PCA {biplotEZ}

Perform Principal Components Analysis (PCA)

Description

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.

V.mat

the matrix containing the right singular vectors of \mathbf{X}.

Sigma.mat

the matrix with the singular values of \mathbf{X} on the diagonal.

U.mat

the matrix containing the left singular vectors of \mathbf{X}.

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()
# create a PCA biplot
biplot(data = iris) |> PCA() |> plot()