Mert Mehmet Can, Filzmoser Peter, Hron Karel
Institute of Statistics and Mathematical Methods in Economics, Vienna University of Technology, Wiedner Hauptstrasse 8-10, 1040 Vienna, Austria.
Department of Mathematical Analysis and Applications of Mathematics, Faculty of Science, Palacký University, 17. listopadu 12, 771 46 Olomouc, Czech Republic.
Math Geosci. 2016;48(8):941-961. doi: 10.1007/s11004-016-9646-x. Epub 2016 Jul 7.
Compositional data, as they typically appear in geochemistry in terms of concentrations of chemical elements in soil samples, need to be expressed in log-ratio coordinates before applying the traditional statistical tools if the relative structure of the data is of primary interest. There are different possibilities for this purpose, like centered log-ratio coefficients, or isometric log-ratio coordinates. In both the approaches, geometric means of the compositional parts are involved, and it is unclear how measurement errors or detection limit problems affect their presentation in coordinates. This problem is investigated theoretically by making use of the theory of error propagation. Due to certain limitations of this approach, the effect of error propagation is also studied by means of simulations. This allows to provide recommendations for practitioners on the amount of error and on the expected distortion of the results, depending on the purpose of the analysis.
成分数据，就像它们在地球化学中通常以土壤样本中化学元素浓度的形式出现那样，如果数据的相对结构是主要关注点，那么在应用传统统计工具之前，需要在对数比坐标中表示。为此有不同的可能性，比如中心对数比系数或等距对数比坐标。在这两种方法中，都涉及成分部分的几何均值，并且尚不清楚测量误差或检测限问题如何影响它们在坐标中的表示。利用误差传播理论对这个问题进行了理论研究。由于这种方法存在某些局限性，还通过模拟研究了误差传播的影响。这使得能够根据分析目的，为从业者提供关于误差量和结果预期失真的建议。
