Hello,
I have two general questions and I am particularly interested in doing these models in OpenMx.

Is there a way to estimate SEMs with input only being pearson's correlations and the standard errors from the pearson correlations? I want to do this without back transforming to the sample size, so essentially the sample size is unknown.

I have a series of pearson's correlations that are estimated with different sample sizes. Is there a way to use the pearson correlations to estimate an SEM and take these differences in sample sizes into consideration for estimation of the liklihood test and standard errors?
Thanks!
One approach might be to use a diagonally weighted least squares approach, with weights proportional to 1/se where se is the standard error of the correlation. Asymptotically this is ok, but deviations from good behavior can occur when the sample size is some distance from its asymptotic value. The problem, however, is that often the different correlations may not be independent, and failure to model this statistically can yield biased standard errors (the parameter estimates are usually ok though). The usual solution here is to use full WLS  which includes information about the correlations between the correlations.
The sample size question 2 seems pretty much the same as question 1, except N is substituted for SE, and has the same solution.
More carefully, can you explain why your data are like this  different N's etc? Possibly a FIML approach would be best, if you have access to the raw data. But perhaps this is metaanalysis of statistics obtained from the literature, for which the luxury of raw data is rarely available.
Thanks for the reply!
So am looking at building models with Diagonal weighted least squares in OpenMx now. I have attempted to add a weighted matrix before in R, but was hoping to design this procedure in a toolbox that others are utilizing. I am curious about two aspects of OpenMx for SEM in particular:
Are there any scripts for this analysis currently available? Specifically, ones that do not require me to enter nobs= for my OpenMx objects? I can work on rewriting the WLS and data functions (i have some familiarity with R), but wanted to see if there is an easier option present in OpenMx currently.
You hit my issue pretty on the nose in terms of data structure. These are correlations from the literature and I do not really have the true n or raw data, just the correlation and standard error. I have thought about calculating the effective sample size from the correlation and its standard error and using that, but each correlation would have a different effective sample size (hence my second question). I am looking for a way to input this information directly now and thought OpenMx flexibility might help. Is there an approach with metaanalytic SEM maybe that would be best?
Thanks again for your advice!
I am just echoing Michael's point that the use of SE or N would not be optimal.
In terms of the implementation, the metaSEM package, which uses OpenMx as the backend, has a wls() function for fitting correlation and covariance structures.
I have two questions:
1. Are you saying there is a way to estimate the models entirely without specifying the N or SE?
These two questions are related. The best way is to conduct a twostage structural equation modeling. You need to have the correlation matrices and their sample sizes (not the average correlation matrix).
In the first stage, the correlation matrices are pooled together. In the second stage, the average correlation matrix with its asymptotic covariance matrix are used to fit SEM with the WLS approach. You may refer to the following examples: https://cran.rproject.org/web/packages/metaSEM/vignettes/Examples.html#twostagestructuralequationmodeling