Distance-based tree models for ranking data

Lee, Paul H. and Yu, Philip L.H. (2010) Distance-based tree models for ranking data. Computational Statistics and Data Analysis, 54 (6), 1672-1682. (doi:10.1016/j.csda.2010.01.027).

Record type: Article

Abstract

Ranking data has applications in different fields of studies, like marketing, psychology and politics. Over the years, many models for ranking data have been developed. Among them, distance-based ranking models, which originate from the classical rank correlations, postulate that the probability of observing a ranking of items depends on the distance between the observed ranking and a modal ranking. The closer to the modal ranking, the higher the ranking probability is. However, such a model basically assumes a homogeneous population and does not incorporate the presence of covariates. To overcome these limitations, we combine the strength of a tree model and the existing distance-based models to build a model that can handle more complexity and improve prediction accuracy. We will introduce a recursive partitioning algorithm for building a tree model with a distance-based ranking model fitted at each leaf. We will also consider new weighted distance measures which allow different weights for different ranks in formulating more flexible distance-based tree models. Finally, we will apply the proposed methodology to analyze a ranking dataset of Inglehart's items collected in the 1999 European Values Studies.

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