Paper #1106

Títol:

Measuring subcompositional incoherence

Autor:

Michael Greenacre

Data:

Agost 2008 (Revisió: Gener 2011)

Resum:

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.

Paraules clau:

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

Codis JEL:

C19, C88

Àrea de Recerca:

Estadística, Econometria i Mètodes Quantitatius

Publicat a:

Mathematical Geosciences, 2011, 43, 681–693

Descarregar el paper en format PDF (108 Kb)