R: Extract Eigenvalues from an Ordination Object

eigenvals {vegan} | R Documentation

## 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

`x` | An object from which to extract eigenvalues.
`object` | An `eigenvals` result object.
`constrained` | Return only constrained eigenvalues.
`...` | Other arguments to the functions (usually ignored)

### 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).

### Value

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

### Author(s)

Jari Oksanen.

### 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.

### See Also

`eigen`, `svd`, `prcomp`, `princomp`, `cca`, `rda`, `capscale`, `wcmdscale`, `cca.object`.

### Examples

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

[Package vegan version 2.4-3 Index]