Principal Component Analysis

method
Principal Component Analysis (PCA) is an unconstrained ordination analysis suitable for linear (monotonic) relationships.
Published

January 26, 2024

Modified

January 25, 2024

Description

Principal component analysis (PCA) is used to reduce dimensionality in multivariate data analysis. This method is widely used in exploratory analysis and is better suited to the assessment of environmental variables. The primary objective of PCA is to transform the original variables into a new set of uncorrelated variables, called principal components, that capture the maximum variance in the data. These components are linear combinations of the original variables and are ranked according to the amount of variance they explain (eigenvalue). This method requires a rescaling of the variables (centering and standardisation) for a proper evaluation of the results.

In community analysis, PCA is better suited to assessing homogeneous vegetation and is prone to double-zero effects (inflated importance of rare species). In this respect, it is recommended to use transformation-based PCA instead.

Example

Ordination applied to the wetlands datase.

library(vegan)
pca_ord <- prcomp(USArrests, scale. = TRUE)
biplot(pca_ord)

Alternative functions

  • stats::prcomp()
  • vegan::rda() if only one table is provided as input
  • ade4::dudi.pca()

Further References