Paper #1278

Títol:

The contributions of rare objects in correspondence analysis

Autor:

Michael Greenacre

Data:

Setembre 2011

Resum:

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.

Paraules clau:

Biplot, canonical correspondence analysis, contribution, correspondence analysis, influence, outlier, scaling

Codis JEL:

C19, C88

Àrea de Recerca:

Estadística, Econometria i Mètodes Quantitatius

Publicat a:

Ecology, 2013, 94(1), 241-249

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