Scaled double symmetry model and decomposition of double symmetry for square tables

For square contingency tables with ordered categories, Tahata and Tomizawa (2010) considered the double linear diagonals-parameter symmetry (DLDPS) model. The present paper proposes the generalized DLDPS model, which implies the structure of both asymmetry with represent to the main diagonal and with respect to the reverse diagonal in the table. Also, the double symmetry (DS) model is separated into the generalized DLDPS model and the moment equality model. Also it is shown that the test statistic for the DS model is asymptotically equivalent to the sum of those for separated models. An example is given.