Draw Conjugate Axes and Parallelogram Surrounding a Covariance Ellipse

Draw Conjugate Axes and Parallelogram Surrounding a Covariance Ellipse

Usage

ellipse.box(
  x,
  center = c(0, 0),
  which = 1:2,
  level = 0.95,
  radius = sqrt(qchisq(level, 2)),
  factor = c("cholesky", "pca"),
  draw = c("box", "diameters", "both"),
  ...
)

Arguments

x

A square positive definite matrix at least 2x2 in size. It will be treated as the correlation or covariance of a multivariate normal distribution.

center

The center of the ellipse

which

An integer vector to select which variables from the object x will be plotted. The default is the first 2.

level

The coverage level of a simultaneous region of the ellipse. The default is 0.95, for a 95\ ellipse.

radius

The size of the ellipsoid may also be controlled by specifying the value of a t-statistic on its boundary. This defaults to the square root of a chi-square statistic for a given level on 2 degrees of freedom, however in a small sample of n observations, a more accurate value is sqrt(2 * qf(level, 2, n - 1 )).

factor

A function defining the conjugate axes used to transform the unit circle into an ellipse. base::chol(), uses the right Cholesky factor of x.

draw

What to draw? "box", "diameters" or "both"

...

Other arguments passed to graphics::lines().

Value

Invisibly returns a 2 column matrix containing the end points of lines.

See also

Other covariance ellipses: covEllipses(), ellipse.axes(), ellipse3d.axes()

Examples

data(iris)
cov <- cov(iris[,3:4])
mu <- colMeans(iris[,3:4])

radius <- sqrt(qchisq(0.68, 2))
plot(iris[,3:4], asp=1)
car::ellipse(mu, cov, radius = radius)
ellipse.axes(cov, center=mu, level = 0.68,
            labels = TRUE)
ellipse.box(cov, center=mu, level = 0.68, 
            factor = "pca", 
            col = "red", lwd = 2 )

res <- ellipse.box(cov, center=mu, level = 0.68, factor = "chol", col = "green", lwd = 2 )

res
#>      Petal.Length Petal.Width
#> [1,]      6.42288   2.6179312
#> [2,]      1.09312   0.4020543
#> [3,]      1.09312  -0.2192645
#> [4,]      6.42288   1.9966124
#> [5,]      6.42288   2.6179312