Estimating the number of clusters in a ranking data context

Abstract

This study introduces two methods for estimating the number of clusters specially designed to identify the number of groups in a finite population of objects or items ranked by several judges under the assumption that these judges belong to a homogeneous population. The proposed methods are both based on a hierarchical version of the classical Plackett–Luce model in which the number of clusters is set as an additional parameter. These methods do not require continuous score data to be available or restrict the number of clusters to be greater than one or less than the total number of objects, thereby enabling their application in a wide range of scenarios. The results of a large simulation study suggest that the proposed methods outperform well-established methodologies (Calinski & Harabasz, gap, Hartigan, Krzanowski & Lai, jump, and silhouette) as well as some recently proposed approaches (instability, quantization error modeling, slope, and utility). They realize the highest percentages of correct estimates of the number of clusters and the smallest errors compared with these well-established methodologies. We illustrate the proposed methods by analyzing a ranking dataset obtained from Formula One motor racing.