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#### This is from the R package
####
#### rrcov : Scalable Robust Estimators with High Breakdown Point
####
#### by Valentin Todorov
### This program is free software; you can redistribute it and/or modify
### it under the terms of the GNU General Public License as published by
### the Free Software Foundation; either version 2 of the License, or
### (at your option) any later version.
###
### This program is distributed in the hope that it will be useful,
### but WITHOUT ANY WARRANTY; without even the implied warranty of
### MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
### GNU General Public License for more details.
###
### You should have received a copy of the GNU General Public License
### along with this program; if not, a copy is available at
## http://www.r-project.org/Licenses/
## I would like to thank Peter Filzmoser for providing the initial code of
## this function.
plot.mcd <-
function(x,
which=c("all", "dd","distance","qqchi2","tolEllipsePlot","screeplot"),
classic= FALSE,
ask = (which[1] == "all" && dev.interactive()),
cutoff = NULL, id.n, labels.id = rownames(x$X), cex.id = 0.75,
label.pos = c(4,2), tol = 1e-7, ...)
{
if (!inherits(x, "mcd"))
stop("Use only with 'mcd' objects")
covPlot(x$X, which= which, classic= classic, ask= ask, m.cov = x,
cutoff= cutoff, id.n = id.n, labels.id, cex.id = cex.id,
label.pos = label.pos, tol = tol, ...)
}
covPlot <-
function(x, which = c("all", "dd", "distance", "qqchi2",
"tolEllipsePlot", "screeplot"),
classic = FALSE,
ask = (which[1] == "all" && dev.interactive()),
m.cov = covMcd(x), cutoff = NULL,
id.n, labels.id = rownames(x), cex.id = 0.75,
label.pos = c(4,2), tol = 1e-7, ...)
{
##@bdescr
## Make plots based on the covariance structure of a data set:
## dd - distance-distance plot: Robust distances versus
## Mahalanobis distances
## distance - a plot of the robust distances
## qqchi2 - a qq-plot of the robust distances versus the
## quantiles of the chi-squared distribution
## tolEllipsePlot- a tolerance ellipse
## screeplot- a screeplot of the eigenvalues ov the covariance matrix
##
## Distance Plot:
## Draw a Distance-Distance Plot: Plots the robust distances
## versus the classical Mahalanobis distances as introduced by
## Rousseeuw, P. J., and van Zomeren, B. C. (1990). Unmasking
## Multivariate Outliers and Leverage Points. Journal of the American
## Statistical Association, 85, 633-639.
##
## The dashed line is the set of points where the robust distance is
## equal to the classical distance.
## The horizontal and vertical dotted lines are drawn at values equal cutoff
## which defaults to square root of the 97.5% quantile of a chi-squared
## distribution with p degrees of freedom. Points beyond these lines can
## be considered outliers.
##
##@edescr
##
##@in x : [matrix] A data.frame or matrix, n > 2*p
##@in which : [character] A plot option, one of:
## classic: index plot of the classical mahalanobis distances
## robust : index plot of the robust mahalanobis distances
## dd : distance-distance plot
## index : parallel index plot of classical and robust distances
## all : all three plots --- this is the default
##
##@in classic : [logical] If true the classical plot will be displayed too
## default is classic = FALSE
##@in m.cov : [list] An object like class "mcd" - only its attributes
## center and cov will be used
##@in cutoff : [number] The cutoff value for the distances
##@in id.n : [number] number of observations to be identified with a label.
## Defaults to the number of observations with
## distance larger than cutoff -- missing is propagated
##@in tol : [number] tolerance to be used for computing the inverse
## - see 'solve'. defaults to 1e-7
## NOTE: The default tolerance 1e-7, will not work for some example
## data sets, like milk or aircraft
myscreeplot <- function(x, m.cov = covMcd(x))
{
erob <- eigen(m.cov$cov,symmetric = TRUE, only.values = TRUE)$values
eclass <- eigen(var(x), symmetric = TRUE, only.values = TRUE)$values
leg.txt <- c("Robust", "Classical")
leg.col <- c("green", "red")
leg.pch <- c(1,24)
leg.lty <- c("solid", "dotted")
eall <- c(erob,eclass)
ylim <- c( min(eall), max(eall))
plot(erob, ylim=ylim, ylab="Eigenvalues", xlab="Index", type="n")
legend("topright", leg.txt, pch = leg.pch, lty = leg.lty, col = leg.col)
lines(erob, type="o", pch= leg.pch[1], lty= leg.lty[1], col=leg.col[1])
lines(eclass, type="o", pch= leg.pch[2], lty= leg.lty[2], col=leg.col[2])
title(main = "Scree plot")
