I have conducted a large scale numerical simulation study to see small
sample properties of SEM and then have the following question:
I would appreciate it if you could teach me why MLEs in a CFA model are
different between analyses of raw data and covariance matrix data in
OpenMx package of R. Are the optimization methods employed different?
The maximum difference I encountered is 0.084267.
When I compare the results, I adjusted their scales, i.e., multiplied by
sqrt(N/N-1) for factor loadings and by N/N-1 for error variances.
The adjustment can approach the two estimates to each other closely.
The code and sample covariance matrix are in the attachment.
I would be glad, if someone helped me.