Odds-symmetry model for cumulative probabilities and decomposition of a conditional symmetry model in square contingency tables

Pub Date : 2021-12-06 DOI:10.1111/anzs.12346
Shuji Ando
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引用次数: 1

Abstract

For the analysis of square contingency tables, it is necessary to estimate an unknown distribution with high confidence from an obtained observation. For that purpose, we need to introduce a statistical model that fits the data well and has parsimony. This study proposes asymmetry models based on cumulative probabilities for square contingency tables with the same row and column ordinal classifications. In the proposed models, the odds, for all i<j, that an observation will fall in row category i or below, and column category j or above, instead of row category j or above, and column category i or below, depend on only row category i or column category j. This is notwithstanding that the odds are constant without relying on row and column categories under the conditional symmetry (CS) model. The proposed models constantly hold when the CS model holds. However, the converse is not necessarily true. This study also shows that it is necessary to satisfy the extended marginal homogeneity model, in addition to the proposed models, to satisfy the CS model. These decomposition theorems explain why the CS model does not hold. The proposed models provide a better fit for application to a single data set of real-world occupational data for father-and-son dyads.

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平方列联表中累积概率的奇数-对称模型及条件对称模型的分解
对于平方列联表的分析,需要从已获得的观测值中估计出具有高置信度的未知分布。为此,我们需要引入一种能够很好地拟合数据并具有简约性的统计模型。本研究提出了基于累积概率的方形列联表的不对称模型,具有相同的行和列顺序分类。在提出的模型中,对于所有i<j,一个观测值将落在第i行类别或以下,列类别j或以上,而不是行类别j或以上,列类别i或以下的几率,仅取决于行类别i或列类别j。尽管在条件对称(CS)模型下,几率是恒定的,不依赖于行和列类别。当CS模型成立时,所提出的模型一直成立。然而,反过来未必正确。研究还表明,在满足CS模型的基础上,还需要满足扩展边际均匀性模型。这些分解定理解释了为什么CS模型不成立。所提出的模型更适合应用于父子二人组真实职业数据的单一数据集。
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