Ellipses: Confidence ellipses

In shipunov: Miscellaneous Functions from Alexey Shipunov

Confidence ellipses

Description

Calculates and plots group confidence ellipses

Usage

Ellipses(pts, groups, match.color=TRUE, usecolors=NULL,
 centers=FALSE, c.pch=0, c.cex=3,
 level=0.95, df=1000, prec=51,
 coords=NULL, plot=TRUE, ...)

Arguments

pts	Data points to plot
groups	Grouping variable
match.color	Match colors
usecolors	Use colors (palette)
centers	Show centers?
c.pch	Color of center points
c.cex	Scale of center points
level	Confidence level for F-distribution
df	Used in calculation of P-content according to F(2, df) distribution
prec	Precision of ellipse plotting (default is 51 points)
coords	Pre-calculated ellipses coordinates: list of two-column matrices named as groups (by default, not required)
plot	Plot?
...	Arguments to lines()

Details

Note that (at least at the moment), ellipses are plotted with line(), therefore shading is not straightforward (but possible, see examples).

Also, with a help from Pinhull() (see its help), it is possible to reveal "outliers", points outside of each ellipse borders.

See also package 'cluster' for ellipsoidhulls() function that allows to draw ellipse-like hulls.

Value

Invisibly returns the list in the form similar to Hulls(), to use as a list of polygons or with Overlap().

Author(s)

Alexey Shipunov

See Also

Hulls, Overlap, Pinhull

Examples

iris.p <- prcomp(iris[, -5])$x[, 1:2]
plot(iris.p, type="n", xlab="PC1", ylab="PC2")
text(iris.p, labels=abbreviate(iris[, 5], 1, method="both.sides"))
iris.e <- Ellipses(iris.p[, 1:2], iris[, 5], centers=TRUE)

## calculate overlap between ellipses
Overlap(iris.e)

## how to plot filled ellipses
plot(iris.p, type="n", xlab="PC1", ylab="PC2")
text(iris.p, labels=abbreviate(iris[, 5], 1, method="both.sides"))
for (i in seq_along(iris.e))
 polygon(iris.e[[i]], border=NA, col=adjustcolor(i, alpha.f=0.2))

## how to reveal (and label) "outliers", points outside of _all_ ellipses
iris.pie <- Pinhull(iris.p, iris.e)
outs <- which(apply(iris.pie, 1, sum) == 0)
points(iris.p[outs, ], cex=2, pch=4)

## embedded convex hulls
plot(iris.p, col=iris$Species)
for (i in seq_along(iris.e)) lines(iris.e[[i]], col=i, lty=2)
mi <- cbind(seq_len(nrow(iris)), as.numeric(iris$Species)) # indexing matrix
## remove "outliers" in broad sense, points which are outside of its "own" ellipse:
emb <- rowSums(iris.pie) == 1 & iris.pie[mi]
Hulls(iris.p[emb, ], iris$Species[emb])

## LDA ellipes
library(MASS)
ch.lda <- lda(Species ~ ., data=chaetocnema[, -2])
ch.lda.pred <- predict(ch.lda, chaetocnema[, -(1:2)])
## ellipses here are by default bigger then plot so use workaround:
ee <- Ellipses(ch.lda.pred$x, chaetocnema$Species, plot=FALSE)
xx <- range(c(do.call(rbind, ee)[, 1], ch.lda.pred$x[, 1]))
yy <- range(c(do.call(rbind, ee)[, 2], ch.lda.pred$x[, 2]))
plot(ch.lda.pred$x, col=chaetocnema$Species, xlim=xx, ylim=yy)
Ellipses(ch.lda.pred$x, chaetocnema$Species, coords=ee)

## search for the maximal level which gives zero overlap
plot(x5 ~ x17, data=haltica, pch=as.numeric(haltica$Species))
for (i in (99:59)/100) {
cat(i, "\n")
ee <- Ellipses(haltica[, c("x17", "x5")], haltica$Species, level=i, plot=FALSE)
print(mean(Overlap(ee), na.rm=TRUE))
cat("\n")
}
Ellipses(haltica[, c("x17", "x5")], haltica$Species, level=.62)

shipunov documentation built on Feb. 16, 2023, 9:05 p.m.