0
$\begingroup$

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?

$\endgroup$
8
  • $\begingroup$ Can you tell us about your real problem? What does the rankings represent? What is your ultimate goal? This is very little for us to build on! $\endgroup$ Jul 10, 2023 at 5:32
  • $\begingroup$ Sure! The rankings represent the outcome of an athletic competition. The competition is between individuals (not teams) and has a fairly loose structure. So I have final rankings for lots of different iterations, sometimes with a few tens of participants and others with thousands. I want to estimate the influence of things like height and age on success (final ranking). Maybe a beta-binomial likelihood? $\endgroup$
    – qsfzy
    Jul 10, 2023 at 15:57
  • $\begingroup$ 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. $\endgroup$
    – qsfzy
    Jul 10, 2023 at 17:28
  • $\begingroup$ Some similar questions: stats.stackexchange.com/questions/8691/…, $\endgroup$ Jul 10, 2023 at 17:31
  • 2
    $\begingroup$ I think it may be best to predict ranking percentile. Rank itself will be hard to predict as that depends not only on the individual's characteristics, but also how many other people there are. A person might be ranked #1 in a competition among 100 people, and #100 in a competition among 10,000, but either way they're in the top 1%. $\endgroup$ Jul 11, 2023 at 14:28

0

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.