Decompositions for 2-Ratios-Parameter Symmetry Model in Square Contingency Tables with Ordered Categoriesat

1987 ◽  
Vol 29 (1) ◽  
pp. 45-55 ◽  
Author(s):  
Sadao Tomizawa
Keyword(s):  
Contingency Tables ◽  
Symmetry Model ◽  
Parameter Symmetry

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.

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.

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