Modelling preference data with the Wallenius distribution

The Wallenius distribution is a generalization 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. Since, in general, the resulting likelihood is not analytically available, we adopt an approximate Bayesian computational approach for estimating the importance of the categories. We illustrate the performance of the estimation procedure on simulated data sets. Finally, we use the new model for analysing two data sets concerning movie ratings and Italian academic statisticians’ journal preferences. The latter is a novel data set collected by the authors.