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
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)
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).