For the analysis of square contingency tables, we propose the Kullback–Leibler information type measure to represent the degree of departure from the quasi-symmetry (QS) model. We introduce the global quasi-symmetry (GQS) model, and show that the QS model holds if and only if both the GQS and extended quasi-symmetry (EQS) models hold. Furthermore, we propose a measure of departure from each of the GQS and the EQS models, and show that the value of measure of QS is equal to the sum of the value of measure of GQS and that of EQS.
"Partitioning measure of quasi-symmetry for square contingency tables." Braz. J. Probab. Stat. 28 (3) 353 - 366, August 2014. https://doi.org/10.1214/12-BJPS211