Migration is considered to be one of the important strategies for the progress and development of rural poor. People migrate from one place to another for the development of their overall living standard and to enhance their social position. Social survey technique and Focused Group Discussion (FGD).
(PDF) Internal Migration and Socio-Economic Status of Migrants: A Study in Sylhet City, Bangladesh (researchgate.net)
Sibsankar Mal Why are you asking about models? Would it not be preferable to collect data that can be analysed using inferential statistics? socio-economic stats are probably ordinal data while migration types might be interval or ordinal depending on what variable is under investigation. This would make life easier for you. but it depends on the type of research that you are conducting. If it would help you please provide more information.
Sibsankar Mal, from the perspective of qualitative migration studies, and following the New Mobilities Paradigm, I think an aspiration-capabilities approach would be recommendable (Carling & Schewel 2017; de Haas 2021). This may help to understand both structures and agency of migrants and their decision to stay or to keep on moving. I hope, it was of some help.