I am working with mixture models. I fitted more than one model to the data and then try to select the most appropriate model using different selection criteria, for example, AIC. My supervisors asked me to use different comparison criteria such as Vuong test. Vuong test is a likelihood ratio test for non-nested models. I have read several papers about mixture models, and almost all of them used selection information criteria as comparison criteria. I did not find any paper that used Vuong test in a mixture context. Is that mean I cannot use Vuong test for mixture models?
Any help, please?