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

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

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