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Calculate Hotelling or data ellipse around some points

hotelling_ellipse.Rd

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

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 Mahalonibis 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.

See also

outliers() for calculating per-point based T2 and Mahalonibis values and geom_hotelling() for plotting of the ellipse with ggplot

Examples

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