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 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.
 CMP posted on Monday, March 23, 2015 - 12:49 pm
Dear Dr Muthen,

I ran an ESEM from which 3 latent factors were extracted (the indicators were continuous). I then regressed the factors on 4 manifest predictors and included 2 interaction (residualised) terms.

I am trying to interpret the interaction. In Kline (2011), to interpret interaction of observed variables, the unstandardized regression equation can be re-arranged so that there is no interaction term, then meaningful values of W (in my case) can be substituted, and the effect on X coefficients is observed.
Would the equation in my case look like this:

1st step
F1 = bX + bW + bXW

2nd step
F1 = (.5 + .2W) X + .4W

1) Am I right to say that as the F1 was not observed there is no intercept in this equation?
2) I have ignored the other main effects and interaction terms which I am not concerned with. Is this OK?
3) Does Mplus calculate the simple slopes of interaction of observed variables? If yes, where can I find this information?

Thank you for your help.
 Bengt O. Muthen posted on Monday, March 23, 2015 - 2:31 pm
See our pdf "Simple slopes" on the Mediation page (left margin under Special Mplus Topics.

Yes, f1 typically has an intercept of zero.
 CMP posted on Tuesday, March 24, 2015 - 2:19 am
I have taken a look at the pdf of the model specified for simple slopes. I am not sure I fully understand it. It says:
In this mediation model the x->m path is moderated by z using an interaction variable zx
I thought it would be x to y path. Why is m being regressed on the other predictors?

Thank you for your help.
 Bengt O. Muthen posted on Tuesday, March 24, 2015 - 8:42 am
Yes, the FAQ example uses a moderator for the X->M path. You can modify that for a moderator of the X->Y path. When you include moderators in the model it is possible that they also influence M. If you are unfamiliar with this, please see the Hayes book on mediation.
 Joe Wasserman posted on Sunday, January 07, 2018 - 8:59 pm
I have a question similar to Kate's original question that I have not been able to find addressed anywhere else.

I am estimating an ESEM model with covariates in which the indicators load on the set of EFA factors dramatically differently than when the EFA was estimated by itself.

Could this factor instability be an indication of potential over-factoring?

Is it appropriate to estimate a CFA with loadings fixed to those estimated in EFA instead of the ESEM? This was the approach used, e.g., here:
 Bengt O. Muthen posted on Monday, January 08, 2018 - 5:33 pm
Are you looking at the standardized estimates for the ESEM run?

I don't think using fixed CFA loadings is the best approach.
 Joe Wasserman posted on Monday, January 08, 2018 - 5:39 pm
Thank you for your response!

Yes, I am looking at the standardized estimates. Items that loaded on separate factors in my EFA now load together in the ESEM with covariates, and an entire factor is left without any moderately strong loadings.
 Tihomir Asparouhov posted on Monday, January 08, 2018 - 6:09 pm
Most likely this is due to left-out direct effects from the covariate to the indicators. Use the output:mod; command to see which direct effects should be included.
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