10. Monoplots

  1. John Gower1,
  2. Sugnet Lubbe2 and
  3. Niël le Roux3

Published Online: 3 NOV 2010

DOI: 10.1002/9780470973196.ch10

Understanding Biplots

Understanding Biplots

How to Cite

Gower, J., Lubbe, S. and Roux, N. l. (2011) Monoplots, in Understanding Biplots, John Wiley & Sons, Ltd, Chichester, UK. doi: 10.1002/9780470973196.ch10

Author Information

  1. 1

    The Open University, UK

  2. 2

    University of Cape Town, South Africa

  3. 3

    University of Stellenbosch, South Africa

Publication History

  1. Published Online: 3 NOV 2010
  2. Published Print: 7 JAN 2011

ISBN Information

Print ISBN: 9780470012550

Online ISBN: 9780470973196



  • biplot;
  • monoplots;
  • multidimensional scaling;
  • numerical algorithms;
  • principal coordinates analysis (PCO);
  • Skew-symmetry


In general, multidimensional scaling is concerned with finding an r-dimensional matrix Z whose rows generate Pythagorean distances δii that approximate the observed values dii presented in a symmetric proximity matrix D. Different methods of multidimensional scaling depend on the criterion specified for measuring the discrepancy between observed, D, and fitted distances, Δ, and the numerical algorithms used for optimizing the chosen criterion. This chapter discusses the simplest metric multidimensional scaling method is classical scaling/principal coordinates analysis (PCO). Skew-symmetry is reflected in the angular sense in which the area is measured. The chapter takes the anticlockwise sense to be positive, so that OPiPj = —OPj Pi. The area representation of asymmetry can also be used with genuine biplots. The chapter provides the following R functions for constructing the monoplots: MonoPlot.cov, MonoPlot.cor, MonoPlot.cor2, MonoPlot.coefvar and MonoPlot.skew.

Controlled Vocabulary Terms

biplot; multidimensional scaling