Chi-square value Mplus vs. Lisrel PreviousNext
Mplus Discussion > Confirmatory Factor Analysis >
 Bart Meuleman posted on Tuesday, November 07, 2006 - 11:30 am
Hi all,

I recently switched from Lisrel to Mplus. While I was rerunning some measurement models, I was suprised by large differences in the chi-square values that are reported by Mplus and Lisrel. Is there a simple explanation for this difference? (sorry if this question has been answered already...)

Model specifications:
one factor loads on 4 categorical (ordinal) indicators (4 categories each). WLS-estimation is specified.

Lisrel and Mplus report very similar (though not equal) estimates for the factor loadings, factor variance and the thresholds. However, the reported chi-square values, and consequently the derived fit indices, differ widly:
Lisrel: Minimum Fit Function Chi-Square = 12.98 (df=2), RMSEA = 0,057
Mplus: Chi-Square Value = 74.107 (df=2), RMSEA = 0,146

Thanks for your help!

 Linda K. Muthen posted on Tuesday, November 07, 2006 - 12:54 pm
I think the difference is that you are using WLSMV in Mplus and WLSM in LISREL. The only value that is relevant for WLSMV is the p-value. The chi-square value and the degrees of freedom are not the regular statistics. The following paper discusses the Mplus estimators:

Muthén, B., du Toit, S.H.C. & Spisic, D. (1997). Robust inference using weighted least squares and quadratic estimating equations in latent variable modeling with categorical and continuous outcomes. Accepted for publication in Psychometrika. (#75)

You can request it from
 Bart Meuleman posted on Tuesday, November 07, 2006 - 2:21 pm
Thanks for your immediate reply.

I think in both analyses wls was used (and thus not wlsm or wlsmv), because I specified this explicitely in the model (in mplus: 'estimator=wls', in Lisrel 'wls' as output option). But maybe I am doing something wrong.

My question is in the first place a practical one. The Lisrel fit indices suggest that the model is maybe not good but acceptable, the mplus indices completely reject the model. How do I decide which option is the correct one?
 Bengt O. Muthen posted on Tuesday, November 07, 2006 - 2:32 pm
The Muthen et al paper (#75) that you requested describes how WLS performs poorly unless the model is very small and the sample very large. It shows that the Mplus WLSMV estimator works well. I would use WLSMV. In terms of fit indices I would largely rely on CFI. I, however, am more inclined to work with neighboring models, testing the model at hand against not the totally unrestricted model, but against a somewhat less restrictive model. This can be done in Mplus using DIFFEST (see the UG).
 Mahdi posted on Friday, May 02, 2014 - 9:17 am
Dears Prof. Muthen,
I run the example 3.11(Path analysis with continuous dependent variables) of your users guide in V6.
Then I run the model on LISREL v 8.54(2003). Data, model specification, number of parameters, DF and method of estimation (ML) are same in two packages but the results is different in Chi2 value, RMSEA, parameters estimation and . . . !!

### model in Lisrel:
Raw Data from file 'C:\PA.psf'
Sample Size = 500
Y1 = X1 X2 X3
Y2 = X1 X2 X3
Y3 = Y1 X2 Y2
Print Residual
Options: ND=3
Path Diagram
End of Problem

Also I run this model with covariance matrix in LISREL and there was still the problem. As you seen following is the result of LISREL:

Chi-Square=609.02, df=3, P-value=0.00000, RMSEA=0.638, (RMSEA < 0.05) = 0.000
RMSEA = (0.596 ; 0.681)
What causes this problem?
Thaks a lot
 Linda K. Muthen posted on Friday, May 02, 2014 - 10:39 am
I would need to see the output from Mplus and the output from LISREL and your license number to be able to say anything about this.
 Mahdi posted on Friday, May 02, 2014 - 10:50 am
Dear Dr.Mutten,
Thank you for immediate response. What is your E-mail?
 Mahdi posted on Friday, May 02, 2014 - 12:16 pm
I sent the Outputs to this Email:
Thank you again.
Back to top
Add Your Message Here
Username: Posting Information:
This is a private posting area. Only registered users and moderators may post messages here.
Options: Enable HTML code in message
Automatically activate URLs in message