM model as stated. These values were obtained from LISREL and there may be some slight variation from LISREL to Mplus, but I cannot seem to get Mplus to give me the latent variables to use to re-parameterize the SEM model.

Thanks,
Eric
 Bengt O. Muthen posted on Wednesday, January 25, 2012 - 8:26 pm
The values you used to fix the factor residual variances are probably slightly off. Perhaps you used too few decimals for the parameters when you computed them.
 Eric Teman posted on Thursday, January 26, 2012 - 12:09 pm
Is there a way for Mplus to compute these values? I had LISREL compute them, and maybe there is a slight different between LISREL's values and Mplus's values.
 Bengt O. Muthen posted on Thursday, January 26, 2012 - 12:41 pm
You get them by expressing the formulas in Model Constraint using Model parameter labels.
 Eric Teman posted on Thursday, January 26, 2012 - 1:02 pm
I'm not at all familiar with expressing the formulas to compute the latent variances. Is this extremely difficult or simple? Any advice on how to express the model constraint formulas for the models I have above to find the latent variances?
 Bengt O. Muthen posted on Thursday, January 26, 2012 - 4:10 pm
Take a look at UG ex5.20. That shows the principles involved, in that case expressing model-derived variances for observed DVs.