Adjusted Quantile Plot
The function aq.plot plots the ordered squared robust Mahalanobis distances of the observations against the empirical distribution function of the $MD^2_i$. In addition the distribution function of $chisq_p$ is plotted as well as two vertical lines corresponding to the chisq-quantile specified in the argument list (default is 0.975) and the so-called adjusted quantile. Three additional graphics are created (the first showing the data, the second showing the outliers detected by the specified quantile of the $chisq_p$ distribution and the third showing these detected outliers by the adjusted quantile).
aq.plot(x, delta=qchisq(0.975, df=ncol(x)), quan=1/2, alpha=0.05)
x |
matrix or data.frame containing the data; has to be at least two-dimensional |
delta |
quantile of the chi-squared distribution with ncol(x) degrees of freedom. This quantile appears as cyan-colored vertical line in the plot. |
quan |
proportion of observations which are used for mcd estimations; has to be between 0.5 and 1, default ist 0.5 |
alpha |
Maximum thresholding proportion (optional scalar, default: alpha = 0.05) |
The function aq.plot plots the ordered squared robust Mahalanobis distances of the observations against the empirical distribution function of the $MD^2_i$. The distance calculations are based on the MCD estimator.
For outlier detection two different methods are used. The first one marks observations as outliers if they exceed a certain quantile of the chi-squared distribution. The second is an adaptive procedure searching for outliers specifically in the tails of the distribution, beginning at a certain chisq-quantile (see Filzmoser et al., 2005).
The function behaves differently depending on the dimension of the data. If the data is more than two-dimensional the data are projected on the first two robust principal components.
outliers |
boolean vector of outliers |
Moritz Gschwandtner <e0125439@student.tuwien.ac.at>
Peter Filzmoser <P.Filzmoser@tuwien.ac.at>
http://cstat.tuwien.ac.at/filz/
P. Filzmoser, R.G. Garrett, and C. Reimann. Multivariate outlier detection in exploration geochemistry. Computers & Geosciences, 31:579-587, 2005.
# create data: set.seed(134) x <- cbind(rnorm(80), rnorm(80), rnorm(80)) y <- cbind(rnorm(10, 5, 1), rnorm(10, 5, 1), rnorm(10, 5, 1)) z <- rbind(x,y) # execute: aq.plot(z, alpha=0.1)
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