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Mplus Discussion > Exploratory Factor Analysis >
 Xu, Man posted on Wednesday, May 01, 2013 - 11:20 am
Dear Dr.s Muthen

I was running some analysis using ESEM. I look at EFA structure of a set of items, with and without an external predictor of these EFA factors. I found that, the factor loadings of the EFA part of the ESEM model change a bit when compared to the EFA only analysis (when without the external co variate).

Although the change in factor loadings is not particularly large in the ESEM model, I guess in some situations someone might argue which the primary factor should be for a particular item.

This reminds me of the 3-step mixture model method - but I might be making a very crude analogy.

I was wondering if you could give some advice/suggestions for this situation?

Thanks a lot!

 Linda K. Muthen posted on Wednesday, May 01, 2013 - 1:28 pm
When you regress the factor on a covariate, you assume the covariate influences the indicator only through the factor and not directly. This may not be the case. There may be a need for direct effects from the covariate to the indicator.
 Xu, Man posted on Wednesday, May 01, 2013 - 2:45 pm
Thank you. Yes, I can now see this point. Just to be sure, is this only specific (or more relevant) to ESEM or it is applicable also to the more traditional SEM models with CFA measurement model?

I can understand that, in traditional SEM, it is always good to check mediation effect from co variates to item intercepts using MIMIC method. But since the focus is on relationship between covariates and the factor, and item intercepts, I would not have thought that factor loadings would be affected as much - but I might be understanding this wrongly..

I guess, in SEM, usually a CFA model is used, so meaning of factors is always clearly defined. But in ESEM, the meaning of a factor is quite heavily relying on magnitudes of factor loading, hence things are more complicated here.

I'd really appreciate your further views/suggestions. Thank you very much in advance!

 Linda K. Muthen posted on Wednesday, May 01, 2013 - 4:10 pm
This is applicable to any model where adding a new observed variable results in many zero paths that may or may not be needed.
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