Diagonals-Parameter Symmetry Model for Cumulative Probabilities in Square Contingency Tables with Ordered Categories

Biometrics ◽  
1993 ◽  
Vol 49 (3) ◽  
pp. 883 ◽  
Author(s):  
Sadao Tomizawa
Keyword(s):  
Contingency Tables ◽  
Ordered Categories ◽  
Symmetry Model ◽  
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.

scholarly journals Log-normal Distribution Type Symmetry Model for Square Contingency Tables with Ordered Categories

2018 ◽  
Vol 47 (3) ◽  
pp. 39-48
Author(s):  
Kiyotaka Iki
Keyword(s):  
Normal Distribution ◽  
Contingency Tables ◽  
Ordered Categories ◽  
Symmetry Model ◽  
Proposed Model ◽  
Type Symmetry ◽  
The Difference ◽  
Log Normal ◽  
Distribution Type ◽  
Log Normal Distribution

For the analysis of square contingency tables with the same row and column ordinal classications, this article proposes a new model which indicates that the log-ratios of symmetric cell probabilities are proportional to the difference between log-row category and log-column category. The proposed model may be appropriate for a square ordinal table if it is reasonable to assume an underlying bivariate log-normal distribution. Also, this article gives the decomposition of the symmetry model using the proposed model with the orthogonality of test statistics. Examples are given. The simulation studies based on bivariate log-normal distribution are given.

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