  The analysis of rank ordered data has a long history in the statistical
literature across a diverse range of applications. In this paper we consider
the Extended Plackett-Luce model that induces a flexible (discrete)
distribution over permutations. The parameter space of this distribution is a
combination of potentially high-dimensional discrete and continuous components
and this presents challenges for parameter interpretability and also posterior
computation. Particular emphasis is placed on the interpretation of the
parameters in terms of observable quantities and we propose a general framework
for preserving the mode of the prior predictive distribution. Posterior
sampling is achieved using an effective simulation based approach that does not
require imposing restrictions on the parameter space. Working in the Bayesian
framework permits a natural representation of the posterior predictive
distribution and we draw on this distribution to address the rank aggregation
problem and also to identify potential lack of model fit. The flexibility of
the Extended Plackett-Luce model along with the effectiveness of the proposed
sampling scheme are demonstrated using several simulation studies and real data
examples.
