Two‐way contingency tables arise in many fields, such as in medical studies, where the relation between two discrete random variables or responses is to be assessed. We propose to analyze and visualize a sample of 2 × 2 tables in the context of single‐subject repeated measurements design by means of compositional data (CoDa) methods. First, we propose to visualize the tables in a quaternary diagram. Second, we show how to represent these tables by means of logratios indicating the relationship between the two variables as well as their strength and direction of dependency. Finally, we describe a technique to model those tables with a simplicial regression model. Data from a real‐world study of self‐prediction of migraine attack onset is used to illustrate this methodology. For each individual, the 2 × 2 table of their migraine expectation vs next day migraine occurrence is computed, generating a sample of tables. Then we visualize and interpret the prediction ability of individuals both in the simplex and in terms of logratios of components. Finally, we model the self‐prediction ability with respect to demographic variables, days tracked and disease characteristics. Our application demonstrates that CoDa can be a useful tool for visualizing, modeling, and interpreting the components of 2 × 2 tables.

中文翻译：

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使用成分数据分析对双向列联表进行建模和可视化：偏头痛日个人自我预测的案例研究

双向列联表在许多领域中都出现，例如医学研究中，需要评估两个离散随机变量或响应之间的关系。我们建议在单对象重复测量设计的背景下，通过成分数据（CoDa）方法分析和可视化2×2表的样本。首先，我们建议将表格可视化为四元图。其次，我们展示如何通过对数表示来表示这些表，该对数表示两个变量之间的关系以及它们的强度和依赖性方向。最后，我们描述了一种使用简单回归模型对这些表进行建模的技术。来自对偏头痛发作的自我预测的真实世界研究的数据用于说明这种方法。对于每个人，计算他们的偏头痛期望值与第二天偏头痛发生率的2×2表，生成表样本。然后，我们以单纯形和组件对数形式可视化并解释个体的预测能力。最后，我们针对人口变量，追踪天数和疾病特征对自我预测能力进行建模。我们的应用程序证明CoDa可以成为可视化，建模和解释2×2表组成部分的有用工具。