Defining subjects distance in hierarchical cluster analysis by copula approach

• Published in: Quality & quantity Vol. 51; no. 2; pp. 859 - 872
• Main Authors: Bonanomi, Andrea, Nai Ruscone, Marta, Osmetti, Silvia Angela
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.03.2017; Springer; Springer Nature B.V
• Subjects: Agreements; Algorithms; Classification; Cluster analysis; Clustering; Consumers; Data analysis; Methodology of the Social Sciences; Preferences; Random variables; Ratings & rankings; Social Sciences; Studies; New York; United States > US; Italy; Copula function; Hierarchical cluster analysis; Ordinal data
• ISSN: 0033-5177; 1573-7845
• DOI: 10.1007/s11135-016-0444-9

We propose a new measure to evaluate the distance between subjects expressing their preferences by rankings in order to segment them by hierarchical cluster analysis. The proposed index builds upon the Spearman’s grade correlation coefficient on a transformation, operated by the copula function, of the position/rank denoting the level of the importance assigned by subjects under classification to k objects. In particular, by using the copula functions with tail dependence we obtain an index suitable for emphasizing the agreement on top ranks, when the top ranks are considered more important than the lower ones. We evaluate the performance of our proposal by an example on simulated data, showing that the resulting groups contain subjects whose preferences are more similar on the most important ranks. A further application with real data confirms the pertinence and the importance of our proposal.