eigenvals: Extract Eigenvalues from an Ordination Object

Description

Function extracts eigenvalues from an object that has them. Many multivariate methods return such objects.

Usage

eigenvals(x, ...)
## S3 method for class 'cca':
eigenvals(x, constrained = FALSE, ...)
## S3 method for class 'eigenvals':
summary(object, ...)

Arguments

An object from which to extract eigenvalues.

object

An eigenvals result object.

constrained

Return only constrained eigenvalues.

...

Other arguments to the functions (usually ignored)

Value

An object of class "eigenvals" which is a vector of eigenvalues.

Details

This is a generic function that has methods for cca, wcmdscale, pcnm, prcomp, princomp, dudi (of ade4), and pca and pco (of labdsv) result objects. The default method also extracts eigenvalues if the result looks like being from eigen or svd. Functions prcomp and princomp contain square roots of eigenvalues that all called standard deviations, but eigenvals function returns their squares. Function svd contains singular values, but function eigenvals returns their squares. For constrained ordination methods cca, rda and capscale the function returns the both constrained and unconstrained eigenvalues concatenated in one vector, but the partial component will be ignored. However, with argument constrained = TRUE only constrained eigenvalues are returned.

The summary of eigenvals result returns eigenvalues, proportion explained and cumulative proportion explained. The result object can have some negative eigenvalues (wcmdscale, capscale, pcnm) which correspond to imaginary axes of Euclidean mapping of non-Euclidean distances (Gower 1985). In these cases, the sum of absolute values of eigenvalues is used in calculating the proportions explained, and real axes (corresponding to positive eigenvalues) will only explain a part of total variation (Mardia et al. 1979, Gower 1985).

References

Gower, J. C. (1985). Properties of Euclidean and non-Euclidean distance matrices. Linear Algebra and its Applications 67, 81--97.

Mardia, K. V., Kent, J. T. and Bibby, J. M. (1979). Chapter 14 of Multivariate Analysis, London: Academic Press.

Examples

Run this code

data(varespec)
data(varechem)
mod <- cca(varespec ~ Al + P + K, varechem)
ev <- eigenvals(mod)
ev
summary(ev)

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