Perform Principal Components Analysis (PCA)

This function appends the biplot object with elements resulting from performing PCA.

Usage

PCA(bp, dim.biplot = c(2, 1, 3), e.vects = 1:ncol(bp$X),
group.aes = NULL, show.class.means = FALSE, correlation.biplot = FALSE)

Arguments

bp: an object of class biplot obtained from preceding function biplot().
dim.biplot: the dimension of the biplot. Only values 1, 2 and 3 are accepted, with default 2.
e.vects: the vector indicating which eigenvectors (principal components) should be plotted in the biplot, with default 1:dim.biplot.
group.aes: a vector of the same length as the number of rows in the data matrix for differentiated aesthetics for samples.
show.class.means: a logical value indicating whether group means should be plotted in the biplot.
correlation.biplot: a logical value. If FALSE, the distances between sample points are optimally approximated in the biplot. If TRUE, the correlations between variables are optimally approximated by the cosine of the angles between axes. Default is FALSE.

Value

An object of class PCA with the following elements:

X: the matrix of the centered and scaled numeric variables.
Xcat: the data frame of the categorical variables.
raw.X: the original data.
classes: the vector of category levels for the class variable. This is to be used for colour, pch and cex specifications.
na.action: the vector of observations that have been removed.
center: a logical value indicating whether \(\mathbf{X}\) is centered.
scaled: a logical value indicating whether \(\mathbf{X}\) is scaled.
means: the vector of means for each numerical variable.
sd: the vector of standard deviations for each numerical variable.
n: the number of observations.
p: the number of variables.
group.aes: the vector of category levels for the grouping variable. This is to be used for colour, pch and cex specification.
g.names: the descriptive names to be used for group labels.
g: the number of groups.
Title: the title of the biplot rendered.
Z: the matrix with each row containing the details of the points that are plotted (i.e. coordinates).
Lmat: the matrix for transformation to the principal components.
Linv: the inverse of \(\mathbf{L}\).
eigenvalues: the vector of eigenvalues of the covariance matrix of \(\mathbf{X}\).
ax.one.unit: one unit in the positive direction of each biplot axis.
e.vects: the vector indicating which principal components are plotted in the biplot.
Vr: the 1:dim.biplot columns of \(\mathbf{V}\).
dim.biplot: the dimension of the biplot.
class.means: a logical value indicating whether group means are plotted in the biplot.
Zmeans: the matrix of class mean coordinates that are plotted in the biplot.

References

Gabriel, K.R. (1971) The biplot graphic display of matrices with application to principal component analysis. Biometrika. 58(3):453–467.

Examples

biplot(iris[,1:4]) |> PCA()
#> Object of class biplot, based on 150 samples and 4 variables.
#> 4 numeric variables.
# create a PCA biplot
biplot(data = iris) |> PCA() |> plot()