ellipse.default {ellipse}R Documentation

Produces an ellipse from a covariance matrix or a correlation

Description

This function produces an ellipse representing a pairwise confidence region for two parameters, given a covariance or correlation matrix or just a correlation, and a position.

Usage

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

Arguments

x 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.
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. Default c(0,0).
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.

Details

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

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.

References

Murdoch, D.J. and Chow, E.D. (1994). A graphical display of large correlation matrices. Mathematical preprint #1994-09, Department of Mathematics and Statistics, Queen's University, Kingston, Canada.

See Also

ellipse

Examples

#  Make a 2 x 2 covariance matrix, and plot the corresponding 95%
#  confidence region
cov <- matrix(c(1,0.5,0.5,1), 2,2)
plot(ellipse(cov))