Exploratory Structural Equation Modeling Mplus syntax

Most of the Mplus syntax I have seen using ESEM is as follows:

f1-f3 by y301-y313 (*1);

You would get the same results using an EFA with a 3-factor solution.

This next example seems like a proper ESEM model:

f1-f2 BY y1-y6 (*1); f3 BY y7-y9;
f4 BY y10-y12;
f3 ON f1-f2;
f4 ON f3;

Which has both an EFA/CFA component, which is what I thought an ESEM model were.

I guess I'm confused by people's use of ESEM and most of the models look like an EFA to me in Mplus. Any clarification would be great beyond knowing ESEM provides SE.

Thank you for your help.


Can't make spagetti
without a structural equation part, ESEM = EFA. the only real difference (at least from a mathematical point of view) is the use of Jennrich's oblique rotation methods. but then again calling the analysis ESEM instead of EFA just because you're using one specific rotation method is really nothing more than semantics.