Linear Diagonals-Parameter Symmetry and Quasi-Symmetry Models for Cumulative Probabilities in Square Contingency Tables with Ordered Categories

2004 ◽  
Vol 46 (6) ◽  
pp. 664-674 ◽  
Author(s):  
Nobuko Miyamoto ◽  
Wataru Ohtsuka ◽  
Sadao Tomizawa
Keyword(s):  
Contingency Tables ◽  
Ordered Categories ◽  
Parameter Symmetry ◽  
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.

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