Chi-square value Mplus vs. Lisrel
Message/Author
 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.

Results:
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

Bart
 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 bmuthen@ucla.edu.
 Bart Meuleman posted on Tuesday, November 07, 2006 - 2:21 pm

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
Relationships
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
 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: support@statmodel.com
Thank you again.