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How do I go about obtaining the normal theory weighted leastsquares (NTWLS) chisquare value for a CFA model with continuous indicators, when using maximumlikelihood estimation in Mplus 6? 


That would be the GLS estimator in Mplus. 


Thanks for clarifying, Linda! I see it now, on page 533 of the Mplus manual. 


I'm estimating two versions of a twofactor CFA model with 8 continuous indicators (N = 803)a baseline model (M1) that frees all nonreferent loadings, and a nested model M0) that constrains two nonreferent loadings to be equal. For each model, I've compared the ML, MLM, and GLS chisquare values obtained using Mplus 6, EQS 6, and LISREL 8. Comparing results across the 3 software programs for model M1, I find(a) for ML estimation: Mplus = 43.072, EQS = 42.974, LISREL = 42.970; (b) for MLM estimation: Mplus = 36.214, EQS = 36.827, LISREL = 36.053; and (c) for GLS estimation: Mplus = 39.917, EQS = 43.899, LISREL = 43.896. Comparing results across the 3 software programs for model M0, I find(a) for ML estimation: Mplus = 108.584, EQS = 108.443, LISREL = 108.451; (b) for MLM estimation: Mplus = 92.755, EQS = 94.251, LISREL = 91.715; and (c) for GLS estimation: Mplus = 91.405, EQS = 111.455, LISREL = 111.466. Note that for both models, ML and MLM results are reasonably close across the 3 software programs. But, GLS results, in contrast, differ more noticeably for Mplus compared to EQS or LISREL. I wondered if you could help me understand the source of this discrepancy in GLS results. Is this due to a difference in the formula used for computing GLS chisquare for Mplus versus EQS and LISREL? Thanks in advance for your help with this. 


Please send one Mplus output and the corresponding Lisrel output along with your license number to support@statmodel.com. 


In my initial post, I was comparing (a) the NTWLS chisquare values that LISREL and EQS report when using ML estimation with (b) the chisquare that Mplus reports when using GLS estimation. But when I run GLS estimation with LISREL and with EQS, then the minimum fit function LISREL reports (39.913) and the chisquare value that EQS reports (39.917) is identical or virtaully identical with the the chisquare value that Mplus reports when using GLS estimation (39.917). So that explains the apparent difference I thought I had found earlier. When all three programs use GLS estimation, then they find the same goodnessoffit chisquare value. Good to know. Sorry to take your time with this. 

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