Correspondence Analysis

Correspondence analysis (CA) is yet another ordination method, somewhat similar to PCA but for counted data (e.g. Legendre & Legendre 1998). For comparing associations (columns) containing counts of taxa, or counted taxa (rows) across associations, CA is the more appropriate algorithm. Also, CA is more suitable if you expect that species have unimodal responses to the underlying parameters, that is they favour a certain range of the parameter, becoming rare for lower and higher values (this is in contrast to PCA, which assumes a linear response).

The CA routine finds the eigenvalues and eigenvectors of a matrix containing the Chi-squared distances between all rows (or columns, if that is more efficient – the result is the same). The algorithm follows Greenacre (2010), with SVD. The eigenvalue, giving a measure of the similarity accounted for by the corresponding eigenvector, is given for each eigenvector. The percentages of similarity accounted for by these components are also given.

The scatter plot allows you to see all your data points (rows) plotted in the coordinate system given by the CA. If you have grouped rows, the different groups can be shown using separate convex hulls and concentration ellipses.

In addition, the variables (columns, associations) can be plotted in the same coordinate system (Q mode), optionally including the column labels. If your data are 'well behaved', taxa typical for an association should plot in the vicinity of that association.

Missing data is supported by column average substitution.


Greenacre, M. 2010. Biplots in practice. Fundación BBVA, 237 pp.
Legendre, P. & L. Legendre. 1998. Numerical Ecology, 2nd English ed. Elsevier, 853 pp.

Published Aug. 31, 2020 7:54 PM - Last modified Aug. 31, 2020 7:55 PM