Identification of the Unchanging Reference Component of Compositional Data from the Propperties of the Coefficient of Variation
Identification of the Unchanging Reference Component of Compositional Data from the Propperties of the Coefficient of Variation
复制标题
从变异系数的性质识别成分数据不变的参考成分
DOI：
10.1007/s11004-011-9332-y
复制
发表时间：
2011
影响因子：
2.6
通讯作者：
Noda A.
中科院分区：
文献类型：
--
作者：
Ohta T.;Arai H.;Noda A.
在成分数据的分析中，重要的是选择一个合适的不变的组件作为参考，以检测孤立的单个变量的行为。本文介绍了两个测试的基础上，一种新的方法，利用成分比的变异系数检测不变的成分。也就是说，当不变组分在分母和分子之间切换时，组成比的变异系数发生变化，并且当不变组分相对于任何任意组分作为分母出现时，变异系数趋于小（测试1）。此外，给出最低变异系数的组分对的比率最有可能代表两个不变组分（试验2）。然而，测试1和2不是唯一找到不变分量的充分必要条件。为了验证测试的有效性，分析了500个人工数据集，结果表明测试能够识别不变的成分，尽管当数据集包括偏度大于0.5的成分时测试1表现不佳，当数据集包括相关系数大于0.75的成分时测试2失败。这些缺陷可以通过以互补的方式解释两个测试结果来克服。所提出的测试提供了强大而简单的标准，用于识别成分数据中的不变成分，然而，这种方法的可靠性需要在进一步的研究中进行评估。
In analyses of compositional data, it is important to select a suitable unchanging component as a reference to detect the behavior of a single variable in isolation. This paper introduces two tests for detecting the unchanging component, based on a new approach that utilizes the coefficient of variation of component ratios. That is, the coefficient of variation of a compositional ratio is subject to change when the unchanging component is switched between the denominator and numerator, and the coefficient of variation tends to be small when the unchanging component occurs as the denominator against any arbitrary components (Test 1). In addition, the ratio of the component pair that gives the lowest coefficient of variation is most likely to represent the two unchanging components (Test 2). However, Tests 1 and 2 are not necessary and sufficient conditions for uniquely finding the unchanging component. To verify the effectiveness of the tests, 500 artificial datasets were analyzed and the results suggest that the tests are able to identify the unchanging component, although Test 1 underperforms when the dataset includes a component with skewness greater than 0.5, and Test 2 fails when the dataset includes components with a correlation coefficient greater than 0.75. These defects can be overcome by interpreting the two test results in a complementary manner. The proposed tests provide powerful yet simple criteria for identifying the unchanging component in compositional data; however, the reliability of this approach needs to be assessed in further studies.