confidenceEllipse {MVQuickGraphs}

Bivariate Normal Confidence Ellipse

Description

Draws a (1-alpha)100% confidence ellipse (two dimensional) for a multivariate normal distribution using the eigendecomposition of the covariance matrix.

Usage

confidenceEllipse(X.mean = c(0,0), eig, n, p,
xl = NULL, yl = NULL,
axes = TRUE, center = FALSE,
lim.adj = 0.02,
alpha = 0.05,
...)

Arguments

X.mean

a column matrix giving the mean of the two dimensions of the p-dimensional multivariate normal distribution.

eig

the eigenvalues and eigenvectors of the covariance matrix. This should be of the same form as the output of eigen, namely a list with two components: values and vectors. It is assumed that the largest eigenvalue is given first.

n

the number of observations.

p

the number of dimensions of the multivariate normal distribution. (The resulting graph will always be a two-dimensional confidence region for the two dimensions of a p-dimensional multivaraite normal distribution under consideration.)

xl

a vector giving the lower and upper limits of the x-axis for plotting. If xl = NULL (default), then reasonable values are computed automatically.

yl

a vector giving the lower and upper limits of the y-axis for plotting. If yl = NULL (default), then reasonable values are computed automatically.

axes

logical. If axes = TRUE (default) then the major and minor axes of the ellipse are plotted.

center

logical. If axes = TRUE then the center of the ellipse is indicated with a point and dashed lines are drawn to the x-axis and y-axis.

lim.adj

a value giving an adjustment to the x-axis and y-axis limits computed if either xl = NULL or yl = NULL. Essentially this is a way to have some coarse control over these limits for quick graphing: positive values will increase the distance between the upper and lower limits (making the ellipse appear smaller) while negative values will decrease the distance (and make the ellipse appear larger).

alpha

a value giving the value of alpha to be used when computing the contour. Contours are drawn at the 1-alpha level.

...

other arguments to be passed to the graphing functions.

Value

None

References

Johnson, R. A., & Wichern, D. W. (2007). Applied multivariate statistical analysis (6th ed). Pearson Prentice Hall.

Examples

# 90% Confidence Ellipse for Reading and Vocab from ability.cov
x.bar <- ability.cov$center[5:6]
Sigma <- ability.cov$cov[5:6,5:6]
n <- ability.cov$n.obs
p <- length(ability.cov$center)

confidenceEllipse(X.mean = x.bar,
                  eig = eigen(Sigma),
                  n = n, p = p,
                  alpha = 0.10)