Make an ellipse

A generic function returning an ellipse or other outline of a confidence region for two parameters.

Usage

ellipse(x, ...)
# S3 method for default
ellipse(x, scale = c(1, 1), centre = c(0, 0), level = 0.95,
    t = sqrt(qchisq(level, 2)), which = c(1, 2), npoints = 100, center = centre,
    ...)

Arguments

x: An object. In the default method the parameter x should be a correlation between -1 and 1 or a square positive definite matrix at least 2x2 in size. It will be treated as the correlation or covariance of a multivariate normal distribution.
...: Descendant methods may require additional parameters.
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), so no rescaling will be done.
centre: The centre of the ellipse will be at this position.
level: The confidence level of a pairwise confidence region. The default is 0.95, for a 95% region. This is used to control the size of the ellipse being plotted. A vector of levels may be used.
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 pair of variables from the matrix will be plotted. The default is the first 2.
npoints: The number of points used in the ellipse. Default is 100.
center: An alternative to centre to accommodate US spelling.

Value

An npoints x 2 matrix is returned with columns named according to the row names of the matrix x (default 'x' and 'y'), suitable for plotting.

Details

The default method uses the (cos(theta + d/2), cos(theta - d/2)) parametrization of an ellipse, where cos(d) is the correlation of the parameters.

References

Murdoch, D.J. and Chow, E.D. (1996). A graphical display of large correlation matrices. The American Statistician 50, 178-180. doi:10.2307/2684435 .

Examples

# Plot an ellipse corresponding to a 95% probability region for a
# bivariate normal distribution with mean 0, unit variances and 
# correlation 0.8.
plot(ellipse(0.8), type = 'l')