Non-independence in an ordinal model

I am examining inter- and intra-individual variation (both magnitude and frequency of change) across time for a particular metric. The metric is a ranked ordinal variable in the form of a list of 1-54. Each individual can only occupy one position in each time period but can shift position in the next time period. It’s then not a “standard” ordinal model because there is only one individual in each “category”.

My go to strategy for looking at variation across time is a gamm using an individual-level spline such as something like s(Period, by=ID, bs=“tp”). However, I am not convinced that that is appropriate given that the data are truly non-independent. Individual A is only ranked first because individual B is ranked second etc. Similarly, individual A only descends the hierarchy because someone else ascends. If I was interested in what predicts ranking at a single time point, this would be less of an issue. Another option would be to look at repeatability of position (see Hertel et al., 2020) but that doesn’t quite get at my question and does have similar issues.

My question is then two-fold:

  1. How, if at all, could this be accounted for in a gamm?
  2. Are there any alternative ways to approach this kind of question aside of a repeatability measure?

Many thanks!