<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>This study proposes two original asymmetry models based on ordered scores for square contingency tables with the same row and column ordinal classifications. The proposed models can be applied to cases in which the scores of all categories are known or unknown. In the proposed models, the log odds for an observation falling in the (<italic>i, j</italic>)th cell instead of the (<italic>j, i</italic>)th cell are inversely proportional to the difference of the ordered scores corresponding to categories <italic>i</italic> and <italic>j</italic>. The asymmetry parameter of the proposed model can be useful for inferring whether the row variable is stochastically greater than the column variable or vice versa. The proposed models constantly hold when the symmetry model holds, but the converse is not necessarily true. This study also examines what is necessary for a model, in addition to the proposed models, to satisfy the symmetry model, and gives separations of the symmetry model using the proposed and marginal mean equality models. We apply real data to show the utility of the proposed models. The proposed models provide a better fit than that of the existing models.</p>
</abstract>

This study proposes two original asymmetry models based on ordered scores for square contingency tables with the same row and column ordinal classifications. The proposed models can be applied to cases in which the scores of all categories are known or unknown. In the proposed models, the log odds for an observation falling in the (i, j)th cell instead of the (j, i)th cell are inversely proportional to the difference of the ordered scores corresponding to categories i and j. The asymmetry parameter of the proposed model can be useful for inferring whether the row variable is stochastically greater than the column variable or vice versa. The proposed models constantly hold when the symmetry model holds, but the converse is not necessarily true. This study also examines what is necessary for a model, in addition to the proposed models, to satisfy the symmetry model, and gives separations of the symmetry model using the proposed and marginal mean equality models. We apply real data to show the utility of the proposed models. The proposed models provide a better fit than that of the existing models.

Asymmetry models based on ordered score and separations of symmetry model for square contingency tables

Department of Information and Computer Technology, Faculty of Engineering

Biometrical Letters

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

This study proposes two original asymmetry models based on ordered scores for square contingency tables with the same row and column ordinal classifications....

Asymmetry models based on ordered score and separations of symmetry model for square contingency tables

Published Online: Jun 24, 2021

Page range: 27 - 39

DOI: https://doi.org/10.2478/bile-2021-0002

Keywords
asymmetry, midpoint, necessary and sucient condition, ordered category, power parameter, ridit, symmetry

© 2021 Shuji Ando, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Asymmetry models based on ordered score and separations of symmetry model for square contingency tables

Published Online: Jun 24, 2021

Page range: 27 - 39

DOI: https://doi.org/10.2478/bile-2021-0002

Keywordsasymmetry, midpoint, necessary and sucient condition, ordered category, power parameter, ridit, symmetry

© 2021 Shuji Ando, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
asymmetry, midpoint, necessary and sucient condition, ordered category, power parameter, ridit, symmetry