Second order ESEM PreviousNext
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 Philippe Golay posted on Friday, October 08, 2010 - 7:06 am
Is it possible to define a second order CFA latent variable defined on the basis of first order EFA factors ?

On the opposite, is it possible to do EFA on a set of CFA first order factors ?

Many thanks in advance

 Linda K. Muthen posted on Friday, October 08, 2010 - 7:37 am
No, this is not possible.
 Philippe Golay posted on Friday, October 08, 2010 - 8:25 am
Ok and thank you for your answer. Is it a mathematical/statistical limitation (that cannot be overcome) or that may be implemented later in the software ?
 Linda K. Muthen posted on Friday, October 08, 2010 - 8:36 am
This may be implemented later. We have been thinking about it.
 Philippe Golay posted on Friday, October 08, 2010 - 8:42 am
Great ! thanks

 Alexandre Morin posted on Friday, October 08, 2010 - 8:46 am
Hi Philippe,
When stuck with a similar problem, I used EFA-within-CFA (see slides 133-146 of the Mplus short courses handouts 1). In fact, we coined it ESEM-within-CFA in that we followed the methods of EFA-within-CFA and used the specific results from the full ESEM model as starts values for the first order factors (to the degree of fixing the cross loadings that need to be fixed for identification purposes to their ESEM values rather than 0). Then, you simply need to load them on the second order factor (and to ensure they are identified).
No sure how to do the reverse: first order CFA model and second order EFA.
 Philippe Golay posted on Friday, October 08, 2010 - 9:12 am
Thank you for this suggestion Alexandre. I'll give it a try !!

 Daniel Gucciardi posted on Tuesday, January 17, 2012 - 1:55 am
Further to the discussion above, I was wondering whether a higher-order ESEM model can be performed in Mplus 6.12?

I am aware of the approach adopted by Marsh, Muthen et al. (2009) published in SEM in which they employed the correlations between the first-order factors as the input for the second-order latent variable.

 Linda K. Muthen posted on Tuesday, January 17, 2012 - 10:19 am
No, a second-order ESEM is not possible in Mplus.
 Cecily Na posted on Saturday, April 21, 2012 - 7:13 pm
I am doing a CFA with two-level latent variables.

friend (a higher order latent variable)is indicated by two lower order latent variables 1) close friend, and 2) other friend, AND a measured indicator 3) contact frequency with friends.

I did the following:
closef by c1-c3;
otherf by c4-c6;
friend by closef otherf freq;

the output however shows the path from friend to frequency is set to 1. Why is it the case? Is my syntax okay?
Thank you!
 Linda K. Muthen posted on Sunday, April 22, 2012 - 2:11 pm
The first factor loading is fixed to one as the default to set the metric of the factor. I don't know why the third is being fixed to one. Please send the output and your license number to
 Cheng posted on Tuesday, January 26, 2016 - 9:11 am
I just wonder is higher-order ESEM model can be performed in Mplus 7.3?
 Linda K. Muthen posted on Tuesday, January 26, 2016 - 2:56 pm
This is not available but check with Herb Marsh. He may have a way to do this.
 Paulo Alexandre Ferreira Martins posted on Sunday, October 09, 2016 - 10:06 am
Dear Linda and Beng Muttén,

Sorry for the inconvenience, but I have two questions regarding Model Respecification:

1. My model showed multicollinearity with all 3 Factors. However, as i simple can't do a single or two factor model, i’ve conducted a 2nd Order Factor.
As Fit indices are still a bit far from standard cut-offs, i tested a few cross-loadings.
The question is: which method should i use? Trust ESEM suggestions from 1st Order Factors and run higher cross-loads or instead trust Mod Indices as i’m already running a 2nd Factor Order Model?

2. In one of my competing models (within 2nd Order Factors) i tested not to fix 1st Order Factors variance to 1. The result was one negative residual factor.
From hear, i constrained this factor variance to zero, resulting in far better Fit Indices.
Does it make any sense?

Thank you very much!
 Bengt O. Muthen posted on Sunday, October 09, 2016 - 5:28 pm
1. Do ESEM on the first-order factors. The second-order factor structure is just-identified with only 3 1st-order factors so it doesn't contribute to misfit.

2. I don't see how fixing a negative residual variance can give better fit indices - unless you are talking about BIC.
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