We've been fitting quite a lot of ESEM recently. I'm in the process of writing up an analysis that has been somewhat puzzling.
The measurement model involves a use of target rotation with Kaiser normalization to a bifactor structure. It appears to be quite stable and the factors are overidentified (between 5 and 9 indicators), for a total of six (one general and five bifactors).
However, when we add the structural regression component on three factors, the loadings on the measurement component on the first set of items shifts quite a bit. These items are in their own block for ESEM (so *1 and then *2 for the other set).
When I set the model up as an interbattery factor analysis, it fits the same (i.e., the chi square and all related numbers are identical, as are the residuals) but has different loadings still.
My hunch is that the reason the loadings shift is due to standardization but I'm somewhat puzzled as we write these results up.
Thanks. Based on what I saw of the unstandardized solution I'm pretty sure this is what happens. Unfortunately ESEM that's pure factor analysis only seems to output the standardized solution insofar as the solution that's output and stdyx are exactly the same. The results make reasonable sense though.