Modelling marginal ranking distributions: the uncertainty tree

In this paper a novel approach is proposed for ranking data analysis that is based on marginal distributions. The marginal scores for one of the items to be ranked can be considered as a proxy of preference ratings and thus they can be employed to investigate drivers of the outcome. The rationale is that a model for the univariate marginal distributions should suitably convey information about the veracity of ordinal scores given that it would disregard the ranking constraints. The method relies on CUBREMOT (CUB REgression MOdel Trees), a tool for growing trees for ordinal resposes based on the local estimation of CUB models, a class of models able to explain both preferences and related uncertainty. Here we propose the Uncertainty Tree to disclose preference patterns on the basis of the model uncertainty component. Two applications on real data are discussed; comparison with other model-based trees is provided and a synthetic index for the selection of the best CUBREMOT is also advanced.