The Power of ESEM ? PreviousNext
Mplus Discussion > Exploratory Factor Analysis >
 Dominique W posted on Thursday, August 01, 2013 - 4:26 am
I think I see the superiority of ESEM and yet wonder about its potential use beyond factor structure exploration and construct testing.

More specifically, I understand ESEM to be a powerful EFA based on the SEM framework. Thus, as has been published, one may use it to explore the number of sensible factors for new constructs, evaluate item cross loadings, test construct invariance etc.

I still like to better understand the power of ESEM for e.g. path models that test IV-DV relationships.

1) For instance, example 5.25 from the manual, when would one employ such a model?

2) Many 'established' measures in psychology were developed 'before' SEM became popular. Often these measures do not show ideal psychometric properties: i.e. conceptually distinct latent constructs show insufficient divergent validity (e.g. items overlap and tap into the same mental phenomenon).
Assuming a CFA measurement model shows inadmissible fit due to those existing measures employed as IVs, would one use ESEM to explore the construct nature of the IVs? And next estimate paths to DVs at the same time? (again example 5.25 from the manual) If so, would this be accepted practice, working backwards and re-interpreting what substantively may constitutes these revised factors that 'predict' an outcome?
 Bengt O. Muthen posted on Thursday, August 01, 2013 - 8:18 am
1) You may for instance have a new measurement instrument y1-y6 which you don't have enough experience with to formulate a CFA, but can instead use EFA. And it can be related to the CFAs of y7-y9 and y10-y12, representing more established instruments for which CFA can be formulated. So here the predictive validity of the new instrument y1-y6 can be explored.

2) Answers to all 3 of your questions would be Yes.

Note also the existence of BSEM methodology as a companion technique to ESEM. With BSEM you assume that there is a bit more knowledge than with ESEM, so that BSEM is a bit closer to CFA. See the discussion in

Muthén, B. & Asparouhov, T. (2012). Bayesian SEM: A more flexible representation of substantive theory. Psychological Methods, 17, 313-335.

which is available on our website.

I think ESEM and BSEM represent big steps forward for SEM and should find increasing use.
 Dominique W posted on Friday, August 02, 2013 - 1:55 am
Thank you Benqt! While I still need time to digest the BSEM paper, some follow-up questions already, please.

I agree that ESEM represents a big step forward for SEM. Let's be honest, many items don't exclusively reflect just one construct because constructs are often interrelated.

Now, if relating overlapping latent constructs as IVs via ESEM to some DVs modelled via CFA ..

1) How 'established' should those DV constructs be? Even established constructs show cross-loadings.

2) Returning to my question 2) from the prior post: using ESEM in a path model. Has this been published? Especially, working backwards and re-interpreting what substantively may constitutes these revised IV factors?

3) Who has experience or views on what justifies an ESEM (for reviewers)?
Does the conceptual overlap of constructs suffice or must it be established that a conventional CFA does not fit the data?
And if the latter, how would one argue that it is not a function of given study design or newly developed measure?
 Bengt O. Muthen posted on Friday, August 02, 2013 - 6:16 am
1) Researchers should have found a well-fitting and substantively acceptable CFA for the constructs, preferably using many different samples so that the measurement model is not in question in the SEM analysis. That may include a limited number of cross-loadings assuming they are substantively motivated.

2) Not sure it has been published. You may want to search the papers under Applications on our ESEM page:

3) Also see the applied articles just referred to.

I look forward to seeing your contributions to the ESEM (and BSEM) literature.
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