Odds‐symmetry model for cumulative probabilities and decomposition of a conditional symmetry model in square contingency tables

2021 ◽  
Author(s):  
Shuji Ando
Keyword(s):  
Contingency Tables ◽  
Conditional Symmetry ◽  
Symmetry Model ◽  
Cumulative Probabilities

scholarly journals Measure of Departure from Conditional Symmetry Based on Cumulative Probabilities for Square Contingency Tables

Symmetry ◽  
2021 ◽  
Vol 13 (10) ◽  
pp. 1897
Author(s):  
Yusuke Saigusa ◽  
Yuta Teramoto ◽  
Sadao Tomizawa
Keyword(s):  
Social Mobility ◽  
Contingency Tables ◽  
Occupational Status ◽  
Main Diagonal ◽  
Asymmetric Structure ◽  
Conditional Symmetry ◽  
Ordered Categories ◽  
Symmetry Model ◽  
Status Data ◽  
Cumulative Probabilities

For the analysis of square contingency tables with ordered categories, a measure was developed to represent the degree of departure from the conditional symmetry model in which there is an asymmetric structure of the cell probabilities with respect to the main diagonal of the table. The present paper proposes a novel measure for the departure from conditional symmetry based on the cumulative probabilities from the corners of the square table. In a given example, the proposed measure is applied to Japanese occupational status data, and the interpretation of the proposed measure is illustrated as the departure from a proportional structure of social mobility.

scholarly journals Diagonal Exponent Conditional Symmetry Model for Square Contingency Tables with Ordered Categories

2016 ◽  
Vol 5 (4) ◽  
pp. 38
Author(s):  
Kiyotaka Iki ◽  
Akira Shibuya ◽  
Sadao Tomizawa
Keyword(s):  
Contingency Tables ◽  
Main Diagonal ◽  
Test Statistics ◽  
Conditional Symmetry ◽  
Exponential Form ◽  
Ordered Categories ◽  
Expected Frequency ◽  
Symmetry Model ◽  
Proposed Model ◽  
New Models

For square contingency tables with ordered categories, this article proposes new models which indicate that in addition to the structure of asymmetry of the probabilities with respect to the main diagonal of the table, the expected frequency has an exponential form along every subdiagonal of the table. Also it gives the new three kinds of decompositions using the proposed model and proves the orthogonality of the test statistics.

scholarly journals A Measure of Departure from Average Symmetry for Square Contingency Tables with Ordered Categories

2016 ◽  
Vol 38 (2) ◽  
Author(s):  
Kouji Tahata ◽  
Kouji Yamamoto ◽  
Noriyuki Nagatani ◽  
Sadao Tomizawa
Keyword(s):  
Contingency Tables ◽  
Conditional Symmetry ◽  
Ordered Categories ◽  
Maximum Value ◽  
Symmetry Model ◽  
Square Tables

For the analysis of square contingency tables, Tomizawa (1994), Tomizawa, Seo, and Yamamoto (1998), and Tomizawa, Miyamoto, and Hatanaka (2001) considered measures to represent the degree of departure from symmetry. However, the maximum value of these measures cannot distinguish two kinds of complete asymmetry (say, complete-upper-asymmetry and complete-lower-asymmetry). The present paper proposes a measure which can distinguish two kinds of complete asymmetry for square tables with ordered categories. Especially the proposed measure is useful for representingthe degree of departure from symmetry when the conditional symmetry model holds. Examples are given.

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.

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