An anti-sum-symmetry model and its orthogonal decomposition for ordinal square contingency tables with an application to grip strength test data
An anti-sum-symmetry model and its orthogonal decomposition for ordinal square contingency tables with an application to grip strength test data
复制标题
序数方列联表的反对和对称模型及其正交分解及其在握力测试数据中的应用
DOI：
10.2478/bile-2021-0004
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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 为了分析 R × R 方列联表，我们需要从获得的观测值中以高置信度估计未知的概率分布。为此，我们需要使用能够很好地拟合数据并且具有简单解释的统计模型来执行分析。本研究提出了两个原始模型，它们在行和列变量之和为 t 的概率之间具有对称和不对称结构，对于 t = 2，。 。 ., R，以及行和列变量之和为 2(R + 1) − t 的概率。研究还表明，为了满足所提出的对称模型，除了所提出的不对称模型之外，还必须满足反全局对称模型。该分解定理有助于解释为什么所提出的对称模型不成立。此外，我们表明所提出的对称模型的似然比卡方统计量的值等于分解模型的似然比卡方统计量的总和。我们通过将所提出的模型应用于现实世界的握力数据来评估其实用性。
Summary For the analysis of R × R square contingency tables, we need to estimate an unknown probability distribution with high confidence from obtained observations. For that purpose, we need to perform the analysis using a statistical model that fits the data well and has a simple interpretation. This study proposes two original models that have symmetric and asymmetric structures between the probability with which the sum of row and column variables is t, for t = 2, . . ., R, and the probability with which the sum of row and column variables is 2(R + 1) − t. The study also reveals that it is necessary to satisfy the anti-global symmetry model, in addition to the proposed asymmetry model, in order to satisfy the proposed symmetry model. This decomposition theorem is useful to explain why the proposed symmetry model does not hold. Moreover, we show that the value of the likelihood ratio chi-squared statistic of the proposed symmetry model is equal to the sum of those of the decomposed models. We evaluate the utility of the proposed models by applying them to real-world grip strength data.