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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 crossloadings. How can I interpret these findings (the CFA model better than ESEM model)? 


What are the chisquare 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 


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\ESEMMplus.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: f1f3 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; 


Yes. 


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 don¡¯t know how to specify my 50 files in the FILE OPTION(rep1.datrep50.dat). If it is the latter, I don¡¯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 


Just do one run, generating the data (using Model Population) with the crossloadings and analyze (using Model) with CFA ignoring them. 


Thank you very much! 


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 chisquare (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 crossloading. Thank you very much for your help, Luis 


Please send the two output and your license number to support@statmodel.com. 


Hi again, Regarding my first question, I just realized that the answer was simply that the robust chisquare 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) chisquare value. Indeed, I estimated the same models using ML and treating the variables as continuous, and the SEMCFA produced a higher chisquare than the SEMESEM. 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 


Choose ESEM if its crossloadings that are fixed at zero in the CFA are significant. 

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