Draw classical and robust covariance ellipses for one or more groups

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.

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.

They can also be used to visualize the difference between classical and robust covariance matrices by overlaying the two in a single plot (via add=TRUE).

Usage

covEllipses(x, ...)

# S3 method for class 'data.frame'
covEllipses(
  x,
  group,
  pooled = TRUE,
  method = c("classical", "mve", "mcd"),
  ...
)

# S3 method for class 'matrix'
covEllipses(
  x,
  group,
  pooled = TRUE,
  method = c("classical", "mve", "mcd"),
  ...
)

# S3 method for class 'formula'
covEllipses(x, data, ...)

# S3 method for class 'boxM'
covEllipses(x, ...)

# Default S3 method
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,
  ...
)

Arguments

x: 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
group: a factor defining groups, or a vector of length n=nrow(x) doing the same. If missing, a single covariance ellipse is drawn.
pooled: Logical; if TRUE, the pooled covariance matrix for the total sample is also computed and plotted
method: the covariance method to be used: classical product-moment ("classical"), or minimum volume ellipsoid ("mve"), or minimum covariance determinant ("mcd").
data: For the formula method, a data.frame in which to evaluate.
means: 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.
df: For the default method, a vector of the degrees of freedom for the covariance matrices
labels: 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
variables: 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.
level: equivalent coverage of a data ellipse for normally-distributed errors, defaults to 0.68.
segments: number of line segments composing each ellipse; defaults to 40.
center: If TRUE, the covariance ellipses are centered at the centroid.
center.pch: character to use in plotting the centroid of the data; defaults to "+".
center.cex: size of character to use in plotting the centroid (means) of the data; defaults to 2.
col: a color or vector of colors to use in plotting ellipses— recycled as necessary— see Details. 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").
lty: vector of line types to use for plotting the ellipses— recycled as necessary— see Details. Defaults to 1.
lwd: vector of line widths to use for plotting the ellipses— recycled as necessary— see Details. Defaults to 2.
fill: A logical vector indicating whether each ellipse should be filled or not— recycled as necessary— see Details. Defaults to FALSE.
fill.alpha: 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.pos: 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).
xlab: x-axis label; defaults to name of the x variable.
ylab: y-axis label; defaults to name of the y variable.
vlabels: Labels for the variables can also be supplied through this argument, which is more convenient when length(variables) > 2.
var.cex: character size for variable labels in the pairs plot, when length(variables) > 2.
main: main plot label; defaults to "", and presently has no effect.
xlim: x-axis limits; if absent, will be computed from the data.
ylim: y-axis limits; if absent, will be computed from the data.
axes: Whether to draw the x, y axes; defaults to TRUE
offset.axes: proportion to extend the axes in each direction if computed from the data; optional.
add: if TRUE, add to the current plot; the default is FALSE. This argument is has no effect when more than two variables are plotted.

Value

Nothing is returned. The function is used for its side-effect of producing a plot.

Details

The arguments labels, col, lty, lwd, fill, fill.alpha and label.pos are used to draw the ellipses for the groups and also for the pooled, within-group covariance, which is the last in a list when these are computed by the functions. These arguments are each taken in the order specified, and recycled as necessary.

Author

Michael Friendly

Examples



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
#> 
#> 	Box's M-test for Homogeneity of Covariance Matrices
#> 
#> data:  iris[, 1:4]
#> Chi-Sq (approx.) = 140.94, df = 20, p-value < 2.2e-16
#> 
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)