An adaptation of correspondence analysis for square tables

Abstract

The application of correspondence analysis to square asymmetric tables is often unsuccessful because of the strong role played by the diagonal entries of the matrix, obscuring the data off the diagonal. A simple modification of the centering of the matrix, coupled with the corresponding change in row and column masses and row and column metrics, allows the table to be decomposed into symmetric and skew--symmetric components, which can then be analyzed separately. The symmetric and skew--symmetric analyses can be performed using a simple correspondence analysis program if the data are set up in a special block format.