Maxim K posted on Tuesday, November 29, 2011 - 8:42 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.
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.