I am wondering what the following phrase from the Stan User’s Guide section on Ordinal Logistic Regression https://mc-stan.org/docs/2_18/stan-users-guide/ordered-logistic-section.html means.
“The noise term is fixed by the form of regression, with examples for ordered logistic and ordered probit models.”
Does this mean that the noise distribution can be anything?
Sorry, not an expert on this, but since nobody else answered, I will give it a try.
Yes, in principle I think the noise could be anything, you would just replace Phi in the ordered probit example by a different cumulative distribution function. But you generally would want the distribution to be fixed and not depend on any parameters as that could make the model identified.
Also I don’t think having a custom noise distribution is necessarily a sensible idea. Paul Burkner argues in his ordinal regression paper that the choice of specific noise model rarely influences results
Does that make sense? Please double check my reasoning.