Decomposition of Bivariate Symmetric Density Function

1996 ◽  
Vol 46 (1-2) ◽  
pp. 129-134
Author(s):  
Takashi Sadao Tomizawa Seo ◽  
Jun-Ichiro Minaguchi
Keyword(s):  
Density Function ◽  
Contingency Tables ◽  
Marginal Homogeneity ◽  
Symmetric Density ◽  
Symmetry Model ◽  
Bivariate Density

For the analysis of square contingency tables, it is known that the symmetry model holds if and only if both the quasi-symmetry and the marginal homogeneity models hold (Caussinus, 1965; Bishop et al., 1975, p. 287). This paper shows that a similar decomposition for bivariate density function (instead of cell probabilities) holds.

Decomposition of Bivariate Point-Symmetric Density Function

1998 ◽  
Vol 48 (1-2) ◽  
pp. 21-28
Author(s):  
Sadao Tomizawa ◽  
Tomono Konuma
Keyword(s):  
Density Function ◽  
Point Symmetry ◽  
Symmetric Density ◽  
Symmetry Model ◽  
Bivariate Density

For the analysis of contigency tables, it is known that the point-symmetry model holds if and only if both the quasi-point symmetry and the marginal point-symmetry models hold (Tomizawa, 1985). This paper shows that a similar decomposition for bivariate density function (instead of cell probabilities) holds.

Moment Symmetry Models and Decompositions of Symmetry for Multi-way Contingency Tables

2019 ◽  
Vol 71 (2) ◽  
pp. 83-98
Author(s):  
Takuya Yoshimoto ◽  
Kouji Tahata ◽  
Kiyotaka Iki ◽  
Sadao Tomizawa
Keyword(s):  
Present Article ◽  
Contingency Tables ◽  
Second Order ◽  
Subject Classification ◽  
Order Moment ◽  
Marginal Homogeneity ◽  
Symmetry Model

For square contingency tables, Caussinus[ 1 ] demonstrated that the symmetry model holds if and only if both the quasi-symmetry and marginal homogeneity models hold. Bishop, Fienberg, and Holland[ 2 , p. 307] and Bhapkar and Darroch[ 3 ] provided similar theorems for multi-way tables. The present article proposes a moment symmetry model and unique decompositions of the symmetry model. For two-way tables, the second-order moment symmetry model decomposes the symmetry model into the second-order moment symmetry and marginal homogeneity models, while the [Formula: see text]th-order moment symmetry model decomposes the [Formula: see text]th-order marginal symmetry model using the [Formula: see text]th-order marginal symmetry model for multi-way tables. AMS 2000 subject classification: 62H17

A Decomposition of the Marginal Homogeneity Model for Square Contingency Tables with Ordered Categories

1993 ◽  
Vol 43 (1-2) ◽  
pp. 123-126 ◽  
Author(s):  
Sadao Tomizawa
Keyword(s):  
Contingency Tables ◽  
Short Note ◽  
Monotonic Function ◽  
Ordered Categories ◽  
Marginal Homogeneity ◽  
Statist Assoc

For square contingency tables, with ordered categories, this short note decomposes the marginal homogeneity (MH) model into an extended MH model and the model of equality of expectation of monotonic function of row and column variables. This decomposition is a generalization of the decomposition of the MH model which was earlier considered by Tomizawa (1991, Cal. Statist. Assoc. Bull., 41, 201-207).

scholarly journals Measure of Departure From Local Symmetry for Square Contingency Tables

2019 ◽  
Vol 8 (2) ◽  
pp. 140
Author(s):  
Yusuke Saigusa ◽  
Mitsuhiro Takami ◽  
Aki Ishii ◽  
Sadao Tomizawa
Keyword(s):  
Shannon Entropy ◽  
Diversity Index ◽  
Contingency Tables ◽  
Local Symmetry ◽  
Harmonic Mean ◽  
Symmetric Structure ◽  
Symmetry Model

For square contingency tables, this paper considers the local symmetry model which indicates that there is a symmetric structure of probabilities for only one of pairs of symmetric cells. Also it proposes the measure to express the degree of departure from the local symmetry model. The measure is expressed as the weighted harmonic mean of the diversity index including the Shannon entropy. Examples are given.

scholarly journals Two-Dimensional Measure Vector of Departure from Marginal Homogeneity in Square Contingency Tables

2019 ◽  
Vol 4 (3) ◽  
Author(s):  
Shuji Ando ◽  
◽  
Takashi Takeuchi ◽  
Kiyotaka Iki ◽  
Sadao Tomizawa ◽  
...  
Keyword(s):  
Contingency Tables ◽  
Two Dimensional ◽  
Marginal Homogeneity ◽  
Dimensional Measure
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