Dear Monica,

Please read the papers of: Peter Schmidt, Eldad Davidov and Jan Cieciuch. Three of them are here, on RG. They work on invariance issues and with datasets containing many groups.

 Thank you Jonathon. I am not used to use many complicated equations but I will read the paper carefully. In fact, with the whole sample (six countries) I got metric invariance but not variance invariance. If the alignment method help me to fix the invariance problem it will help. 

Best

 Thank you Marina. I will look for the paper in RG. Best