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 Thomas A. Schmitt posted on Tuesday, August 04, 2009 - 9:54 am

Is there a method for comparing models in the EFA framework? The fit statistics are very useful but it's difficult to say which model actually is the "best" fitting model. Is EFA in the CFA framework the method of choice for EFA model comparison? Also, is it possible with the WLSMV estimator? Thank you!

 Linda K. Muthen posted on Tuesday, August 04, 2009 - 11:40 am
I think the EFA models are nested so a chi-square difference test could be used.
 Thomas A. Schmitt posted on Wednesday, August 05, 2009 - 11:06 am
Is it possible then to use the DIFFTEST option subcommand in EFA to compare models when using the WLSMV estimator?
 Tihomir Asparouhov posted on Wednesday, August 05, 2009 - 1:46 pm
No, but you can use the WLSM or WLS estimators with EFA.

Alternatively, you can use DIFFTEST and WLSMV within ESEM, that is, setup the EFA model directly:
f1-f5 by y1-y20 (*1); for example or see Example 1 in

Note, however, that testing m-1 factors against m factors is susceptible to overfactoring and inflated Type I error, see Hayashi, K., Bentler, P. M., & Yuan, K. (2007). On the likelihood ratio test for the number of factors in exploratory factor analysis. Structural Equation Modeling, 14, 505526.
 Thomas A. Schmitt posted on Thursday, August 06, 2009 - 7:05 am
So you can use DIFFTEST with WLSM or you can use the chi-square difference test? How does WLSM perform compared to WLSMV?
 Thomas A. Schmitt posted on Thursday, August 06, 2009 - 7:29 am
Okay, so you can not use chi-square for difference testing, so I'm assuming you can use DIFFTEST with WLSM? How would the code work with EFA in that you have to specify two factor structures?
 Linda K. Muthen posted on Thursday, August 06, 2009 - 7:31 am
The DIFFTEST option is used only with WLSMV. With WLSM a scaling correction factor is given that is used when hand calculating the chi-square difference test. WLSM and WLSMV perform pretty much the same.
 Thomas A. Schmitt posted on Thursday, August 06, 2009 - 7:51 am
Thanks Linda. I did run the DIFFTEST in EFA with WLSMV and it did work. But I assume the output file is meaningless?
 Metin Ozdemir posted on Monday, February 08, 2010 - 5:15 am
Which relative fit indexes do you recommend for EFA with MPlus? My model gives a low CFI (.88), but good RMSEA (.06) and SRMR (.03), and the factor structures make theoretical sense. Can I rely on RMSEA and SRMR in such a case?

 Linda K. Muthen posted on Monday, February 08, 2010 - 8:17 am
I would also look at chi-square. The low CFI may be because of low correlations.
 Wim Van den Broeck posted on Wednesday, March 03, 2010 - 6:08 am
I have an EFA model with categorical items. The estimator is WLSM. How can I compare the models ( e.g. a model with 5 factors vs. a model with 6 factors)? There is a warning about comparing the chi-squares. Should I use the formula's in the technical appendix on difference testing, however, there is only mentioned ML, MLM or MLR as estimators?
 Linda K. Muthen posted on Wednesday, March 03, 2010 - 8:15 am
The test for WLSM is the same as for MLR and MLM as shown on the website under How To.
 Kathy Xiao posted on Tuesday, April 10, 2018 - 7:19 am
Hi Dr. Muthen,

I had the EFA results like below. The eigenvalue suggests 1 factor model, but the model fit information and comparison results seem to suggest the opposite. None of the p-values are non-significant.

In this case, may I know how can I judge which model is the best fitting one?

Thanks very much!!

Model Parameters Chi-Square Freedom P-Value

1-factor 12 220.827 54 0.0000
2-factor 23 96.752 43 0.0000
3-factor 33 56.894 33 0.0060
4-factor 42 45.955 24 0.0045
5-factor N/A

Degrees of
Models Compared Chi-Square Freedom P-Value

1-factor against 2-factor 146.903 11 0.0000
2-factor against 3-factor 45.806 10 0.0000
3-factor against 4-factor 17.940 9 0.0359

1 2 3 4 5
________ ________ ________ ________ ________
1 8.300 0.766 0.628 0.465 0.385
 Bengt O. Muthen posted on Tuesday, April 10, 2018 - 3:40 pm
You can use the Parallel option to settle on the number of factors. Also, these general analysis strategy questions are better suited for SEMNET.
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