Asymmetrical “relational association coefficients” are described. Measurements of these coefficients are expressed as inertia in the individual–space with a “relational inner product”. This geometrical and mechanical point of view on associations analysis, leads to a synthesis, an extension, of classical data analysis methods, based on the research of principal axes of a configuration of points, and to new methods. We propose a factor analysis fitted to a family of asymmetrical association coefficients between two qualitative variables, including the Goodman–Kruskal tau and its weighted or equally weighted extensions. This analysis improves results proposed by D’Ambra and Lauro, and gives a wide scope of applications. Besides, it is interesting to note that Correspondence Factor Analysis is obtained by applying the proposed analysis to the symmetrical Pearson’s mean square contingency association coefficient. One example on simulated data is described.
