Modelling preference data with the Wallenius distribution

The Wallenius distr ibution is a generalization of the hypergeometric distributionwhere weights are assigned to balls of different colours.This naturally defines a model for rankingcategor ies which can be used for classification. Since, in general, the resulting likelihood is notanalytically available, we adopt an approximate Bayesian computational approach for estimatingthe importance of the categories. We illustrate the performance of the estimation procedure onsimulated data sets. Finally, we use the new model for analysing two data sets concerningmovie ratings and Italian academic statisticians’ journal preferences. The latter is a novel dataset collected by the authors.