Comparing Interpoint Distances in Correspondence Analysis: A Clarification

In a recent JMR article, Carroll, Green and Schaffer (1986) described and illustrated a correspondence analysis scaling that permitted both within-set and between-set squared distance comparisons. This note clarifies the relationship between the proposed scaling and another scaling in which the diagonal matrix of singular values is applied to both X and Y coordinates. Using a data set from Greenacre (1984), conceptual and empirical contrasts among three alternative scalings are examined.