DISTANCE‐BASED DECISION TREES FOR RANKING DATA: THE ROLE OF THE WEIGHT SYSTEMS

Abstract

In everyday life ranking and classification are basic cognitive skills that people use in order to grade everything that they experience. Grouping and ordering a set of elements is considered easy and communicative; thus, rankings of sport‐teams, universities, countries and so on are often observed. A particular case of ranking data is represented by preference data, where individuals show their preferences over a set of items. When individuals specific characteristics are available, an important issue concerns the identification of the profiles of respondents (or judges) giving the same/similar rankings. In order to incorporate respondent‐specific covariates distance‐based decision tree models (D'Ambrosio 2007, Lee and Yu 2010, Yu et al. 2010, D’Ambrosio and Heiser, 2016, Plaia and Sciandra, 2017) have been recently proposed. Actually, it can happen that one or some of the k items is more important than others, or, similarly, the top of the ordering can deserve more attention than the bottom. In these situations, changing the rank of very important items or changing the top of the ranking require different “weighting”. In this contribution we want analyze the role of element and positional information (Kumar and Vassilvitskii 2010) when some distance measures for rankings are evaluated. Several weighting structures will be assumed for both positional and item weights, and we aim at identifying some particular behavior in the distance measures used. Analysis will be carried out both by simulation and by application to real dataset, especially in the framework of tree‐based methods for rank data.