8. Multiple Correspondence Analysis

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

Published Online: 3 NOV 2010

DOI: 10.1002/9780470973196.ch8

Understanding Biplots

Understanding Biplots

How to Cite

Gower, J., Lubbe, S. and Roux, N. l. (2011) Multiple Correspondence Analysis, in Understanding Biplots, John Wiley & Sons, Ltd, Chichester, UK. doi: 10.1002/9780470973196.ch8

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



  • Burt matrix;
  • category-level points;
  • chi-squared distances;
  • correspondence analysis (CA);
  • extended matching coefficient (EMC);
  • homogeneity analysis;
  • two-way contingency table


This chapter examines biplots for more than two categorical variables. One way of generalizing correspondence analysis (CA) is to treat the categorical data matrix G as if it were a two-way contingency table. Although the chi-squared distances based on the Burt matrix are functions of those of the correspondence analysis of a contingency table, they differ from the row chi-squared distances used in the analysis of G. Gower and Hand suggested the extended matching coefficient (EMC) which expresses the number of matches for every pair of samples as a ratio of the number p of variables. Category-level points have been used extensively above. The chapter supplies an amplified discussion and an introduction to the concept of prediction regions. In homogeneity analysis the chapter seeks scores z = (z1, z2, . . . , zp ), often termed quantifications, that replace G by Gz.

Controlled Vocabulary Terms

Chi-square test for homogeneity; correspondence analysis; two-way tables