Asymmetry models based on ordered score and separations of symmetry model for square contingency tables
Asymmetry models based on ordered score and separations of symmetry model for square contingency tables
复制标题
基于有序分数的不对称模型和方形列联表的对称模型分离
DOI：
10.2478/bile-2021-0002
复制
发表时间：
2021
期刊：
影响因子：
--
通讯作者：
S. Ando
中科院分区：
文献类型：
--
作者：
S. Ando
摘要本研究提出了两个原始的不对称模型的基础上，有序分数的平方列联表具有相同的行和列顺序分类。所提出的模型可以应用于所有类别的分数已知或未知的情况。在所提出的模型中，落在第（i，j）个单元格而不是第（j，i）个单元格中的观察的对数几率与对应于类别i和j的有序分数的差成反比。所提出的模型的不对称参数可以用于推断行变量是否随机大于列变量，反之亦然。当对称性模型成立时，所提出的模型总是成立的，但匡威则不一定成立。本研究还探讨了什么是必要的模型，除了所提出的模型，以满足对称模型，并给出了分离的对称模型，使用建议和边际平均平等模型。我们应用真实的数据来显示所提出的模型的实用性。所提出的模型提供了一个更好的拟合比现有的模型。
Summary 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.