Paradigm for link function switching in ordinal response models

[bgoodri]

I think my answer would be.

1. Compute quantity of interest for various link functions, using the posterior predictive distribution under counterfactuals when it is not computable directly from the posterior distribution
2. Weight the quantity of interest using stacking weights (M-open) or model weights (M-closed)
3. Report the weighted distribution of the quantity of interest

The idea of using the posterior predictive distribution to compute things like this has come up before

Binomial regression with a log link

The key is to think about relative risks (or whatever is of interest) as an implication of the generative process you are trying to model instead of necessarily being a parameter in that model. In the simple case, you could estimate a Bernoulli or a binomial model with a good link function (not log), obtain the posterior distribution of the probabilities under different scenarios, and then divide to obtain a relative risk ratio. In rstanarm (or brms) it would look like library(rstanarm) post <-…

but it probably has the highest ratio of usefulness to utilization. I guess with an ordinal model you are interested in the ratio of the probability that the outcome is less than or equal to y divided by the probability that the outcome is greater than y?