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From available documentation, I see that Mplus defines the SatorraBentler (SB) scaled chisquare for a given model as the maximumlikelihood (ML) chisquare value for that model divided by the scaling correction factor (c). When specifying MLM (the SB scaled chisquare) as the estimator, Mplus automatically includes the value of c in the output under the section labeled “Tests of Model Fit.” However, when I multiply the MLM (SB) chisquare value for a particular model times c for that model, the result is not exactly equal to the ML chisquare value for the model. For example, using Mplus 6, I have a CFA model for which MLM = 36.214, c = 1.188, and ML = 43.072. For this model, (MLM)(c) = (36.214)(1.188) = 43.022 which is smaller than the ML value reported for the model in the output by 0.055. Also, dividing ML by c: 43.072 / 1.188 = 36.256, which is larger than the MLM value reported for the model in the output by 0.042. Can you explain the source of these apparent discrepancies? Are they due to rounding error? Related to this question, is there any way to obtain more than three decimals in the values reported in the Mplus output? 


The differences are due to using less decimals than Mplus uses. You can use the RESULTS option to save the results with more decimals. I don't see that the differences are large enough to worry about. 


Thanks for clarifying, Linda. It's great to have the option of using more decimals, if the scaled chisquare value happens to fall just barely below the critical value at p = .05. I appreciate your help with this. 


Using the RESULTS option with the SAVEDATA command provides up to 8 decimals for each estimated model parameter. But it does not display more decimals for the model's goodnessoffit chisquare value. Is there a way to obtain more than 3 decimals for the latter? 


All fit statistics are saved in the same way as the parameter estimates. If you can't find them in the file, please send the saved results file, your output, and your license number to support@statmodel.com. 


In carefully matching each element in the RESULTS output to the estimates in the initial output, I now see that the former contains everything that Mplus estimated, including the model's goodnessoffit chisquare. The goodnessoffit statistics are at the very end of the RESULTS output. This is excellent, and is just what I need. Thanks for clarifying this for me, Linda. What a great resource this forum provides in conducting SEM with this powerful and versatile program! 


If you look at the end of the output, it lists what is saved and the order in which it is saved. 


Yes, at the end of the analysis output file I see the ordered listing of each specific estimate that's stored in the RESULTS output. WOW  Mplus is a very welldesigned program indeed! Very impressive! Thanks for your helpful feedback, Linda. 

Steve posted on Sunday, September 22, 2013  9:25 am



Hello, I am doing SEM model comparisons and using MLR. In the case of Chisquare difference testing I am using SatorraBentler scaled chisquare difference test as provided on your website. However, for nonnested situations I am comparing fit indices (CFI, RMSEA, SRMR)  and also Chisquare to degrees of freedom ratio which I have been advised to include by reviewers. However, while I have seen this done in the literature, I just wanted to check with you to see if Chisquare/df ratio can still be done with MLR by simply using the chisquare value provided in the MLR output? Or  if some kind of scaling correction method (like in difference testing) needs to be employed to produce an accurate Chisquare/df ratio? Thank you very much for your help. 


We do not recommend using a chisquare to degrees of freedom approach. Instead use RMSEA. 


Hello, I am comparing a twofactor secondorder CFA solution (with five 1st order factors) to the measurement model with only the five 1st order factors  using the WLSMV estimator. The difftest suggests a significant difference (23.708, df=4, p<.0001), but I am a little concerned that the measurement model has a higher chisquare (SB chisq(142)=724.926, p<0.001) than the model with the secondorder factors (SB chisq(146)= 686.125, p<.0001). This seems counterintuitive that the more constrained model appears to fit better, is it something to be concerned about? Many thanks. 


Chisquare with WLSMV In Mplus does not preserve the ordering of the least restrictive model getting the lowest chisquare. So this type of comparison should not be done. This is why the DIFFTEST option was developed to obtain a correct chisquare difference test using the derivatives from the two models not the chisquare values. 

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