GRAPHICAL METHODS FOR RANKING DATA


ALVO M., ERTAS K.

CANADIAN JOURNAL OF STATISTICS-REVUE CANADIENNE DE STATISTIQUE, vol.20, no.4, pp.469-482, 1992 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 20 Issue: 4
  • Publication Date: 1992
  • Doi Number: 10.2307/3315616
  • Journal Name: CANADIAN JOURNAL OF STATISTICS-REVUE CANADIENNE DE STATISTIQUE
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.469-482
  • Keywords: RANKING DATA, DIVERSITY, GENERALIZED SINGULAR-VALUE DECOMPOSITION, MATRIX APPROXIMATION, INERTIA, GRAPHICAL DISPLAY, AVERAGE KENDALL-TAU, CONCORDANCE, DIVERSITY, MATRICES
  • Dokuz Eylül University Affiliated: Yes

Abstract

Graphical methods are presented for the analysis of ranking data collected from g groups of rankers. The data provided by a single individual consist of the ranks of r objects. The sample space is the space of all permutations and has cardinality r! In order to reduce the dimensionality of the data and to study the interrelationships among rankers and items, a two-stage approach is proposed. First, transformations motivated by various metrics on permutations are defined. In particular, the Kendall metric gives rise to pairwise comparisons. Then, the transformed data are analyzed using results in connection with the generalized singular-value decomposition of a matrix. The methods are illustrated on two examples.