A Recursive Partitioning Method for the Prediction of Preference Rankings Based Upon Kemeny Distances

• Published in: Psychometrika 2016-09, Vol.81 (3), p.774-794
• Main Authors: D’Ambrosio, Antonio, Heiser, Willem J.
• Format: Article
• Language: English
• Subjects: Assessment; Behavioral Science and Psychology; Busing; Clustering; Consensus; Consumer Behavior; Data Analysis; Generalized linear models; Humanities; Humans; Law; Maximum Likelihood Statistics; Methods; Models, Statistical; Monte Carlo Method; Monte Carlo Methods; Multidimensional Scaling; Preferences; Principal components analysis; Principals; Psychology; Psychometrics; Ratings & rankings; Regression (Statistics); Statistical Theory and Methods; Statistics for Social Sciences; Testing and Evaluation
• ISSN: 0033-3123; 1860-0980
• DOI: 10.1007/s11336-016-9505-1

Preference rankings usually depend on the characteristics of both the individuals judging a set of objects and the objects being judged. This topic has been handled in the literature with log-linear representations of the generalized Bradley-Terry model and, recently, with distance-based tree models for rankings. A limitation of these approaches is that they only work with full rankings or with a pre-specified pattern governing the presence of ties, and/or they are based on quite strict distributional assumptions. To overcome these limitations, we propose a new prediction tree method for ranking data that is totally distribution-free. It combines Kemeny’s axiomatic approach to define a unique distance between rankings with the CART approach to find a stable prediction tree. Furthermore, our method is not limited by any particular design of the pattern of ties. The method is evaluated in an extensive full-factorial Monte Carlo study with a new simulation design.