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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 Philippe 


No, this is not possible. 


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 ? 


This may be implemented later. We have been thinking about it. 


Great ! thanks Philippe 


Hi Philippe, When stuck with a similar problem, I used EFAwithinCFA (see slides 133146 of the Mplus short courses handouts 1). In fact, we coined it ESEMwithinCFA in that we followed the methods of EFAwithinCFA 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. 


Thank you for this suggestion Alexandre. I'll give it a try !! Philippe 


Further to the discussion above, I was wondering whether a higherorder 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 firstorder factors as the input for the secondorder latent variable. Regards, Daniel 


No, a secondorder ESEM is not possible in Mplus. 

Cecily Na posted on Saturday, April 21, 2012  7:13 pm



Hello, I am doing a CFA with twolevel 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 c1c3; otherf by c4c6; 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! Cecily 


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 support@statmodel.com. 

Cheng posted on Tuesday, January 26, 2016  9:11 am



I just wonder is higherorder ESEM model can be performed in Mplus 7.3? 


This is not available but check with Herb Marsh. He may have a way to do this. 


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 cutoffs, i tested a few crossloadings. The question is: which method should i use? Trust ESEM suggestions from 1st Order Factors and run higher crossloads 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! 


1. Do ESEM on the firstorder factors. The secondorder factor structure is justidentified with only 3 1storder 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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