Clustering ranked preference data using sociodemographic covariates

Abstract

Ranked preference data arise when a set of judges rank, in order of their preference, a set of objects. Such data arise in preferential voting systems and market research surveys. Covariate data associated with the judges are also often recorded. Such covariate data should be used in conjunction with preference data when drawing inferences about judges. To cluster a population of judges, the population is modelled as a collection of homogeneous groups. The Plackett-Luce model for ranked data is employed to model a judge’s ranked preferences within a group. A mixture of Plackett-Luce models is employed to model the population of judges, where each component in the mixture represents a group of judges. Mixture of experts models provide a framework in which covariates are included in mixture models. Covariates are included through the mixing proportions and the component density parameters. A mixture of experts model for ranked preference data is developed by combining a mixture of experts model and a mixture of Plackett-Luce models. Particular attention is given to the manner in which covariates enter the model. The mixing proportions and group specific parameters are potentially dependent on covariates. Model selection procedures are employed to choose optimal models. Model parameters are estimated via the ‘EMM algorithm’, a hybrid of the Expectation-Maximization and the Minorization-Maximization algorithms. Examples are provided through a menu survey and through Irish election data. Results indicate mixture modelling using covariates is insightful when examining a population of judges who express preferences.