plot.mcd: Robust Distance Plots

Description

Shows the Mahalanobis distances based on robust and classical estimates of the location and the covariance matrix in different plots. The following plots are available:

index plot of the robust and mahalanobis distances
distance-distance plot
Chisquare QQ-plot of the robust and mahalanobis distances
plot of the tolerance ellipses (robust and classic)
Scree plot - Eigenvalues comparison plot

Usage

## S3 method for class 'mcd':
plot(x,
     which = c("all", "dd", "distance", "qqchi2", "tolEllipsePlot", "screeplot"),
     classic = FALSE, ask = (which=="all" && dev.interactive()),
     cutoff, id.n, tol = 1e-7, ...)

Arguments

a mcd object, typically result of covMcd.

which

string indicating which plot to show. See the Details section for a description of the options. Defaults to "all".

classic

whether to plot the classical distances too. Default is FALSE.

ask

logical indicating if the user should be asked before each plot, see par(ask=.). Defaults to which == "all" && dev.interactive().

cutoff

the cutoff value for the distances.

id.n

number of observations to be identified by a label. If not supplied, the number of observations with distance larger than cutoff is used.

tol

tolerance to be used for computing the inverse, see solve. Defaults to tol = 1e-7.

...

other parameters to be passed through to plotting functions.

Details

This function produces several plots based on the robust and classical location and covariance matrix. Which of them to select is specified by the attribute which. The possible options are:

distance - index plot of the robust distances;

dd - distance-distance plot;

qqchi2 - a qq-plot of the robust distances versus the quantiles of the chi-squared distribution

tolEllipsePlot - a tolerance ellipse

screeplot - an eigenvalues comparison plot - screeplot

The Distance-Distance Plot, introduced by Rousseeuw and van Zomeren (1990), displays the robust distances versus the classical Mahalanobis distances. The dashed line is the set of points where the robust distance is equal to the classical distance. The horizontal and vertical lines are drawn at values equal to the 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.

References

P. J. Rousseeuw and van Zomeren, B. C. (1990). Unmasking Multivariate Outliers and Leverage Points. Journal of the American Statistical Association 85, 633--639.

P. J. Rousseeuw and K. van Driessen (1999) A fast algorithm for the minimum covariance determinant estimator. Technometrics 41, 212--223.

Examples

Run this code

data(Animals, package ="MASS")
brain <- Animals[c(1:24, 26:25, 27:28),]
mcd <- covMcd(log(brain))

plot(mcd, which = "distance", classic = TRUE)# 2 plots
plot(mcd, which = "dd")
plot(mcd, which = "tolEllipsePlot", classic = TRUE)
op <- par(mfrow = c(2,3))
plot(mcd) ## -> which = "all" (5 plots)
par(op)
op <- par(mfrow = c(3,3))
plot(mcd, classic = TRUE) ## -> which = "all" (7 plots)
par(op)