Avoiding Degeneracies in Ordinal Unfolding Using Kemeny-Equivalent Dissimilarities for Two-Way Two-Mode Preference Rank Data

Multivariate Behavioral Research, vol. 57, pp. 679–699

Abstract

In this paper a simple but effective procedure to avoid degeneracies in ordinal Unfolding for preference rank data based on the Kemeny distance is proposed. Considering Unfolding as a particular MDS procedure with missing within-set proximities, unknown proximities are first estimated using correlations related to the Kemeny distance, and then the complete proximity matrix is analyzed in a standard MDS framework. A simulation study shows that our proposal is able to both recover the order of the preferences and reproduce the position of both rankings and objects in a geometrical space. Several applications on real data sets show that our procedure returns non-degenerate Unfolding solutions.

Authors 3

1. Antonio D’Ambrosio corresponding

   University of Naples Federico II

   Affiliation as printed

   Department of Economics and Statistics, University of Naples Federico II

2. J. Fernando Vera

   Universidad de Granada

   Affiliation as printed

   Department of Statistics and O.R, University of Granada

3. Willem J. Heiser Aachen Faculty of Social and Behavioral Sciences

   Leiden University

   Affiliation as printed

   Faculty of Social and Behavioral Sciences, Leiden University