Normal Theory Weighted Least-Squares ...
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 Fred B. Bryant posted on Saturday, September 11, 2010 - 1:56 pm
How do I go about obtaining the normal theory weighted least-squares (NTWLS) chi-square value for a CFA model with continuous indicators, when using maximum-likelihood estimation in Mplus 6?
 Linda K. Muthen posted on Saturday, September 11, 2010 - 2:53 pm
That would be the GLS estimator in Mplus.
 Fred B. Bryant posted on Saturday, September 11, 2010 - 3:44 pm
Thanks for clarifying, Linda! I see it now, on page 533 of the Mplus manual.
 Fred B. Bryant posted on Wednesday, September 15, 2010 - 11:39 am
I'm estimating two versions of a two-factor CFA model with 8 continuous indicators (N = 803)--a baseline model (M1) that frees all non-referent loadings, and a nested model M0) that constrains two non-referent loadings to be equal. For each model, I've compared the ML, MLM, and GLS chi-square 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 chi-square for Mplus versus EQS and LISREL? Thanks in advance for your help with this.
 Linda K. Muthen posted on Thursday, September 16, 2010 - 10:05 am
Please send one Mplus output and the corresponding Lisrel output along with your license number to support@statmodel.com.
 Fred B. Bryant posted on Thursday, September 16, 2010 - 9:52 pm
In my initial post, I was comparing (a) the NTWLS chi-square values that LISREL and EQS report when using ML estimation with (b) the chi-square 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 chi-square value that EQS reports (39.917) is identical or virtaully identical with the the chi-square 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 goodness-of-fit chi-square value. Good to know. Sorry to take your time with this.
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