Detection of threshold differences
Message/Author
 Thomas Klausch posted on Thursday, March 15, 2012 - 11:50 am
Dear support group,

I am trying to understand how invariance testing with ordinal MG-CFA models works in Mplus. I have simulated data for three groups in R. The CFA model consists of one factor with 4 indicators in all groups. The threshold structures vary strongly across groups.

If I fit a model separately in each group (by selecting cases with USEOBSERVATIONS ARE), the different threshold structures are correctly estimated after standardization (STDXY).

If I fit a multi-group model with Mplus using the default equivalent thresholds, it has, however, excellent fit (RMSEA close to zero, CFI=1). There is no indication of the apparent measurement bias.

Instead Mplus gives estimates that are close to the thresholds of the first group, but far from those of groups 2 and 3.

I do not understand why. Could you speculate on a potential reason for my finding?

Thanks, Thomas
 Thomas Klausch posted on Thursday, March 15, 2012 - 2:40 pm
I should add that the groups are about equal in size. The thresholds are -1.5, -1, 0, 1 for all indicators. They are shifted by +1 and +1.5 to the right for groups 2 and 3.
 Bengt O. Muthen posted on Friday, March 16, 2012 - 8:36 am
The way you are varying your thresholds across the groups makes for a perfect fit to group-invariant thresholds with group-varying factor means - the Mplus default. In your Mplus analysis, the reference group which has zero factor mean is the group that recovers your first group's thresholds. You are shifting all thresholds by the same amount in a group which means that the shift is absorbed in the non-zero factor mean. If instead, you shift your thresholds by different amounts, you won't get perfect fit.
 Thomas Klausch posted on Sunday, March 18, 2012 - 5:42 am
Thanks a lot for your response. Since the mean was not shifted for these groups, I suppose that an equivalent test would hence be constraining all means to be equal (or to zero). Alternatively I will vary the thresholds.
 Bengt O. Muthen posted on Sunday, March 18, 2012 - 9:39 am
That's right.
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