I have a bifactor model with categorical indicators: 4-option Likert-type items. One of my research objectives involves testing measurement invariance between two groups. I have been doing it as follows:

1. A configural model in which all loadings are allowed to vary between groups. Factors' variances are set to 1 in both groups. One threshold per item is constrained to be equal across groups, but the rest of them are freely estimated. (The model does not converge if this constraints are not included).

2. A scalar model in which equality constraints are applied upon all items and factor loadings. (I have read that metric invariance should not be tested alone in nonlinear MG-CFA).

Despite the increasing popularity of bifactor models and categorical CFA, I have not been able to find clear guidelines about how to conduct such an analysis. Am I doing this right? Is there an expert consensus about how to evaluate invariance in categorical bifactor models (e.g. Δχ², ΔCFI, DIFFTEST)?

Any suggestion will be appreciated. I am working with lavaan in R.

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