Make an ellipsoid — ellipse3d • rgl

A generic function and several methods returning an ellipsoid or other outline of a confidence region for three parameters.

ellipse3d(x, ...)
# Default S3 method
ellipse3d(x, scale = c(1, 1, 1), centre = c(0, 0, 0), level = 0.95, 
  t = sqrt(qchisq(level, 3)), which = 1:3, subdivide = 3, smooth = TRUE, ...)
# S3 method for class 'lm'
ellipse3d(x, which = 1:3, level = 0.95, t = sqrt(3 * qf(level, 
                                                3, x$df.residual)), ...)     
# S3 method for class 'glm'
ellipse3d(x, which = 1:3, level = 0.95, t, dispersion, ...) 
# S3 method for class 'nls'
ellipse3d(x, which = 1:3, level = 0.95, t = sqrt(3 * qf(level, 
                                                3, s$df[2])), ...)

Arguments

x: An object. In the default method the parameter x should be a square positive definite matrix at least 3x3 in size. It will be treated as the correlation or covariance of a multivariate normal distribution.
...: Additional parameters to pass to the default method or to qmesh3d.
scale: If x is a correlation matrix, then the standard deviations of each parameter can be given in the scale parameter. This defaults to c(1, 1, 1), so no rescaling will be done.
centre: The centre of the ellipse will be at this position.
level: The confidence level of a simultaneous confidence region. The default is 0.95, for a 95% region. This is used to control the size of the ellipsoid.
t: The size of the ellipse may also be controlled by specifying the value of a t-statistic on its boundary. This defaults to the appropriate value for the confidence region.
which: This parameter selects which variables from the object will be plotted. The default is the first 3.
subdivide: This controls the number of subdivisions (see subdivision3d) used in constructing the ellipsoid. Higher numbers give a smoother shape.
smooth: If TRUE, smooth interpolation of normals is used; if FALSE, a faceted ellipsoid will be displayed.
dispersion: The value of dispersion to use. If specified, it is treated as fixed, and chi-square limits for t are used. If missing, it is taken from summary(x).

Value

A mesh3d object representing the ellipsoid.

Examples

# Plot a random sample and an ellipsoid of concentration corresponding to a 95% 
# probability region for a
# trivariate normal distribution with mean 0, unit variances and 
# correlation 0.8.
if (requireNamespace("MASS", quietly = TRUE)) {
  Sigma <- matrix(c(10, 3, 0, 3, 2, 0, 0, 0, 1), 3, 3)
  Mean <- 1:3
  x <- MASS::mvrnorm(1000, Mean, Sigma)
  
  open3d()
  
  plot3d(x, box = FALSE)
  
  plot3d( ellipse3d(Sigma, centre = Mean), col = "green", alpha = 0.5, add = TRUE)
}  
3D plot


# Plot the estimate and joint 90% confidence region for the displacement and cylinder
# count linear coefficients in the mtcars dataset

data(mtcars)
fit <- lm(mpg ~ disp + cyl , mtcars)

open3d()
plot3d(ellipse3d(fit, level = 0.90), col = "blue", alpha = 0.5, aspect = TRUE)
3D plot