A Decomposition of Linear Diagonals-Parameter Symmetry Model for Square Contingency Tables with Ordered Categories

2007 ◽  
Vol 32 (6) ◽  
pp. 761-766 ◽  
Author(s):  
Sadao Tomizawa
Keyword(s):  
Contingency Tables ◽  
Ordered Categories ◽  
Symmetry Model ◽  
Parameter Symmetry

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.

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.

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