GRAPHICAL METHODS FOR RANKING DATA

ALVO M., ERTAS K.

CANADIAN JOURNAL OF STATISTICS-REVUE CANADIENNE DE STATISTIQUE, cilt.20, sa.4, ss.469-482, 1992 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 20 Sayı: 4
  • Basım Tarihi: 1992
  • Doi Numarası: 10.2307/3315616
  • Dergi Adı: CANADIAN JOURNAL OF STATISTICS-REVUE CANADIENNE DE STATISTIQUE
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.469-482
  • Anahtar Kelimeler: RANKING DATA, DIVERSITY, GENERALIZED SINGULAR-VALUE DECOMPOSITION, MATRIX APPROXIMATION, INERTIA, GRAPHICAL DISPLAY, AVERAGE KENDALL-TAU, CONCORDANCE, DIVERSITY, MATRICES
  • Dokuz Eylül Üniversitesi Adresli: Evet

Özet

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.