Hi Matteo,

it's not completely clear to me what you mean by conditioned on, but I think what you are eluding to is an ordinal response, where 0,1,2 are monotonic (have some directionality to them) and where the intervals between the positions cannot be easily defined.

The best tutorial/guidance I'm aware of for fitting such models is here:

Burkner & Vuorre (2018) Ordinal Regression Models in Psychology: A Tutorial

https://psyarxiv.com/x8swp/

More specifically I think you want to fit a 'sequential model' for ordinal data: "where the response can be understood as being the result of a sequential process, such that a higher response category is possible only after all lower categories are achieved". It might come under different names but this should get you looking in the right place.

Hope that's a useful place to continue your search, and if you need some help with coding such a model and checking its assumptions in brms then there is a nice dedicated forum (https://discourse.mc-stan.org/c/interfaces/brms/36 ).

Some other options for fitting ordinal models which should cover your case is provided from page 66 of the following pdf: http://users.stat.ufl.edu/~aa/ordinal/agresti_ordinal_tutorial.pdf

cheers,

Jack

The multinomial logit model assumes that one choice is independent of others ( independence of irrelevant alternatives IIA).

If this is violated, other alternative models should be applied. Think about Mixed Logistic regression that solves this problem to an extent. This is even better than nested logit models.