Correspondence Analysis

Abstract

Correspondence analysis (CA) is applicable to data in the form of rectangular tables, where the entries are nonnegative measures of association between the row and column entities. The primary example of a table suitable for CA is a cross-tabulation, or contingency table, although the method extends smoothly to the analysis of almost any table of nonnegative numbers measured on the same scale, where the relative values in each row and in each column are of interest. The results of CA are one or more sets of scale values for the rows and columns, values that have a geometric interpretation leading to visualizations of the similarities between rows and between columns, as well as the row–column associations. Important variants of CA are multiple correspondence analysis, applicable to multivariate respondent-level categorical data, and canonical correspondence analysis, where the CA solution is linearly constrained by external explanatory variables.