WLSMV vs LISREL's DWLS PreviousNext
Mplus Discussion > Categorical Data Modeling >
 Jaume Aguado Carné posted on Wednesday, June 08, 2005 - 9:09 am

What are the differences between the estimators mentioned in the title? I've used both with similar but not equal results and I wonder what are the differences.

Thank you
 bmuthen posted on Wednesday, June 08, 2005 - 6:24 pm
They have similar philosophies, but use different asymptotic approximations in estimating the asymptotic covariance matrix of the estimated sample statistics used to fit the model (i.e. the weight matrix) - see the papers from both camps. So the larger the sample gets, the closer the results should be.

Note also that the scope of models that can be handled by the two approaches is different. As shown in Mplus Web Note #4, it is my opinion that the Mplus approach is advantageous with multiple-group modeling and with longitudinal modeling.
 Jaume Aguado Carné posted on Thursday, June 09, 2005 - 2:28 am
Thank you very much. Just a little question more, is it possible to compute a RMSEA confidence interval with the WLSMV estimator?, I ask this because Lisrel does it with DWLS and I don't know if it makes sense at all.

Thanks again
 Linda K. Muthen posted on Thursday, June 09, 2005 - 8:29 am
We have not yet developed the theory for doing confidence intervals for WLSMV RMSEA. I don't know what Lisrel does for their DWLS confidence intervals. You would need to check with them on that.
 Tracy Zhao posted on Monday, November 17, 2014 - 2:29 pm

Can you please give the full name of a reference where I can find a detailed description of the WLSMV chi-square used in Mplus 7? Information I will need include the fit function used, how the weight matrix calculated, etc. The more details, the better. I recently conducted a simulation study that compared WLSMV and LISREL DWLS chi-squares and fit indices and found some differences, and now I need information to explain these differences.

Thanks a lot!
 Bengt O. Muthen posted on Monday, November 17, 2014 - 2:40 pm
See the paper on our website under Papers, SEM:

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. Unpublished technical report.

It also gives further references.
 Tracy Zhao posted on Monday, November 17, 2014 - 2:49 pm
Thanks. Just to make sure: so the WLSMV chi-square in Mplus 7, which is developed/improved around 2012, is the same thing as its original form in 1997?

I know that there was some improvement/change for WLSMV chi-square when the Mplus version 6 came out. Now at the very least, unlike version 6, the degrees of freedom in the 7 is not adjusted, but calculated in the "normal" way. Does this mean that the version 7 abandoned the changes made in version 6 and retreat to its original form?

 Bengt O. Muthen posted on Monday, November 17, 2014 - 3:12 pm
You are right - the 1997 paper approach was modified per the Technical Appendix for version 6

"Simple second order chi-square correction"

which you find at


No change has been made after that.
 Tracy Zhao posted on Tuesday, November 18, 2014 - 2:18 pm
Thanks a lot! Allow me to ask another question: you said that no changes has been made to the WLSMV chi-square statistic since Mplus 6. However, in Mplus 7, the degrees of freedom of the WLSMV chi-square statistic is calculated in the traditional way instead of "estimated" like in Mplus 6. Is there a reason for such a change? Is it because you believe that the p values in this way is more accurate? Is there any documentation that explains such a change? Thanks a lot!
 Tihomir Asparouhov posted on Tuesday, November 18, 2014 - 4:27 pm
Table 1 page 5 has simulation study to illustrate the performance.


Also we did not "change" the way we do it, we added an additional computational option which is now the default. You can still get the "estimated DF version" using
Satterthwaite=ON; option.

The reason to prefer Satterthwaite=OFF; version is because it gives the chi-square on a metric that is well established and independent of the data and model and can be used for comparative purposes across data set / estimation methods / non-nested models etc.
 Tracy Zhao posted on Wednesday, November 19, 2014 - 8:07 am
I see... Thank you very much!
 Bengt O. Muthen posted on Wednesday, November 19, 2014 - 9:15 am
We haven't done anything on this since V6. You can see what's done when in our Version History:

 Tracy Zhao posted on Thursday, November 20, 2014 - 8:20 am
Dear Dr. Asparouhov,

Could you please check if I understand everything correctly:

In the paper "Simple second order chi-square correction", you discussed three chi-squares, T1, T2, and T3. T1 and T2 refers to the old WLSM and WLSMV chi-square statistics proposed in the Muthen (1997) paper. The only difference between T1 and T2 is that in the calculation of T2, the degree of freedom D is substituted with D-hat, which is an estimated degree of freedom. The newly proposed T3 was adjusted by not only a scale factor but also a shift parameter so that its degree of freedom is exactly D. Do I understand this part correctly?
 Tracy Zhao posted on Thursday, November 20, 2014 - 8:23 am
(sorry the system wouldn't allow me to post long message, so I had to cut it)
Then here comes my questions: in this paper it is said that the default of the Mplus 6 when WLSMV is requested is T3, unless "Satterthwaite=ON" is requested, then T2 will be generated, right? Then why did I still get estimated df as default when I used Mplus 6 (back then I performed a simulation study, and with the same sample size and same model I got different dfs for different replications)? Shouldn't T3 be naturally associated with the regular df? A more important question concerns now. Now I am using Mplus 7 to do another simulation study. You said that the new default of Mplus 7 is Satterthwaite=OFF. According to Table 1 page 5 in "Simple second order chi-square correction", Satterthwaite=OFF means T2. Then is the new default of Mplus 7 giving T2 instead of T3 now? But that can't be right, because the default gives the regular df instead of the estimated df. I am thus confused.

Could you please clear up my confusion? In Mplus 7, is the default T3 or T2? Thanks so much for your time!
 Linda K. Muthen posted on Thursday, November 20, 2014 - 12:18 pm
Please send the two outputs and your license number to support@statmodel.com.
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