Correspondence analysis of square asymmetric matrices

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 centring 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 analysed separately. The symmetric and skew symmetric analyses can be performed by using a simple correspondence analysis program if the data are set up in a special block format. The methodology is demonstrated on a social mobility table from the first democratically elected Parliament in Germany, the Frankfurter Nationalversammlung. The table cross-tabulates the jobs of parliamentarians when first entering the labour market and their jobs in May 1848 when the Parliament started its first session.