ord_pca: PCA with randomization test
In phytomosaic/ecole: ecole: School of Ecology Package

Description Usage Arguments Details Value References See Also Examples

Principal components analysis with randomization test for stopping rules.

1	ord_pca(x, B = 999, ...)

`x`	array, where rows = SUs and cols = variables such as environmental or traits values
`B`	numeric, number of randomizations
`...`	further arguments passed to other methods

PCA with stopping rules based on RndLambda, RndF, AvgRnd, or broken-stick (Peres-Neto et al. 2005). The current implementation hard-codes the cross-products matrix as a correlation matrix (i.e., data are scaled and centered).

List containing items returned by 'stats::prcomp', appended with further items:
- eig: eigenvalues.
- varexpl: proportion of variance explained.
- cumvar: cumulative variance explained.
- V: matrix of correlations between variables and the PCA scores.
- tab: table of randomization results by PCA axis.
- stopping: number of suggested dimensions, based on different stopping rules.

Peres-Neto, P.R., D.A. Jackson, and K.M. Somers. 2005. How many principal components? stopping rules for determining the number of non-trivial axes revisited. Computational Statistics and Data Analysis 49:974–997.

prcomp

data(smoky)
pc <- ord_pca(smoky$env)                    # PCA with randomization
plot(pc$x, type='n', asp=1) ; text(pc$x, cex=0.7)  # plot first two axes
head(pc$tab)                                # better format than `summary()`
pc$stopping                                 # number of dimensions
pc$V                                        # V = correlations with PC axes