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.

翻译：与名义规模相比,绝对结果变量的正态尺度具有使共变效应具有实际意义的单一性假设特性。这一假设在常用的成比例差模型中编码,但与其他参数假设如线性与相加性相结合。在这里,考虑的模型是非参数性的,唯一的条件是,结果类别共变的效应是按正态尺度的单色单色度。我们不知道存在其他可资比较的可比较的多变模型,适合推断。我们通过广泛的模拟研究来研究拟议方法的绩效,并在两个真实数据实例中展示其实际应用。