Journal
MATHEMATICAL GEOSCIENCES
Volume 42, Issue 1, Pages 129-134Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s11004-008-9212-2
Keywords
Compositional data analysis; Contingency ratios; Distributional equivalence; Log-ratios; Power transformation; Spectral mapping
Funding
- Fundacion BBVA in Madrid, Spain
- Spanish Ministry of Education and Science [MEC-SEJ2006-14098]
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It is common practice in compositional data analysis to perform the log-ratio transformation in order to preserve sub-compositional coherence in the analysis. Correspondence analysis is an alternative approach to analyzing ratio-scale data and is often contrasted with log-ratio analysis. It turns out that if one introduces a power transformation into the correspondence analysis algorithm, then the limit of the power-transformed correspondence analysis, as the power parameter tends to zero, is exactly the log-ratio analysis. Depending on how the power transformation is applied, we can obtain as limiting cases either Aitchison's unweighted log-ratio analysis or the weighted form called spectral mapping. The upshot of this is that one can come as close as one likes to the log-ratio analysis, weighted or unweighted, using correspondence analysis.
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