VIA CFA with ordinal indicators and the WLSMV estimator, I've obtained two latent variables of concepts that are of interest to me, say X and Y. Fit of the model is excellent, and I'd like to move on to full SEM where I test the following--A large gap between the respondent's location on factor X and their location on Factor Y drives evaluations of Z. I have read up on the warnings associated with using saved factor scores in a separate analysis, so is there a way to combine factors in an additive or subtractive manner?
Dear MPlus Team, I have exactly the same problem described here, and I am not sure that I understand the solution that is hinted at in this thread. I need to work with the DIFFERENCE of two latent variables X and Y, and I am aware that you should not simply subtract the factor scores. You suggest now that it is indeed correct to "create another latent variable that somehow is the difference between the two" by "something similar to latent change modelling" and by introducing "a phantom difference factor". Could you please elaborate on that? What is the reference case in the user's manual? How would the exact commands have to look like? I think this could be of great interest for many users.
I built a model according to the scripts that you recommended.
I want to work with the DIFFERENCE of the latent variables L1 and L2, following the idea that L1 together with (L2 minus L1) might explain my outcome.
ANALYSIS: MODEL= NOCOVARIANCES;
MODEL: !!First the Latent true scores L1 BY x1@1x2@1x3@1; L2 BY x4@1x5@1x6@1; [L1*]; L1; [L2@0]; L2@0; [x1-x6@0 ]; x1-x6; !!!Different from Grimm's model I think I should not constrain the residual variance of x1 to x6 to be equal, as x1 to x6 are different variables, so x4-x6 is not the (t+1) equivalent to x1-x3.
!!! Now the Difference score, equivalent to a latent change score diff BY L2@1; [diff]; diff; diff WITH L1;
!!!Finally, the regression I am really interested in Y ON L1 diff;
However, I regularly get the error message: WARNING: THE LATENT VARIABLE COVARIANCE MATRIX (PSI) IS NOT POSITIVE DEFINITE. (....)PROBLEM INVOLVING VARIABLE DIFF. Do you have an idea what might be the problem here?