Cumulative and CUB Models for Rating Data: A Comparative Analysis

Ordinal measurements as ratings, preference and evaluation data are very common in applied disciplines, and their analysis requires a proper modelling approach for interpretation, classification and prediction of response patterns. This work proposes a comparative discussion between two statistical frameworks that serve these goals: the established class of cumulative models and a class of mixtures of discrete random variables, denoted as CUB models, whose peculiar feature is the specification of an uncertainty component to deal with indecision and heterogeneity. After surveying their definition and main features, we compare the performances of the selected paradigms by means of simulation experiments and selected case studies. The paper is tailored to enrich the understanding of the two approaches by running an extensive and comparative analysis of results, relative advantages and limitations, also at graphical level. In conclusion, a summarising review of the key issues of the alternative strategies and some final remarks are given, aimed to support a unifying setting.