Journal of Statistics: Advances in Theory and ApplicationsAuthor's: Kouji Tahata and Sadao Tomizawa
Pages: [19] - [33]
Received Date: March 9, 2009
Submitted by:
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.
decomposition, likelihood ratio statistic, linear diagonals-parameter symmetry, orthogonality, separability, square contingency table, symmetry.
