title: Clustering ranked preference data using sociodemographic covariates
speaker: Brendan Murphy (joint work with Claire Gormley)
abstract:
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 (ex-
ploded 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 com-
bining 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 hy-
brid 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.