outCoDa: Outlier detection for compositional data

In robCompositions: Compositional Data Analysis

Outlier detection for compositional data

Description

Outlier detection for compositional data using standard and robust statistical methods.

Usage

outCoDa(x, quantile = 0.975, method = "robust", alpha = 0.5, coda = TRUE)

## S3 method for class 'outCoDa'
print(x, ...)

## S3 method for class 'outCoDa'
plot(x, y, ..., which = 1)

Arguments

x	compositional data
quantile	quantile, corresponding to a significance level, is used as a cut-off value for outlier identification: observations with larger (squared) robust Mahalanobis distance are considered as potential outliers.
method	either “robust” (default) or “standard”
alpha	the size of the subsets for the robust covariance estimation according the MCD-estimator for which the determinant is minimized, see covMcd.
coda	if TRUE, data transformed to coordinate representation before outlier detection.
...	additional parameters for print and plot method passed through
y	unused second plot argument for the plot method
which	1 ... MD against index 2 ... distance-distance plot

Details

The outlier detection procedure is based on (robust) Mahalanobis distances in isometric logratio coordinates. Observations with squared Mahalanobis distance greater equal a certain quantile of the chi-squared distribution are marked as outliers.

If method “robust” is chosen, the outlier detection is based on the homogeneous majority of the compositional data set. If method “standard” is used, standard measures of location and scatter are applied during the outlier detection procedure. Method “robust” can be used if the number of variables is greater than the number of observations. Here the OGK estimator is chosen.

plot method: the Mahalanobis distance are plotted against the index. The dashed line indicates the (1 - alpha) quantile of the chi-squared distribution. Observations with Mahalanobis distance greater than this quantile could be considered as compositional outliers.

Value

mahalDist	resulting Mahalanobis distance
limit	quantile of the Chi-squared distribution
outlierIndex	logical vector indicating outliers and non-outliers
method	method used

Note

It is highly recommended to use the robust version of the procedure.

Author(s)

Matthias Templ, Karel Hron

References

Egozcue J.J., Pawlowsky-Glahn, V., Mateu-Figueras, G., Barcelo-Vidal, C. (2003) Isometric logratio transformations for compositional data analysis. Mathematical Geology, 35 (3) 279-300.

Filzmoser, P., and Hron, K. (2008) Outlier detection for compositional data using robust methods. Math. Geosciences, 40, 233-248.

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

See Also

pivotCoord

Examples

data(expenditures)
oD <- outCoDa(expenditures)
oD
## providing a function:
oD <- outCoDa(expenditures, coda = log)
## for high-dimensional data:
oD <- outCoDa(expenditures, method = "robustHD")

robCompositions documentation built on Aug. 25, 2023, 5:13 p.m.