Some New Log-Bilinear Models for the Analysis of Asymmetry in a Square Contingency Table

The authors propose some new log-bilinear models for the analysis of asymmetry in square contingency tables. In these models the logarithm of the expected frequency is split up into two parts: (a) a symmetric or a quasi-symmetric part, and (b) a skew-symmetric part. The skew-symmetric part is decomposed using the so-called Gower decomposition of skew-symmetric matrices. It is shown how graphical representations of this decomposition can simplify the interpretation.