Discrete Beta and Shifted Beta-Binomial models for rating and ranking data

Ranking and rating methods for preference data result in a different underlying organization of data that can lead to manifold probabilistic approaches to data modelling. As an alternative to existing approaches, two new flexible probability distributions are discussed as a modelling framework: the Discrete Beta and the Shifted Beta-Binomial. Through the presentation of three real-world examples, we demonstrate the practical utility of these distributions. These illustrative cases show how these novel distributions can effectively address real-world challenges, with a particular focus on data derived from surveys concerning environmental issues. Our analysis highlights the new distributions’ capability to capture the inherent structures within preference data, offering valuable insights into the field.