Outlier Detection

## Usage

outliers(object, ...)

# S4 method for CompositionMatrix
outliers(
object,
center = NULL,
cov = NULL,
robust = TRUE,
alpha = 0.5,
level = 0.975
)

## Arguments

object
...

Currently not used.

center

A numeric vector giving the mean vector of the distribution. If missing, will be estimated from x.

cov

A numeric matrix giving the covariance of the distribution. If missing, will be estimated from x.

robust

A logical scalar: should robust location and scatter estimation be used (see robustbase::covMcd())?

alpha

A length-one numeric vector controlling the size of the subsets over which the determinant is minimized (see robustbase::covMcd()). Only used if robust is TRUE.

level

A length-one numeric vector giving the significance level. level is used as a cut-off value for outlier detection: observations with larger (squared) Mahalanobis distance are considered as potential outliers.

## Value

An OutlierIndex object.

## Details

An outlier can be defined as having a very large Mahalanobis distance from all observations. In this way, a certain proportion of the observations can be identified, e.g. the top 2% of values (i.e. values above the 0.98th percentile of the Chi-2 distribution).

On the one hand, the Mahalanobis distance is likely to be strongly affected by the presence of outliers. Rousseeuw and van Zomeren (1990) thus recommend using robust methods (which are not excessively affected by the presence of outliers).

On the other hand, the choice of the threshold for classifying an observation as an outlier should be discussed. There is no apparent reason why a particular threshold should be applicable to all data sets (Filzmoser, Garrett, and Reimann 2005).

## References

Filzmoser, P., Garrett, R. G. & Reimann, C. (2005). Multivariate outlier detection in exploration geochemistry. Computers & Geosciences, 31(5), 579-587. doi:10.1016/j.cageo.2004.11.013 .

Filzmoser, P. & Hron, K. (2008). Outlier Detection for Compositional Data Using Robust Methods. Mathematical Geosciences, 40(3), 233-248. doi:10.1007/s11004-007-9141-5 .

Filzmoser, P., Hron, K. & Reimann, C. (2012). Interpretation of multivariate outliers for compositional data. Computers & Geosciences, 39, 77-85. doi:10.1016/j.cageo.2011.06.014 .

Rousseeuw, P. J. & van Zomeren, B. C. (1990). Unmasking Multivariate Outliers and Leverage Points. Journal of the American Statistical Association, 85(411): 633-639. doi:10.1080/01621459.1990.10474920 .

Santos, F. (2020). Modern methods for old data: An overview of some robust methods for outliers detection with applications in osteology. Journal of Archaeological Science: Reports, 32, 102423. doi:10.1016/j.jasrep.2020.102423 .

Other outlier detection methods: plot_outliers

N. Frerebeau

## Examples

## Coerce to chemical data
data("hongite")
coda <- as_composition(hongite)

## Detect outliers
out <- outliers(coda)

## Plot
plot(out, qq = TRUE)

plot(out, qq = FALSE)