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?
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.
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?