Decomposition of symmetry using two-ratios-parameter symmetry model and orthogonality for square contingency tables

摘要: Tomizawa [19] proposed the two-ratios-parameter symmetry (TRPS) model which is an extension of the symmetry (S) model. The TRPS model includes the conditional symmetry (CS) model and the linear diagonals-parameter symmetry (LDPS) model in special cases. Caussinus [7] showed that the S model holds if and only if both the quasi-symmetry and marginal homogeneity models hold. Read [14] pointed out that the S model holds if and only if both the CS and global symmetry models hold. Yamamoto et al.[20] showed that the S model holds if and only if both the LDPS and marginal means equality models hold. This paper gives the decompositions of the S model into two or three models using the TRPS model, and considers an orthogonal decomposition such that the goodness-of-fit test statistic for the S model is asymptotically equivalent to the sum of those for the TRPS model and the other model. An example is given.