ellipse.default: 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
## S3 method for class '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)
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.
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.
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 (cos(theta + d/2), cos(theta - d/2)) parametrization of an ellipse is
used, 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.
# Make a 2 x 2 covariance matrix, and plot the corresponding 95\%# confidence regioncov <- matrix(c(1, 0.5, 0.5, 1), 2, 2)
plot(ellipse(cov), type = 'l')