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)?
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?
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.
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.