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

ellipse3d(x, ...)
# S3 method for default
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 lm
ellipse3d(x, which = 1:3, level = 0.95, t = sqrt(3 * qf(level,
3, x$df.residual)), ...) # S3 method for glm ellipse3d(x, which = 1:3, level = 0.95, t, dispersion, ...) # S3 method for nls ellipse3d(x, which = 1:3, level = 0.95, t = sqrt(3 * qf(level, 3, s$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. 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. The centre of the ellipse will be at this position. 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. 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. This parameter selects which variables from the object will be plotted. The default is the first 3. This controls the number of subdivisions (see subdivision3d) used in constructing the ellipsoid. Higher numbers give a smoother shape. If TRUE, smooth interpolation of normals is used; if FALSE, a faceted ellipsoid will be displayed. 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)
}

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