Ordinal data are very common in applied disciplines, and modelling such data is a basic issue for interpretation, classification and prediction. In this work, we compare two frameworks that have been introduced for taking the ordinal nature of the available observations into account: the classic cumulative models and an alternative class of models based on a mixture of discrete random variables,
... [Show full abstract] known as cub models. After a brief survey of their features, we compare the main characteristics and performances of both frameworks by means of simulation experiments and real data. A comparative discussion and some final remarks conclude the paper.