Joint Learning from Heterogeneous Rank Data

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.