Concentration ellipses (\(\kappa\)-ellipses)

This function produces \(\kappa\)-ellipses, which is a useful geometrical description of the data points about the sample mean.

Usage

ellipses(bp, df=2, kappa = NULL, which = NULL,
alpha = 0.95, col = bp$sample$col[which], lty = 1, lwd = 1,
opacity = 0.25, trace = TRUE)

Arguments

bp: an object of class biplot.
df: degrees of freedom, with default 2.
kappa: value to construct \(\kappa\)-ellipse (the value of \(\kappa\)).
which: the selection of the group for ellipse construction.
alpha: size of \(\alpha\)-bag, with default 0.95.
col: colour of ellipse. Multiple \(\kappa\)-ellipse for one group will be displayed in the same colour.
lty: line type of ellipse. The same line type will be used per value of \(\kappa\).
lwd: line width of ellipse. The same line width will be used per value of \(\kappa\).
opacity: level of opacity, with default 0.25.
trace: logical, indicating progress of computation.

Value

A list with the following components is available:

conc.ellipses: list of coordinates for the \(\kappa\)-ellipses for each group.
col: vector of colours for the \(\kappa\)-ellipses.
lty: vector of line types for the \(\kappa\)-ellipses.
lwd: vector of line widths for the \(\kappa\)-ellipses.
alpha: vector of \(\alpha\) values.

References

Gower, J., Gardner-Lubbe, S. & Le Roux, N. (2011, ISBN: 978-0-470-01255-0) Understanding Biplots. Chichester, England: John Wiley & Sons Ltd.

Examples

biplot (iris[,1:4]) |> PCA(group.aes=iris[,5]) |> ellipses(kappa=2) |> plot()
#> Computing 2 -ellipse for setosa 
#> Computing 2 -ellipse for versicolor 
#> Computing 2 -ellipse for virginica