}
mydistplot <- function(x, cutoff, classic = FALSE, id.n) {
## Index Plot:
## Plot the vector x (robust or mahalanobis distances) against
## the observation indexes. Identify by a label the id.n
## observations with largest value of x. If id.n is not supplied,
## calculate it as the number of observations larger than cutoff.
## Use cutoff to draw a horisontal line.
## Use classic = FALSE/TRUE to choose the label of the vertical axes
n <- length(x)
if(missing(id.n)) # maybe propagated
id.n <- length(which(x > cutoff))
ylab <- paste("Square Root of",
if(classic) "Mahalanobis" else "Robust",
"distance")
plot(x, type = "p", ylab = ylab, xlab = "Index",
main = "Distance Plot")
label(1:n, x, id.n)
abline(h = cutoff)
}
myddplot <- function(md, rd, cutoff, id.n) {
## Distance-Distance Plot:
## Plot the vector y = rd (robust distances) against
## x = md (mahalanobis distances). Identify by a label the id.n
## observations with largest rd. If id.n is not supplied, calculate
## it as the number of observations larger than cutoff. Use cutoff
## to draw a horisontal and a vertical line. Draw also a dotted line
## with a slope 1.
n <- length(md)
if(missing(id.n)) # maybe propagated
id.n <- length(which(rd > cutoff))
xlab <- "Mahalanobis distance"
ylab <- "Robust distance"
plot(md, rd, type = "p", xlab = xlab, ylab = ylab,
main = "Distance-Distance Plot")
label(md, rd, id.n)
abline(0, 1, lty = 2)
abline(v = cutoff, h = cutoff)
}
qqplot <- function(x, p, cutoff = sqrt(qchisq(0.975, p)),
classic = FALSE, id.n)
{
## Chisquare QQ-Plot:
## Plot the vector x (robust or mahalanobis distances) against
## the square root of the quantiles of the chi-squared distribution
## with p degrees of freedom.
## Identify by a label the id.n observations with largest value of x.
## If id.n is not supplied, calculate it as the number of observations
## larger than cutoff.
## Use classic = FALSE/TRUE to choose the label of the vertical axes
## parameters and preconditions
n <- length(x)
if(missing(id.n)) # maybe propagated
id.n <- length(which(x > cutoff))
qq <- sqrt(qchisq(((1:n)-1/3)/(n+1/3), p))
x <- sort(x, index.return = TRUE)
ix <- x$ix
x <- x$x
ylab <- paste(if(classic) "Mahalanobis" else "Robust", "distance")
xlab <- "Square root of the quantiles of the chi-squared distribution"
plot(qq, x, xlab = xlab, ylab = ylab, main = "Chisquare QQ-Plot")
label(qq, x, id.n, ind = (n-id.n+1):n, labs = ix)
abline(0, 1, lty = 2)
} ## end{qqplot}
label <- function(x, y, id.n,
ind = sort.list(y, decreasing = TRUE)[1:id.n],
labs = labels.id, adj.x = TRUE)
{
if(id.n > 0) { ## label the largest 'id.n' y-values
labpos <-
if(adj.x) label.pos[1+ as.numeric(x > mean(range(x)))] else 3
text(x[ind], y[ind], labs[ind],
cex = cex.id, xpd = TRUE, pos = labpos, offset = 0.25)
}
}
## Begin{covPlot} -- arguments checking of preconditions
if(is.data.frame(x))
x <- data.matrix(x)
if(!is.matrix(x) || !is.numeric(x))
stop("x is not a numeric dataframe or matrix.")
n <- dim(x)[1]
p <- dim(x)[2]
if(!is.numeric(m.cov$center) || !is.numeric(m.cov$cov))
stop("argument 'm.cov' must have numeric components 'center' and 'cov'")
if(length(m.cov$center) != p)
stop("Data set and provided center have different dimensions!")
## ?covPlot says it only needs 'cov' and 'center'
## Maybe should be smarter and *test* for non-singularity
if(is.numeric(m.cov$crit) && m.cov$crit == 0)
stop( "The covariance matrix is singular!")
if(is.null(cutoff))
cutoff <- sqrt(qchisq(0.975, p))
## now "more in line" with plot.lm()'s labeling:
if(is.null(labels.id))
labels.id <- as.character(1:n)
if(!missing(id.n) && !is.null(id.n)) {
id.n <- as.integer(id.n)
if(id.n < 0 || id.n > n)
stop(sQuote("id.n")," must be in {1,..,",n,"}")
}
which <- match.arg(which)
md <- sqrt(mahalanobis(x, colMeans(x), var(x), tol = tol))
rd <- sqrt(mahalanobis(x, m.cov$center, m.cov$cov, tol = tol))
## *Never* here : par(mfrow = c(1,1), pty = "m")
op <- if (ask) par(ask = TRUE) else list()
on.exit(par(op))
if(which == "all" || which == "distance") {
if(classic) {
opr <- if(prod(par("mfrow")) == 1)
par(mfrow = c(1,2), pty = "m") else list()
}
## index plot of mahalanobis distances:
mydistplot(rd, cutoff, id.n = id.n)
if(classic) {
## index plot of robust distances:
mydistplot(md, cutoff, classic = TRUE, id.n = id.n)
par(opr)
}
}
if(which == "all" || which == "dd") {
myddplot(md, rd, cutoff = cutoff, id.n = id.n) # distance-distance plot
}
if(which == "all" || which == "qqchi2") {
if(classic) {
opr <- if(prod(par("mfrow")) == 1)
par(mfrow = c(1,2), pty = "m") else list()
}
## qq-plot of the robust distances versus the
## quantiles of the chi-squared distribution
qqplot(rd, p, cutoff = cutoff, id.n = id.n)
if(classic) { ## qq-plot of the mahalanobis distances
qqplot(md, p, cutoff = cutoff, classic = TRUE, id.n = id.n)
par(opr)
}
}
if(which == "all" || which == "tolEllipsePlot") {
if(p == 2)
tolEllipsePlot(x, m.cov = m.cov, cutoff = cutoff,
id.n = id.n, classic = classic, tol = tol)
else if(which != "all")
warning("For tolerance ellipses the dimension 'p' must be 2!")
}
if(which == "all" || which == "screeplot") {
myscreeplot(x, m.cov = m.cov)
}
} ## end { covPlot }
## ddplot <- function(x,...) {
## covPlot(x, which="dd", ...)
## }
## distplot <- function(x,...) {
## covPlot(x, which="distance", ...)
## }
## chi2qqplot <- function(x,...) {
## covPlot(x, which="qqchi2", ...)
## }
## ellipse() exists in other packages
## ellipse <- function(x,...) {
## covPlot(x, which="tolEllipsePlot", ...)
## }
|
