DUGi

Tests for Identifying the Unchanging Reference Component of Compositional Data using the Properties of the Coefficient of Variaiton

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In analyses of compositional data, it is important to select a suitable unchanging component as a reference todetect the behavior of a single variable in isolation. This paper introduces two tests for detecting theunchanging component, based on a new approach that utilizes the coefficient of variation of componentratios. That is, the coefficient of variation of a compositional ratio is subject to change when the unchangingcomponent is switched between the denominator and numerator, and the coefficient of variation tends to besmall 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 torepresent the two unchanging components (Test 2). However, Tests 1 and 2 are not necessary and sufficientconditions for uniquely finding the unchanging component. To verify the effectiveness of the tests, 500artificial data sets were analyzed and the results suggest that the tests are able to identify the unchangingcomponent, although Test 1 underperforms when the data set includes a component with skewness greaterthan 0.5, and Test 2 fails when the data set includes components with a correlation coefficient greater than0.75. These defects can be overcome by interpreting the two test results in a complementary manner. Theproposed tests provide powerful yet simple criteria for identifying the unchanging component incompositional data; however, the reliability of this approach needs to be assessed in further studies

Universitat de Girona. Departament d’Informàtica i Matemàtica Aplicada