Modification indices and different ML... PreviousNext
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 Scott C. Roesch posted on Monday, June 25, 2012 - 5:01 pm
Are the modification indices (MI)generated for models that have used MLM estimation (or MLR for that matter) accurate? Since adjustments need to be made when nested model comparisons are made with this estimator, it got me to wondering if the MIs deserve the same consideration, or does MPlus handle this automatically?
 Bengt O. Muthen posted on Monday, June 25, 2012 - 5:38 pm
Yes, the MIs for MLM and MLR correctly take into account the asymptotic covariance matrix for the parameter estimates which is also used for the SEs. You get different MIs with those estimators than you get with ML.
 Dr. Jan Henning-Kahmann posted on Monday, September 21, 2020 - 11:57 pm
Dear Bengt,

referring to this question and your answer, I wonder if it also applies to estimators for categorical data like WLS, especially robust WLS (WLSMV)?
A colleague seemed to remember that Mplus does not give robust MI with a robust estimator, but just gives the standard MI instead, even though the estimator is different. Is he right?

Kind regards,
Jan
 Bengt O. Muthen posted on Tuesday, September 22, 2020 - 10:04 am
No, he is wrong. MI for WLSMV also takes into account the correct asymptotic covariance matrix for the estimates.
 Dr. Jan Henning-Kahmann posted on Wednesday, September 23, 2020 - 2:36 am
Dear Bengt,

thanks for the clarification!

Related to this, I noticed that EPC values (but not MI!) differ clearly depending on the type of parameterization (delta vs. theta). That is, using 'the detection of misspecification’-procedure (Saris, Satorra, & van der Veld, 2009), Delta works fine and (most often) yields enough power to detect misspecifications. With theta, however, power is far too low to detect anything (with "Jrule for Mplus").
So I guess for my purpose - i.e. CFA with categorical data (WLSMV) and correlated residuals (method effects!) - I should prefer the default, which is Delta. Right?

Thanks in advance & kind regards,
Jan
 Bengt O. Muthen posted on Wednesday, September 23, 2020 - 5:44 pm
The Delta parameterization is not infrequently more advantageous.
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