

Chisquare value Mplus vs. Lisrel 

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Hi all, I recently switched from Lisrel to Mplus. While I was rerunning some measurement models, I was suprised by large differences in the chisquare 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). WLSestimation 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 chisquare values, and consequently the derived fit indices, differ widly: Lisrel: Minimum Fit Function ChiSquare = 12.98 (df=2), RMSEA = 0,057 Mplus: ChiSquare Value = 74.107 (df=2), RMSEA = 0,146 Thanks for your help! Bart 


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 pvalue. The chisquare 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. 


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? 


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). 

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