Double symmetry model and its orthogonal decomposition for multi-way tables

K Yamamoto, F Takahashi… - SUT Journal of …, 2012 - projecteuclid.org
For two-way contingency tables, Tomizawa (1985b) gave a theorem that the double
symmetry (DS) model holds if and only if both the quasi DS and the marginal DS models …

The analysis of symmetry and asymmetry: orthogonality of decomposition of symmetry into quasi-symmetry and marginal symmetry for multi-way tables

S Tomizawa, K Tahata - Journal de la Société française de statistique …, 2007 - numdam.org
For the analysis of square contingency tables, Caussinus (1965) proposed the
quasisymmetry model and gave the theorem that the symmetry model holds if and only if …

Orthogonal decomposition of point-symmetry for multiway tables

K Tahata, S Tomizawa - AStA Advances in Statistical Analysis, 2008 - Springer
For multiway contingency tables, Wall and Lienert (Biom. J. 18: 259–264, 1976) considered
the point-symmetry model. For square contingency tables, Tomizawa (Biom. J. 27: 895–905 …

Orthogonal decomposition of point-symmetry model for two-way contingency tables

S Tomizawa - Journal of Statistical Planning and Inference, 1993 - Elsevier
For the analysis of two-way contingency tables, this paper presents a note on a useful
decomposition of the likelihood ratio (LR) statistic for the point-symmetry (PS) model. The PS …

Symmetry and asymmetry models and decompositions of models for contingency tables

K Tahata, S Tomizawa - SUT journal of Mathematics, 2014 - projecteuclid.org
For analyzing square contingency tables, Bowker [14] proposed the symmetry model.
Caussinus [16] proposed the quasi-symmetry model and gave a decomposition of model …

Decompositions for extended double symmetry models in square contingency tables with ordered categories

K Tahata, S Tomizawa - Journal of the Japan Statistical Society, 2006 - jstage.jst.go.jp
For square contingency tables with ordered categories, Tomizawa (1992) proposed three
kinds of double symmetry models, whose each has a structure of both symmetry about the …

Linear ordinal quasi-symmetry model and decomposition of symmetry for multi-way tables

K Tahata, H Yamamoto, S Tomizawa - Mathematical Methods of Statistics, 2011 - Springer
For multi-way tables with same categories, Bhapkar and Darroch [4] and Agresti [2], p. 440,
considered the general order quasi-symmetry model and the ordinal quasi-symmetry model …

Moment symmetry models and decompositions of symmetry for multi-way contingency tables

T Yoshimoto, K Tahata, K Iki… - Calcutta Statistical …, 2019 - journals.sagepub.com
For square contingency tables, Caussinus demonstrated that the symmetry model holds if
and only if both the quasi-symmetry and marginal homogeneity models hold. Bishop …

Double linear diagonals-parameter symmetry and decomposition of double symmetry for square tables

K Tahata, S Tomizawa - Statistical Methods & Applications, 2010 - Springer
For square contingency tables with ordered category, the present paper proposes the
double linear diagonals-parameter symmetry (D-LDPS) model which implies the structure of …

Measure of departure from double-symmetry for square contingency tables

K Yamamoto, M Komatsu… - Journal of Statistics and …, 2010 - search.proquest.com
For square contingency tables, Tomizawa (1985a) considered the double-symmetry model,
which has the structure of both symmetry and point-symmetry. The present paper proposes a …