Multigroup CFA using modification ind... PreviousNext
Mplus Discussion > Confirmatory Factor Analysis >
 Dan Costa posted on Sunday, June 02, 2013 - 3:56 pm
I'm attempting to conduct multigroup CFA using Yoon and Millsap's (2007) baseline model with the factor variance of one group fixed to 1 and all loadings fixed to equality, then using modification indices to systematically free non-invariant parameters. I feel like I'm missing something obvious, but I'm not sure which are the appropriate modification indices to examine.

For example, one MI is for PF ON Q2, where Q2 is a manifest indicator of the latent PF. But there is also a Q2 ON Q2 and a Q2 with PF. Any advice on which MIs are the appropriate ones for this purpose would be appreciated.
 Bengt O. Muthen posted on Monday, June 03, 2013 - 8:57 am
You should focus on the "y ON f" MIs, where y is a factor indicator and f is the factor.

Note also that in Mplus version 7.1, you can automatically specify the metric model by saying:


in the Analysis command.

Note also that you really want to strive for Scalar invariance, also holding the measurement intercepts equal. In that regard, you may want to take a look at our website showing the new version 7.1 analyses at
 Bengt O. Muthen posted on Monday, June 03, 2013 - 9:08 am
I meant to say that you should focus on the "f BY y" statements.
 Dan Costa posted on Thursday, June 06, 2013 - 12:28 am
Thank you Bengt. I have in fact assessed scalar invariance (using 6.1) and have encountered an unexpected result. I compared a model with all means fixed to 0 to the default with means fixed to 0 in one group only. The model fit for the less constrained model is actually worse than that for the constrained model, according to all of the fit indices (and significantly so using DIFFTEST).

Is there a ready explanation for this type of result? (I have run several multi-group CFAs on other pairs of groups from the same data set and there is only instance of the less constrained model having worse fit).
 Linda K. Muthen posted on Thursday, June 06, 2013 - 10:55 am
Please send the two outputs where you use DIFFTEST and see unexpected results. Note that the WLSMV chi-square values cannot be compared except using DIFFTEST.
 Masa Vidmar posted on Friday, October 02, 2015 - 5:32 am
I used Mplus to run multigroup CFA. I know that group differences on items or latent variables do not necessarily reflect measurement non-invariance, but I don't have the reference for this. Is any of articles written by your group about this?

Is there also a reference about using modification indices to the original model and how does this effect the validity of the original model?

 Bengt O. Muthen posted on Friday, October 02, 2015 - 6:44 am
Group differences may also be due to mean differences in the latent variables. There are many books on measurement invariance; one interesting one is by Millsap, although more technical. You should ask on SEMNET where you also get opinions on modindices.
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