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# Measuring subcompositional incoherence

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## Abstract

Subcompositional coherence is a fundamental property of Aitchison’s approach to compositional data analysis, and is the principal justification for using ratios of components. We maintain, however, that lack of subcompositional coherence, that is incoherence, can be measured in an attempt to evaluate whether any given technique is close enough, for all practical purposes, to being subcompositionally coherent. This opens up the field to alternative methods, which might be better suited to cope with problems such as data zeros and outliers, while being only slightly incoherent. The measure that we propose is based on the distance measure between components. We show that the two-part subcompositions, which appear to be the most sensitive to subcompositional incoherence, can be used to establish a distance matrix which can be directly compared with the pairwise distances in the full composition. The closeness of these two matrices can be quantified using a stress measure that is common in multidimensional scaling, providing a measure of subcompositional incoherence. The approach is illustrated using power-transformed correspondence analysis, which has already been shown to converge to log-ratio analysis as the power transform tends to zero.

## Suggested Citation

• Michael Greenacre, 2008. "Measuring subcompositional incoherence," Economics Working Papers 1106, Department of Economics and Business, Universitat Pompeu Fabra, revised Jan 2011.
• Handle: RePEc:upf:upfgen:1106
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File URL: https://econ-papers.upf.edu/papers/1106.pdf
File Function: Whole Paper

## Citations

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Cited by:

1. Tsagris, Michail & Preston, Simon & T.A. Wood, Andrew, 2016. "Improved classi cation for compositional data using the $\alpha$-transformation," MPRA Paper 67657, University Library of Munich, Germany.
2. Michail Tsagris & Simon Preston & Andrew T. A. Wood, 2016. "Improved Classification for Compositional Data Using the α-transformation," Journal of Classification, Springer;The Classification Society, vol. 33(2), pages 243-261, July.

### Keywords

correspondence analysis; compositional data; chi-square distance; log-ratio distance; multidimensional scaling; stress; subcompositional coherence;

### JEL classification:

• C19 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Other
• C88 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Other Computer Software

### NEP fields

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