University of Kiel, Aschauhof, 24340 Eckernförde-Altenhof, Germany.
Chair of Survey Statistics and Data Analysis, Otto-Friedrich-Universität Bamberg, 96045 Bamberg, Germany.
Int J Environ Res Public Health. 2021 Feb 11;18(4):1741. doi: 10.3390/ijerph18041741.
(1) Background: We present a new statistical approach labeled as "St. Nicolas House Analysis" (SNHA) for detecting and visualizing extensive interactions among variables. (2) Method: We rank absolute bivariate correlation coefficients in descending order according to magnitude and create hierarchic "association chains" defined by sequences where reversing start and end point does not alter the ordering of elements. Association chains are used to characterize dependence structures of interacting variables by a graph. (3) Results: SNHA depicts association chains in highly, but also in weakly correlated data, and is robust towards spurious accidental associations. Overlapping association chains can be visualized as network graphs. Between independent variables significantly fewer associations are detected compared to standard correlation or linear model-based approaches. (4) Conclusion: We propose reversible association chains as a principle to detect dependencies among variables. The proposed method can be conceptualized as a non-parametric statistical method. It is especially suited for secondary data analysis as only aggregate information such as correlations matrices are required. The analysis provides an initial approach for clarifying potential associations that may be subject to subsequent hypothesis testing.
(1) 背景：我们提出了一种新的统计方法，称为“圣尼古拉屋分析”（SNHA），用于检测和可视化变量之间的广泛相互作用。
(2) 方法：我们根据大小对绝对双变量相关系数进行降序排列，并创建由序列定义的层次“关联链”，其中反转起点和终点不会改变元素的顺序。关联链用于通过图形来描述相互作用变量的依赖结构。
(3) 结果：SNHA 描绘了高度相关但也弱相关数据中的关联链，并且对虚假偶然关联具有稳健性。重叠的关联链可以可视化作为网络图形。与标准相关或基于线性模型的方法相比，在独立变量之间检测到的关联要少得多。
(4) 结论：我们提出可逆关联链作为检测变量之间依赖关系的原则。所提出的方法可以被概念化为一种非参数统计方法。它特别适合于二次数据分析，因为只需要聚合信息，例如相关矩阵。该分析提供了一种初步方法，可以澄清可能需要进行后续假设检验的潜在关联。
