Modelling Ranking Data with Wallenius Distribution

Ranking datasets is useful when statements on the order of observations are more important than the magnitude of their differences and little is known about the underlying distribution of the data. The Wallenius distribution is a generalisation of the Hypergeometric distribution where weights are assigned to balls of different colours. This naturally defines a model for ranking categories which can be used for classification purposes. In this paper, we adopt an approximate Bayesian computational (ABC) approach since, in general, the resulting likelihood is not analytically available. We illustrate the performance of the estimation procedure on simulated datasets. Finally, we use the new model for analysing two datasets about movies ratings and Italian academic statisticians' journals preferences. The latter is a novel dataset collected by the authors.