Ranked preference data arise when a set of judges rank, in order of their preference, some or all of a set of objects. Such data arise in a wide range of contexts: in preferential voting systems, in market research surveys and in university application procedures.

Modelling preference data in an appropriate manner is imperative when examining the behaviour of the set of judges who gave rise to the data. Additionally, it is often the case that covariate data associated with the set of judges is recorded when a survey of their preferences is taken. Such covariate data should be used in conjunction with preference data when drawing inferences about a set
of judges.

In order to cluster a population of judges, the population is
modelled as a collection of homogeneous groups of judges. The Plackett-Luce (exploded logit) model for rank data is employed to model a judge's ranked preferences within a group. Thus, a mixture of Plackett-Luce models is employed as an appropriate statistical model for the population of judges, where each component in the mixture represents a group of judges with a specific parameterisation of the Plackett-Luce model.

Mixture of experts models provide a framework in which covariates are included in mixture models. In these models, covariates are included through the mixing proportions and through the parameters of component densities using generalized linear model theory.

A mixture of experts model for 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. Both the mixing proportions and the group specific parameters are potentially dependent on the covariates. Model selection procedures are employed to select both the manner in which covariates enter the model and to select the optimal number of groups within the population.

The model parameters are estimated via the EMM algorithm, a hybrid of the EM and MM algorithms. Illustrative examples are provided through the 1996 Menu Census Survey conducted by the Market Research
Corporation of America and through Irish election data where voters rank electoral candidates in order of their preference. Results indicate mixture modelling using covariates is insightful when examining a population of judges who express preferences.