  Compared to the nominal scale, the ordinal scale for a categorical outcome
variable has the property of making a monotonicity assumption for the covariate
effects meaningful. This assumption is encoded in the commonly used
proportional odds model, but there it is combined with other parametric
assumptions such as linearity and additivity. Herein, the considered models are
non-parametric and the only condition imposed is that the effects of the
covariates on the outcome categories are stochastically monotone according to
the ordinal scale. We are not aware of the existence of other comparable
multivariable models that would be suitable for inference purposes. We
generalize our previously proposed Bayesian monotonic multivariable regression
model to ordinal outcomes, and propose an estimation procedure based on
reversible jump Markov chain Monte Carlo. The model is based on a marked point
process construction, which allows it to approximate arbitrary monotonic
regression function shapes, and has a built-in covariate selection property. We
study the performance of the proposed approach through extensive simulation
studies, and demonstrate its practical application in two real data examples.
