Measuring subcompositional incoherence

Michael Greenacre

Economics Working Papers from Department of Economics and Business, Universitat Pompeu Fabra

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.

Keywords: correspondence analysis; compositional data; chi-square distance; log-ratio distance; multidimensional scaling; stress; subcompositional coherence (search for similar items in EconPapers)
JEL-codes: C19 C88 (search for similar items in EconPapers)
Date: 2008-08, Revised 2011-01
New Economics Papers: this item is included in nep-ecm
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Citations: View citations in EconPapers (6)

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Persistent link: https://EconPapers.repec.org/RePEc:upf:upfgen:1106

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