A unifying perspective to model preference and evaluation data

All models are wrong, but some are useful'': this statement made by G.E.P. Box is a general benchmark that should be supposed in testing different models. Thus, it should be assumed to drive the model specification step. More specifically, the motivation comes from the idea of disclosing the advantageous traits of different modelling strategies for ordinal variables arising in survey analysis of preference and evaluation data. The aim is to compare two paradigms generated by different perspectives: the consolidated and multifold class of cumulative models and the flexible and parsimonious approach afforded by CUB mixture distributions, whose core is to account for uncertainty and heterogeneity. A simulation study and empirical evidence are discussed in order to check for behaviours, strengths, shortcomings and performances of the competing modelling techniques. In conclusion, a unifying proposal is advanced.