Decision tree modeling for ranking data

Ranking/preference data arises from many applications in marketing, psychology, and politics. We establish a new decision tree model for the analysis of ranking data by adopting the concept of classification and regression tree. The existing splitting criteria are modified in a way that allows them to precisely measure the impurity of a set of ranking data. Two types of impurity measures for ranking data are introduced, namelyg-wise and top-k measures. Theoretical results show that the new measures exhibit properties of impurity functions. In model assessment, the area under the ROC curve (AUC) is applied to evaluate the tree performance. Experiments are carried out to investigate the predictive performance of the tree model for complete and partially ranked data and promising results are obtained. Finally, a real-world application of the proposed methodology to analyze a set of political rankings data is presented.