  The statistical modelling of ranking data has a long history and encompasses
various perspectives on how observed rankings arise. One of the most common
models, the Plackett-Luce model, is frequently used to aggregate rankings from
multiple rankers into a single ranking that corresponds to the underlying
quality of the ranked objects. Given that rankers frequently exhibit
heterogeneous preferences, mixture-type models have been developed to group
rankers with more or less homogeneous preferences together to reduce bias.
However, occasionally, these preference groups are known a-priori. Under these
circumstances, current practice consists of fitting Plackett-Luce models
separately for each group. Nevertheless, there might be some commonalities
between different groups of rankers, such that separate estimation implies a
loss of information. We propose an extension of the Plackett-Luce model, the
Sparse Fused Plackett-Luce model, that allows for joint learning of such
heterogeneous rank data, whereby information from different groups is utilised
to achieve better model performance. The observed rankings can be considered a
function of variables pertaining to the ranked objects. As such, we allow for
these types of variables, where information on the coefficients is shared
across groups. Moreover, as not all variables might be relevant for the ranking
of an object, we impose sparsity on the coefficients to improve
interpretability, estimation and prediction of the model. Simulations studies
indicate superior performance of the proposed method compared to existing
approaches. To illustrate the usage and interpretation of the method, an
application on data consisting of consumer preferences regarding various sweet
potato varieties is provided. An R package containing the proposed methodology
can be found on https://CRAN.R-project.org/package=SFPL.
