Calculate Hotelling or data ellipse around some points

Usage

hotelling_ellipse(
  x,
  level = 0.95,
  npoints = 100,
  type = c("t2data", "t2mean", "c2data"),
  robust = FALSE
)

Arguments

x: A two-column matrix or data frame like object
level: Either coverage probability (for type = "t2data" or "c2data") or confidence level (for type = "t2mean").
npoints: Number of points to estimate
type: t2data - Hotelling T2 data ellipse; t2mean - Hotelling confidence interval for the mean; c2data - normal data ellipse (using chi squared distribution).
robust: If TRUE, then robust estimates of mean and covariance are used

Value

A two-column matrix or data frame with npoints rows, containing the coordinates of the ellipse. The columns are named "x" and "y".

Details

Calculate the T2 Hotelling ellipse or a data ellipse for the given coverage probability. There are three types of ellipses which can be plotted:

T2 Hotelling data ellipses, showing data coverage (like the type="t" version of stat_ellipse)
normal multivariate distribution ellipses (like the type="norm" version of the stat_ellipse) which use Mahalanobis distance and chi-squared statistic
T2 Hotelling confidence ellipses of the group means.

The latter (for group means) correspond to the confidence interval for the mean in the univariate world, so the ellipses are very small (depending on the number of points).

The function can also use a robust estimator of location and scatter using the covMcd function, which uses the Maximum Covariance Determinant (MCD) estimator. Note that while this results in ellipses which are more resistent to outliers, the interpretation slightly changes, as the T2 statistic used is only an approximation in this case. In other words, use it for visualisation and QC, but not for statistical testing.

Examples

df <- iris[ iris$Species == "setosa", 1:2 ]
eli <- hotelling_ellipse(df)
plot(df[,1], df[,2])
lines(eli)