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Graphical Representation of Partially Ranked Data

  • Han, Sang-Tae (Department of Informational Statistics, Hoseo University)
  • Received : 20110800
  • Accepted : 20110800
  • Published : 2011.09.30

Abstract

Partially ranked data refers to the situation in which there are p distinct objects; however each judge specifies only first s (s < p) choices. The group theoretic formulation for partially ranked data analysis was set up by Critchlow (1985). We propose a graphical method for partially ranked data by quantifying objects and judges. In a plot for judges, the interpoint distances can be interpreted as Spearman or Kendall distances between two rankings given by respective judges. Similarly, we also construct a plot for objects with a sensible relationship to the previous plot for judges. This study extends the Han and Huh (1995) quantification method of fully ranked data using Gabriel's (1971) biplot technique for multivariate data matrix.

References

  1. Critchlow, D. E. (1985). Metric methods for analyzing partially ranked data, Lecture Notes in Statistics, 34, Springer, New York.
  2. Diaconis, P. (1988). Group representations in probability and statistics, Lecture Notes-Monograph Series, 11, Institute of Mathematical Statistics. CA: Hayward.
  3. Gabriel, K. R. (1971). The biplot graphics of multivariate matrices with applications to principal component analysis, Biometrika, 58, 453-467. https://doi.org/10.1093/biomet/58.3.453
  4. Han, S. T. and Huh, M. H. (1995). Biplot of ranked data, Journal of the Korean Statistical Society, 24, 439-451.
  5. Lebart, L., Morineau, A. and Warwick, K. (1984). Multivariate Descriptive Statistical Analysis: Correspondence Analysis and Related Techniques for Large Matrices, Wiley, New York.