I have clustered data, with about 250 participants clustered within 6 teams. I'm interested in comparing a series of CFA models while also controlling for the clustered nature of my data.
I understand that, with only 6 clusters, TYPE IS COMPLEX is not recommended. However, when I use a "fixed-effects" approach, i.e., by creating 5 dummy variables and adding them to my model as covariates, the CFIs and TLIs are much worse compared to the original (i.e., ignoring clustering) CFIs and TLIs. The RMSEAs remain similar, however.
Why are the CFIs/TLIs so different across the models with/without the dummy variables? Which approach should I favour?
I assume that your 5 dummy vbles influence only the factors of your CFA, which means that you specify full scalar measurement invariance across the 6 teams. That could be the cause of the misfit. When you ignore the grouping you are not addressing that issue. Do an invariance analysis using a 6-group analysis (I assume the 6 samples are independent): configural, metric, scalar. This can be done in one run using those Model= settings.