You are right that there is a simple formula for the standard error for a correlation that depends on only the correlation coefficient value and the sample size. But that simple formula is for a correlation among two observed variables that are normally distributed and where the variables are not part of an over-identified H0 model as in SEM. The correlations you point to involve latent variables and a categorical observed variable which are part of an over-identified H0 model estimated by WLSMV. In that case, the simple formula is not applicable. Instead, standard errors are computed using WLSMV. Their sizes depend on many factors including the model structure in complex ways.
I have a question about the correlation of type=threelevel.
I am interested in the within level correlations. I have run different models with different predictors and I noticed in the correlation matrix from SAMPSTAT that the correlations change as well as I add parameters in my model. I do not understand why this happens. Could you explain to me, how Mplus calculates the correlation coefficients?
In other programs, the correlations remain always the same even if there are more parameters in the matrices because they are bivariate correlations, why do they actually change in Mplus? for example the correlation between x2 and x1 is .23, but if I add more parameters to the model, the bivariate correlation between x2 and x1 changes to .03. It is not results from the model, but from SAMPSTAT. I find this a bit strange.
In principle changes made to the estimated H0 model can not affect sampstat (the H1 model). The H1 model and the H0 model are estimated separately (see tech8 / log-likelihood values). So the changes you are making are affecting the definition of the H1 model. The two most common reasons are as follows:
1. Changing the status of a variable (i.e. on what level it is or if it is being centered or not). Doing something like that will channel correlation from one level to another.
2. Missing data - if you have a variable that is dependent in one model but independent in another affects how missing data is treated (missing data for covariates is deleted while missing data is modeled).