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A Note on the Graphical Representation of Multivariate Binary Data

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  • C. F. Banfield
  • J. C. Gower

Abstract

Various ordination methods for mapping n units characterized by v binary variables are in common use in which the distance between points Pi and Pj, representing units i and j, approximates some function (a similarity coefficient) of (aij, bij, cij, dij), the usual cell‐counts in a 2 × 2 table. Ordination generally requires (n – 1) dimensions to represent the distances exactly, but the quantities bij‐cij can always be represented in one dimension. This leads to a simple graphical extension of ordination that helps with interpretation, reveals discrepancies, screens clustering possibilities and permits the recovery of approximations to all the (a, b, c, d)‐values. Two examples illustrate the technique.

Suggested Citation

  • C. F. Banfield & J. C. Gower, 1980. "A Note on the Graphical Representation of Multivariate Binary Data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 29(3), pages 238-245, November.
    • Handle: RePEc:bla:jorssc:v:29:y:1980:i:3:p:238-245
    DOI: 10.2307/2346897
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    Cited by:

    1. John C. Gower, 2018. "Skew symmetry in retrospect," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 12(1), pages 33-41, March.
    2. Gower, John C., 2000. "Rank-one and rank-two departures from symmetry," Computational Statistics & Data Analysis, Elsevier, vol. 33(2), pages 177-188, April.
    3. Erhard Godehardt & Cajor Braak & Maurice Roux & R. Blashfield & Pascale Rousseau & Peter Bryant & Richard Hathaway, 1991. "Book reviews," Journal of Classification, Springer;The Classification Society, vol. 8(2), pages 269-286, December.

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