Correspondence Analysis

Abstract

Correspondence analysis is a multivariate statistical technique for visualizing and describing the associations between two or more variables. It is particularly applicable to a table of categorical data— for example, counts or percentages—but can also be used to visualize non-negative data on a common ratio scale, such as a table of measurements all in centimeters or all in euros. Its main objective is to represent the rows and columns of a data matrix as points in a spatial representation, called a map or a biplot according to the coordinates chosen. The positions of the points suggest and facilitate interpretations of the data content. The method resembles principal component analysis but distinguishes itself by the way distances are measured between points, adapted to categorical data, and by the differential weighting of rows and columns proportional to their marginal sums in the table. Extensions of correspondence analysis are multiple correspondence analysis (for multivariate categorical data) and canonical correspondence analysis (when an additional set of external explanatory variables is available).