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(1) If I conducted Exploratory Structural Equation Modeling (ESEM), and specify the model as follow:

f1-f2 measured by v1 v2 v3 v4 v5 v6;

Can I also allow regression path between f1 and f2, i.e.:

f1 -> f2?

(2) If the answer in Question 1 is no (I cannot specify regression path between latent variables while doing ESEM), I wonder if there are any other way to twick so that I can estimate the regression path? I am certain that f1 is mainly measured by v1,v2,and v3, and f2 is mainly measured by v4, v5, and v6. However, there are small cross-loadings, such that v4, v5, and v6 cross-load on f1, and v1, v2, and v3 cross-load on f2.

It may be helpful to know that I am using the programme Mplus for ESEM. Thanks for your help!

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The answer to the first question is no.

You can trick the ESEM procedure by first exploring your data, and then using the model that this gives you in a regular SEM framework. If you do this, I think you might run into identification issues though (in the same way that you need identifying constraints in CFA and EFA).

It's kind of weird though, because you're saying "I think that A causes B, but I don't know what A and B actually are." It's possible that in exploratory SEM, A and B swap places - you don't know which variable will end up in which place.

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  • $\begingroup$ Thanks, Jeremy. I agree with you. I guess the only method that allows cross-loadings while estimating structural relationships is Bayesian SEM. Am I right? $\endgroup$ – Joseph May 26 '17 at 10:15
  • $\begingroup$ You can do it with regular SEM (if you're careful about identification) but not ESEM (I believe). $\endgroup$ – Jeremy Miles May 26 '17 at 16:48
  • $\begingroup$ I think you mean common SEM, not regularized SEM recently put forward by Kevin Grimm. $\endgroup$ – Joseph May 27 '17 at 5:05

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