I'm interested in modeling how a ranking depends on a continuous feature. I have many related groups of these rankings, so I want to use partial pooling with the usual Bayesian machinery, but I'm struggling to understand how I should define the model for an outcome variable that represents ranks.
Each set of rankings represents the outcome of an athletic competition. The competitions are between individuals (not teams) and have a fairly loose structure. So I have final rankings for lots of different iterations, sometimes with a few tens of participants and sometimes with thousands. I want to estimate the influence of things like height and age on participants rankings. Maybe a beta-binomial likelihood?
A key issue is that I want to pool parameters between some of these events, so the models for each event can't have different numbers of parameters. It seems like some kind of GLM makes sense, but I haven't worked with ranking data before and don't know much about the options.
Is there a good way to construct something like a GLM for large datasets of rankings like this?
