I'm running model in which I analyze salary of recent graduates. People graduated from different majors and in different years. The dependent variable (salary) is measured using intervals, e.g., "less than 1000", "between 1000 - 2000; "between 2000 - 5000", not the actual amount that people make. Because of the fact that data is hierarchical and the DV is ordinal, I use the Cumulative Link Mixed Model (CLMM) in the ordinal package in R.
The important assumption here is the proportional odds assumption. Unfortunately, I didn't find information on how to test this assumption in multilevel models and from my reading, it is not possible to do in the ordinal package.
That's why I have the following questions:
1) Does it make sense to test the proportional odds assumption using cumulative link model (CLM) which does not take into account the hierarchical structure of the data I have?
2a) if this is not a correct approach, what would you recommend to use as an alternative?
2b) if such a testing makes sense (and the assumption is not met), what should be the alternative model? Is it the multinomial logistic regression model(with the random effects specification)? Could you recommend a package to do it for multilevel data?