Correspondence analysis of two transition tables

Abstract

The case of two transition tables is considered, that is two square asymmetric matrices of frequencies where the rows and columns of the matrices are the same objects observed at three different time points. Different ways of visualizing the tables, either separately or jointly, are examined. We generalize an existing idea where a square matrix is descomposed into symmetric and skew-symmetric parts to two matrices, leading to a decomposition into four components: (1) average symmetric, (2) average skew-symmetric, (3) symmetric difference from average, and (4) skew-symmetric difference from average. The method is illustrated with an artificial example and an example using real data from a study of changing values over three generations.Correspondence analysis, matrix decomposition, skew-symmetry, transition matrices