摘要：For the analysis of square contingency tables with ordered categories,
Agresti (1983) introduced the linear diagonals-parameter symmetry
(LDPS) model. Tomizawa (1991) considered an extended LDPS (ELDPS)
model, which has one more parameter than the LDPS model. These models
are special cases of Caussinus (1965) quasi-symmetry (QS) model. Caussinus
showed that the symmetry (S) model is equivalent to the QS model and
the marginal homogeneity (MH) model holding simultaneously. For square
tables with ordered categories, Agresti (2002, p.430) gave a decomposition
for the S model into the ordinal quasi-symmetry and MH models. This paper
proposes some decompositions which are different from Caussinus¡¯ and
Agresti¡¯s decompositions. It gives (i) two kinds of decomposition theorems
of the S model for two-way tables, (ii) extended models corresponding to the
LDPS and ELDPS, and the generalized model further for multi-way tables,
and (iii) three kinds of decomposition theorems of the S model into their models
and marginal equimoment models for multi-way tables. The proposed
decompositions may be useful if it is reasonable to assume the underlying
multivariate normal distribution.
