Marginal effects for comparing groups in regression models for ordinal outcome when uncertainty is present

This contribution deals with effect measures for covariates in ordinal data models to address the interpretation of the results on the extreme categories of the scales. It provides a simpler interpretation than model parameters both in standard cumulative models with proportional odds assumption and in the recent extension of the CUP models, the mixture models to account for uncertainty in the process of selection of the score. Visualization tools for the effect of covariates are proposed and the measure of relative size and marginal effects based on rates of change are evaluated by use of a case study.