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 Pedro Pinto posted on Wednesday, September 21, 2016 - 7:19 am
I estimated a CFA model with 3 factors and 20 indicators (F1 with 9 indicators; F2 with 5 indicators and F3 with 6 indicators). Because factor correlations showed higher coefficients (r > .80) I performed an ESEM analysis.

However, the CFA model showed a better fit than the ESEM model
CFA: CFI = .950 RMSEA = .031
ESEM: CFI = .722 RMSEA = .120

In the ESEM model the factor correlations are lower (r < 270) and some some indicatores showed cross-loadings.

How can I interpret these findings (the CFA model better than ESEM model)?
 Bengt O. Muthen posted on Wednesday, September 21, 2016 - 9:56 am
What are the chi-square and df values for the two models?
 Pedro Pinto posted on Wednesday, September 21, 2016 - 12:02 pm
Thank you for the reply.

--CFA --
X2 = 159
df = 396.876
8 error covariances were included in the CFA model

-- ESEM --
x2 = 5947.046
df = 190
No error covariances were included in the ESEM model
 Pedro Pinto posted on Wednesday, September 21, 2016 - 12:28 pm
Thank you for the reply.

--CFA --
X2 = 159
df = 396.876
8 error covariances were included in the CFA model

-- ESEM --
x2 = 5947.046
df = 190
No error covariances were included in the ESEM model
 Pedro Pinto posted on Wednesday, September 21, 2016 - 12:31 pm
Thank you for the reply.

--CFA --
X2 = 159
df = 396.876
8 error covariances were included in the CFA model

-- ESEM --
x2 = 5947.046
df = 190
No error covariances were included in the ESEM model
 Bengt O. Muthen posted on Wednesday, September 21, 2016 - 2:42 pm
CFA can fit better than EFA if you add error covariances. You can add error covariances also to the EFA.
 Pedro Pinto posted on Wednesday, September 21, 2016 - 4:54 pm
Thank you for your reply.

Indeed, with the error covariances in the model the ESEM fit better than CFA:

-- ESEM --
CFI = .983
RMSEA = .030
SRMR = .027


I assume that the syntax is correct (is it correct?):
TITLE: ESEM

DATA:
FILE IS "\NOSDRIVE\d\ESEM-Mplus.dat";

VARIABLE:
NAMES ARE m1 m2 m3 m4 m5 m6 m7 m8 m9 l1 l2 l3 l4 l5 afe1 afe2 afe3 afe4 afe5 afe6;

MODEL:
f1-f3 BY m1 m2 m3 m4 m5 m6 m7 m8 m9 l1 l2 l3 l4 l5 afe1 afe2 afe3 afe4 afe5 afe6 (*1);
m1 WITH m2;
m3 WITH m4;
m5 WITH m6;
m7 WITH m8;
l1 WITH l2;
l4 WITH l5;
afe2 WITH afe3;
afe4 WITH afe5;

OUTPUT: STANDARDIZED;
 Bengt O. Muthen posted on Wednesday, September 21, 2016 - 5:12 pm
Yes.
 WEN Congcong posted on Wednesday, April 19, 2017 - 12:59 am
Professors,
Hello! I want to prove the advantages of ESEM and generated 50 data sets with 2 factors, 10 indicators, 2 of which have small cross loading. In your ESEM paper in 2009, after generating the data sets, you analyze them with ESEM and CFA respectively.

I really want to ask: If I want to use CFA which ignores the 2 cross loadings to fit the mplus generated data sets to see CFA get how biased the estimates, I should use a normal CFA syntax in mplus or the type=montecarlo command in mplus? If it is the former, I doní»t know how to specify my 50 files in the FILE OPTION(rep1.dat-rep50.dat). If it is the latter, I doní»t know how do we specify the model part. Just ignore the cross loadings and give the high CFA factor loadings the true values?

Thank you very much!
WEN CONGCONG
 Bengt O. Muthen posted on Friday, April 21, 2017 - 5:55 pm
Just do one run, generating the data (using Model Population) with the cross-loadings and analyze (using Model) with CFA ignoring them.
 WEN Congcong posted on Saturday, April 22, 2017 - 9:03 pm
Thank you very much!
 Luis Garrido posted on Sunday, August 06, 2017 - 2:16 pm
Greetings,

I ran a SEM model (ULSMV estimator) with 4 independent factors measured by a total of 36 items (10x3 + 6) and a dependent factor measured by 10 items. When I compared the SEM model with 4 ESEM factors vs the same model with 4 CFA independent factors, I was surprised to see that the CFA one had a lower chi-square (1,344.376 w/ 979 df) compared to the model with the ESEM factors (1,366.744 w/ 883 df). How is this possible?

Also due to these results, I wanted to ask you what is your criteria for retaining an ESEM model vs. a CFA one? In this case the CFA one has better fit, but the factor correlations in the 4 predictor factors are substantially higher than those from the ESEM with Target rotation. Note that in the ESEM with target rotation all the items have target loadings that are always higher than their largest cross-loading.

Thank you very much for your help,

Luis
 Linda K. Muthen posted on Monday, August 07, 2017 - 5:43 am
Please send the two output and your license number to support@statmodel.com.
 Luis Garrido posted on Saturday, August 12, 2017 - 8:55 am
Hi again,

Regarding my first question, I just realized that the answer was simply that the robust chi-square values cannot be compared like the one does with continuous variables, and that in some cases (such as this one), the more constrained model may produce a lower (robust) chi-square value. Indeed, I estimated the same models using ML and treating the variables as continuous, and the SEM-CFA produced a higher chi-square than the SEM-ESEM.

I am still wrestling with the second question: how to decide whether to retain an ESEM or a CFA. My understanding is that if the solutions produce meaningfully different parameter estimates, then one should retain the ESEM model. I was wondering if you have any particular criteria (cutoffs / magnitude of differences in the estimates) you use to make this decision.

Thanks!

Luis
 Bengt O. Muthen posted on Saturday, August 12, 2017 - 10:43 am
Choose ESEM if its cross-loadings that are fixed at zero in the CFA are significant.
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