摘要：Yamamoto, Iwashita, and Tomizawa (2007) gave the decompositions
of the symmetry (S) model into the extended S and two or three marginal
equimoment models for multi-way tables with ordered categories. However
the goodness-of-fit test statistic for the S model is not asymptotically equivalent
to the sum of those for the decomposed three or four models. This
paper gives, for multi-way tables, the modification of their decompositions
such that the test statistic for the S model is asymptotically equivalent to the
sum of those for the extended S model and one modified marginal equimoment
model, which is the constraints combined the marginal means equality
and variances equality or combined the marginal means equality, variances
equality and correlations equality. Examples are given.
关键词：Likelihood Ratio Statistic, Linear Diagonals-Parameter Symmetry,
Ordinal Quasi-Symmetry, Separability, Square Contingency Table.
