{rrcov}R Documentation

Robust Distance Plots


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)


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

ddplot(x, ...)
distplot(x, ...)
chi2qqplot(x, ...)
ellipse(x, ...)


x a mcd object, typically result of covMcd.
which Which plot to show? See Details for description of the options. Default is which="all".
classic whether to plot the classical distances too. Default is classic=FALSE.
ask logical; if 'TRUE', the user is asked before each plot, see 'par(ask=.)'. Default is ask = which=="all" && dev.interactive().
cutoff The cutoff value for the distances.
id.n Number of observations to identify by a label. If not supplied, the number of observations with distance larger than cutoff is used.
tol.inv tolerance to be used for computing the inverse see 'solve'. Default is tol.inv = 10e-7
... other parameters to be passed through to plotting functions.


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

tolellipse - a tolerance ellipse

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 distribution with p degrees of freedom. Points beyond these lines can be considered outliers.


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.

See Also



mcd <- covMcd(log(brain))

[Package rrcov version 0.2-5 Index]