Sum-symmetry model and its orthogonal decomposition for square contingency tables with ordered categories

For the analysis of square contingency tables, many kinds of symmetry models have proposed. The present paper proposes a new kind of symmetry model, and gives a decomposition of the new model by introducing an extended model of it. Moreover, it shows the orthogonality of statistic for testing goodness-of-fit of the new model. Two unaided vision data analyses are also shown.