Outlier detection for compositional data using standard and robust statistical methods.
Usage
outCoDa(x, quantile = 0.975, method = "robust", h = 1/2)
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
h
the size of the subsets for the robust covariance estimation according the MCD-estimator for which the determinant is
minimized (the default is (n+p+1)/2).
Value
mahalDistresulting Mahalanobis distance
limitquantile of the Chi-squared distribution
outlierIndexlogical vector indicating outliers and non-outliers
methodmethod used
Details
The outlier detection procedure is based on (robust) Mahalanobis distances after a isometric logratio transformation of the data.
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.
References
Egozcue J.J., V. Pawlowsky-Glahn, G. Mateu-Figueras and
C. Barcel'o-Vidal (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.