My goal is to test the equivalence of the model between countries. The model is relatively complex. It consists of 35 items, some of which are continuous and some ordinal, divided into 7 dimensions.

I would like to ask, what method would you recommend (e.g. MGCFA, IRT, ESEM, Alignment, LCFA, BSEM)? I would like to test more methods and compare the results. However, each method is suitable for either continuous (e.g. MGCFA) or ordinal (e.g. IRT), and I do not know if it is possible to apply them when I have both types of variables.

Alternatively, whether the solution would be to transform the response scales to be uniform?

Thank you very much for your answers.

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