A1321
Title: Aitchison geometric characterization of quasi-symmetry in square contingency tables
Authors: Keita Nakamura - Tokyo University of Science (Japan) [presenting]
Tomoyuki Nakagawa - Meisei University (Japan)
Kouji Tahata - Tokyo University of Science (Japan)
Abstract: Quasi-symmetry provides a flexible alternative to complete symmetry in the analysis of square contingency tables. Within Aitchison geometry, tables are treated as compositions and analyzed through the centered log-ratio transform, which endows the simplex with a Euclidean structure suitable for distances, norms, and projections. A table is quasi-symmetric when its interaction component coincides with its transpose, and the set of quasi-symmetric tables forms a linear subspace. An explicit orthogonal projection maps any table to its nearest quasi-symmetric approximation by averaging the interaction component with its transpose while preserving the row and column geometric marginals. Departures from quasi-symmetry are summarized by the simplicial quasi-skewness, defined as the squared Aitchison norm of the skew-symmetric interaction table that is orthogonal to the quasi-symmetric subspace. The quasi-skewness array highlights the signed cell-wise contributions as relative proportions of the total quasi-skewness, thereby quantifying the relative importance of each departure. An application to real data will be presented to illustrate the practical use of the proposed approach.
