When the row and column variables consist of the same category in a two-way contingency table, it is specifically called a square contingency table. Since it is clear that the square contingency tables have an association structure, a primary objective is to examine symmetric relationships and transitions between variables. While various models and measures have been proposed to analyze these structures understanding changes between two variables in behavior at two-time points or cohorts, it is also necessary to require a detailed investigation of individual categories and their interrelationships, such as shifts in brand preferences. This paper proposes a novel approach to correspondence analysis (CA) for evaluating departures from symmetry in square contingency tables with nominal categories, using a power-divergence-type measure. The approach ensures that well-known divergences can also be visualized and, regardless of the divergence used, the CA plot consists of two principal axes with equal contribution rates. Additionally, the scaling is independent of sample size, making it well-suited for comparing departures from symmetry across multiple contingency tables. Confidence regions are also constructed to enhance the accuracy of the CA plot.

翻译：当双向列联表的行变量与列变量包含相同类别时，该表特称为方形列联表。由于方形列联表显然具有关联结构，其主要目标之一是检验变量间的对称关系与转移。尽管已有多种模型和度量被提出来分析这些结构，以理解两个变量在两个时间点或队列间的行为变化，但仍需对个体类别及其相互关系（如品牌偏好转移）进行详细考察。本文提出了一种新颖的对应分析（CA）方法，用于评估具有名义类别的方形列联表中对称性的偏离，该方法采用幂散度型度量。该方案确保著名的散度度量亦可被可视化，且无论使用何种散度，对应分析图均由两个贡献率相等的主轴构成。此外，其标度与样本量无关，因此非常适合用于比较多个列联表间的对称性偏离。本文还构建了置信区域以提高对应分析图的准确性。