The function draws covariance ellipses for one or more groups and optionally
for the pooled total sample. It uses either the classical product-moment
covariance estimate, or a robust alternative, as provided by
cov.rob. Provisions are provided to do this for more
than two variables, in a scatterplot matrix format.
covEllipses(x, ...)# S3 method for data.frame
covEllipses(
x,
group,
pooled = TRUE,
method = c("classical", "mve", "mcd"),
...
)
# S3 method for matrix
covEllipses(
x,
group,
pooled = TRUE,
method = c("classical", "mve", "mcd"),
...
)
# S3 method for formula
covEllipses(x, data, ...)
# S3 method for boxM
covEllipses(x, ...)
# S3 method for default
covEllipses(
x,
means,
df,
labels = NULL,
variables = 1:2,
level = 0.68,
segments = 60,
center = FALSE,
center.pch = "+",
center.cex = 2,
col = getOption("heplot.colors", c("red", "blue", "black", "darkgreen", "darkcyan",
"brown", "magenta", "darkgray")),
lty = 1,
lwd = 2,
fill = FALSE,
fill.alpha = 0.3,
label.pos = 0,
xlab,
ylab,
vlabels,
var.cex = 2,
main = "",
xlim,
ylim,
axes = TRUE,
offset.axes,
add = FALSE,
...
)
Nothing is returned. The function is used for its side-effect of producing a plot.
The generic argument. For the default method, this is a list of
covariance matrices. For the data.frame and matrix methods,
this is a numeric matrix of two or more columns supplying the variables to
be analyzed.
Other arguments passed to the default method for plot,
text, and points
a factor defining groups, or a vector of length
n=nrow(x) doing the same. If missing, a single covariance ellipse is
drawn.
Logical; if TRUE, the pooled covariance matrix for the
total sample is also computed and plotted
the covariance method to be used: classical product-moment
("classical"), or minimum volume ellipsoid ("mve"), or minimum
covariance determinant ("mcd").
For the formula method, a data.frame in which to evaluate.
For the default method, a matrix of the means for all groups
(followed by the grand means, if pooled=TRUE). Rows are the groups,
and columns are the variables. It is assumed that the means have column
names corresponding to the variables in the covariance matrices.
For the default method, a vector of the degrees of freedom for the covariance matrices
Either a character vector of labels for the groups, or
TRUE, indicating that group labels are taken as the names of the
covariance matrices. Use labels="" to suppress group labels, e.g.,
when add=TRUE
indices or names of the response variables to be plotted;
defaults to 1:2. If more than two variables are supplied, the
function plots all pairwise covariance ellipses in a scatterplot matrix
format.
equivalent coverage of a data ellipse for normally-distributed
errors, defaults to 0.68.
number of line segments composing each ellipse; defaults to
40.
If TRUE, the covariance ellipses are centered at the
centroid.
character to use in plotting the centroid of the data;
defaults to "+".
size of character to use in plotting the centroid of the
data; defaults to 2.
a color or vector of colors to use in plotting ellipses ---
recycled as necessary A single color can be given, in which case it is used
for all ellipses. For convenience, the default colors for all plots
produced in a given session can be changed by assigning a color vector via
options(heplot.colors =c(...). Otherwise, the default colors are
c("red", "blue", "black", "darkgreen", "darkcyan", "magenta", "brown",
"darkgray").
vector of line types to use for plotting the ellipses; the first
is used for the error ellipse, the rest --- possibly recycled --- for the
hypothesis ellipses; a single line type can be given. Defaults to
2:1.
vector of line widths to use for plotting the ellipses; the first
is used for the error ellipse, the rest --- possibly recycled --- for the
hypothesis ellipses; a single line width can be given. Defaults to
1:2.
A logical vector indicating whether each ellipse should be filled or not. The first value is used for the error ellipse, the rest --- possibly recycled --- for the hypothesis ellipses; a single fill value can be given. Defaults to FALSE for backward compatibility. See Details below.
Alpha transparency for filled ellipses, a numeric scalar
or vector of values within [0,1], where 0 means fully transparent and
1 means fully opaque. Defaults to 0.3.
Label position, a vector of integers (in 0:4) or
character strings (in c("center", "bottom", "left", "top", "right"))
use in labeling ellipses, recycled as necessary. Values of 1, 2, 3 and 4,
respectively indicate positions below, to the left of, above and to the
right of the max/min coordinates of the ellipse; the value 0 specifies the
centroid of the ellipse object. The default, label.pos=NULL
uses the correlation of the ellipse to determine "top" (r>=0) or
"bottom" (r<0).
x-axis label; defaults to name of the x variable.
y-axis label; defaults to name of the y variable.
Labels for the variables can also be supplied through this
argument, which is more convenient when length(variables) > 2.
character size for variable labels in the pairs plot
main plot label; defaults to "", and presently has no
effect.
x-axis limits; if absent, will be computed from the data.
y-axis limits; if absent, will be computed from the data.
Whether to draw the x, y axes; defaults to TRUE
proportion to extend the axes in each direction if computed from the data; optional.
if TRUE, add to the current plot; the default is
FALSE. This argument is has no effect when more than two variables
are plotted.
Michael Friendly
These plot methods provide one way to visualize possible heterogeneity of within-group covariance matrices in a one-way MANOVA design. When covariance matrices are nearly equal, their covariance ellipses should all have the same shape. When centered at a common mean, they should also all overlap.
The can also be used to visualize the difference between classical and robust covariance matrices.
heplot, boxM,
data(iris)
# compare classical and robust covariance estimates
covEllipses(iris[,1:4], iris$Species)
covEllipses(iris[,1:4], iris$Species, fill=TRUE, method="mve", add=TRUE, labels="")
# method for a boxM object
x <- boxM(iris[, 1:4], iris[, "Species"])
x
covEllipses(x, fill=c(rep(FALSE,3), TRUE) )
covEllipses(x, fill=c(rep(FALSE,3), TRUE), center=TRUE, label.pos=1:4 )
# method for a list of covariance matrices
cov <- c(x$cov, pooled=list(x$pooled))
df <- c(table(iris$Species)-1, nrow(iris)-3)
covEllipses(cov, x$means, df, label.pos=3, fill=c(rep(FALSE,3), TRUE))
covEllipses(cov, x$means, df, label.pos=3, fill=c(rep(FALSE,3), TRUE), center=TRUE)
# scatterplot matrix version
covEllipses(iris[,1:4], iris$Species,
fill=c(rep(FALSE,3), TRUE), variables=1:4,
fill.alpha=.1)
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