data set (matrix or data frame) containing the raw untransformed compositional data
quan
quantity of data used for robust estimation; between 0.5 and 1
alpha
maximum threshold for adaptive outlier detection
col.quantile
quantiles of an average concentration defining the colors
symb.pch
plotting character for symbols
symb.cex
plotting size for symbols
adaptive
if TRUE then the adaptive method for the outlier threshold is used
Details
In a first step, the raw compositional data set in transformed by the isometric logratio
(ilr) transformation to the usual Euclidean space. Then adaptive outlier detection is
perfomed: Starting from a quantile 1-alpha of the chisquare distribution, one looks for the
supremum of the differences between the chisquare distribution and the empirical distribution
of the squared Mahalanobis distances. The latter are derived from the MCD estimator using
the proportion quan of the data. The supremum is the outlier cutoff, and certain colors
and symbols for the outliers are computed: The colors should reflect the magnitude of the
median element concentration of the observations, which is done by computing for each observation
along the single ilr variables the distances to the medians. The mediab of all distances
determines the color (or grey scale): a high value, resulting in a red (or dark) symbol,
means that most univariate parts have higher values than the average, and a low value (blue
or light symbol) refers to an observation with mainly low values. The symbols are according
to the cut-points from the quantiles 0.25, 0.5, 0.75, and the outlier cutoff of the
squared Mahalanobis distances.