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 Nicole Stanoff posted on Monday, February 16, 2009 - 5:10 pm
I'm running various SEM models and comparing the model fit. When comparing the two models, the CFI value will improve, however the RMSEA value gets worse. Which of the two is better to use for improvement in model fit?
 Bengt O. Muthen posted on Monday, February 16, 2009 - 6:24 pm
There is a large SEM literature on this with differing opinions. You want to study this literature. We have many references on our web site. You may also want to consult SEMNET for general questions like this.
 Tammy Tolar posted on Monday, September 14, 2009 - 11:52 am
I have a question about how SRMR is computed.
When modeling growth with different scales of the same measure (i.e., W-scores, raw scores, irt based factor scores), I get relatively small differences in CFI, TLI, and RMSEA, but huge differences in SRMR (see below). The different scales correlate highly with each other (generally greater than .92 at each time point) and produce similar correlation matrices across time points within scale. When I calculate the fit statistics from results (e.g., log likelihoods, model and sample estimated covariances and correlations) reported in MPLUS output using the formulas from the technical appendices, I am able to exactly reproduce all fit statistics except SRMR, but the SRMR’s I am calculating are not hugely different across scales (they show similar differences as the other fits statistics). One question I have is if the diagonal elements of the correlation matrices are the source of the problem. In the SRMR formula, the use of p*(p+1) / 2 in the denominator implies that the variances are being included in the SRMR. However, the residuals of the diagonal elements of the correlation matrix are 0. Is MPLUS doing something special for diagonal elements?

W-Scores Raw Scores
Calculated Mplus Calculated Mplus
CFI 0.969 0.969 0.982 0.982
RMSEA 0.118 0.118 0.092 0.092
SRMR 0.019 0.528 0.012 0.051
 Linda K. Muthen posted on Wednesday, September 16, 2009 - 3:12 pm
Can you send the full output that shows those SRMR values to support@statmodel.com.
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