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 Maxim K posted on Tuesday, November 29, 2011 - 2:42 am

I have a problem doing measurement invariance testing on a group of 66 individuals in a sample of approximately 300. I have a model which fits the total sample well. Fitting it to the control group (300 minus 66) goes well, but the fit is lost when it is applied to the group of 66.

The model is relatively complex, having 150+ free parameters. My guess is that the bad fit is due to overly small group size.

The question is, what are the implications thereof? Does it mean I should abandon the invariance testing? Chisq difference between the base and strictly invariant model confirms the invariance in the grouped model.
 Linda K. Muthen posted on Tuesday, November 29, 2011 - 11:45 am
The first step is testing measurement invariance is to be sure that the same model fits in each group separately. You cannot do that for the small group given the number of parameters in your model. I don't think it is feasible to test for measurement invariance in your case. With low power you may also not be able to trust your results.
 Manni posted on Saturday, March 11, 2017 - 2:56 am
Dear MPlus team,

I have one factor measured with 4 ordinal indicators across two time-points within three groups. I tested measurement invariance first in each group. In each group partial strict measurement invariance holds (all loadings equal, all threshold equal, 3 of four scales equal). Now I am struggling to form a baseline model within the multigroup setting which can be used to test the added invariance constrains across groups. I thought about this model: fixing the means of t1 at zero in each group, specifying longitudinal invariance within each group, but allowing thresholds/lodings differ between groups. Since the T1 scale factors are fixed at 1 in all groups the model seem identified. In the next step I woul add equality constraints across groups in additiin to free the means in the non reference groups. Is this okay? Many thanks in Advance.
 Bengt O. Muthen posted on Saturday, March 11, 2017 - 8:04 am
Measurement equality across time (but not group) should let the scale factors change over time (fixed at 1 only for T1).
 Manni posted on Saturday, March 11, 2017 - 8:46 am
Many thanks for your quick reply!

Just to make sure I get it right:

For the baseline model: I fix the T1 scale factor to one in each group, allow the T2 scale factor to be freely estimated in each group, specify within group longitudinal invariance but allow loadings/thresholds to differ between groups and fix the T1-means to zero in each group and estimate T2 means freely in each group - correct?

A brief follow up question: When I add equality constraints on thresholds and loadings across groups, i should free the T1 scales in the non-reference group?

Many thanks!
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