The Contributions of Rare Objects in Correspondence Analysis

Michael Greenacre

No 571, Working Papers from Barcelona School of Economics

Abstract: Correspondence analysis, when used to visualize relationships in a table of counts (for example, abundance data in ecology), has been frequently criticized as being too sensitive to objects (for example, species) that occur with very low frequency or in very few samples. In this statistical report we show that this criticism is generally unfounded. We demonstrate this in several data sets by calculating the actual contributions of rare objects to the results of correspondence analysis and canonical correspondence analysis, both to the determination of the principal axes and to the chi-square distance. It is a fact that rare objects are often positioned as outliers in correspondence analysis maps, which gives the impression that they are highly influential, but their low weight offsets their distant positions and reduces their effect on the results. An alternative scaling of the correspondence analysis solution, the contribution biplot, is proposed as a way of mapping the results in order to avoid the problem of outlying and low contributing rare objects.

Keywords: Biplot; canonical correspondence analysis; contribution; correspondence analysis; influence; outlier; scaling (search for similar items in EconPapers)
JEL-codes: C19 C88 (search for similar items in EconPapers)
Date: 2015-09
New Economics Papers: this item is included in nep-ecm
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Related works:
Working Paper: The contributions of rare objects in correspondence analysis (2011)
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Persistent link: https://EconPapers.repec.org/RePEc:bge:wpaper:571

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