Sorry for taking so long to reply. Iâ€™m a bit uncertain myself of suitable priors, but my hope is that @martinmodrak could help, or find the expertise to do it :)

is indeed extremely wide - but hey, as long as you have enough data to constrain it, it should not be a problem. To be safe, I would also consider running the model with a narrower (say normal(0,1)) prior on kappa and see if your inferences change. If not, you are probably good.

Here is a quick code I wrote to visualise bivariate marginal distributions from the prior to let me better understand it (you could work this out analytically, but I write code faster than I do math, so I chose simulation :-)

This model is part of a more complicated model, which involves a multivariate ordered probit, and iâ€™m using a hierarchical induced-dirichlet model on the latent cutpoints. For prior predictive checks for this part of the model, I have been plotting the posteriors for the cumulative probabilities. I have incorporated domain expertise into other aspects on the model, and I donâ€™t want to for this part of the model which uses ordered regression (as there isnt much available). In this case would I want the priors for the cumulative probabilities to be approximately uniform? Or, should I not look at the cumulative probabilities for prior predictive checks? I guess just because these are uniform it doesnâ€™t mean it is less informative, since the priors might be â€śforcingâ€ť them to be more uniformâ€¦

I actually get better mixing and less divergent transitions (none) with normal(0, 5) vs normal(0,1) on kappa. I guess N(0, 1) is conflicting with the likelihood too much as the posterior median for kappa is 4.81 with this prior.