The following are returned as an object to be saved for subsequent display, etc.:

mainby default (recommended) the input data matrix name.

inputthe data matrix name, `input = deparse(substitute(xx))`

, retained to be used by post-processing display functions.

procthe robust procedure used, the value of `proc`

will be `"mcd"`

, `"mve"`

or `"wts"`

.

nthe total number of individuals (observations, cases or samples) in the input data matrix.

ncthe number of individuals remaining in the ‘core’ data subset following the robust estimation, i.e. the sum of those individuals with `wts = 1`

.

pthe number of variables on which the multivariate operations were based.

ifilrflag for `gx.md.plot`

, set to `TRUE`

.

matnamesthe row numbers or identifiers and column headings of the input matrix.

wtsthe vector of weights for the `n`

individuals arising from the robust estimation of the covariance matrix and means.

meanthe length `p`

vector of clr-based weighted means for the variables.

covthe `p`

by `p`

weighted clr-based covariance matrix for the n by p data matrix.

cov.invthe `p`

by `p`

weighted clr-based inverse of the covariance matrix, for use by function gx.mvalloc.closed.

sdthe length `p`

vector of weighted clr-based standard deviations for the variables.

sndthe `n`

by `p`

matrix of clr-based weighted standard normal deviates.

rthe `p`

by `p`

matrix of weighted clr-based Pearson product moment correlation coefficients.

eigenvaluesthe vector of `p`

eigenvalues of the scaled clr-based Pearson robust correlation matrix for RQ analysis, see Grunsky (2001).

econtribthe vector of `p`

robustly estimated eigenvalues each expressed as a percentage of the sum of the eigenvalues.

eigenvectorsthe `n`

by `p`

matrix of clr-based robustly estimated eigenvectors.

rloadthe `p`

by `p`

matrix of robust clr-based Principal Component (PC) loadings.

rcrthe `p`

by `p`

matrix containing the percentages of the variability of each variable (rows) expressed in each robust clr-based PC (columns).

rqscorethe `n`

by `p`

matrix of the n individuals scores on the p robust clr-based PCs.

vcontriba vector of `p`

variances of the columns of `rqscore`

.

pvcontribthe vector of `p`

variances of the columns of `rqscore`

expressed as percentages. This is a check on vector `econtrib`

, the values should be identical for a classical PCA. However, for robust PCAs this is not so as the trimmed individuals from the robust estimation have been re-introduced. As a consequence `pvcontrib`

can be very different from `econtrib`

. The plotting of PCs containing high proportions of the variance in robust PCAs can be useful for identifying outliers.

cpvcontribthe vector of `p`

cumulative sums of `pvcontrib`

, see above.

mdthe vector of `n`

robust ilr-based Mahalanobis distances (MDs) for the `n`

by `p`

input matrix.

ppmthe vector of /coden robust ilr-based predicted probabilities of population membership, see Garrett (1990).

epmthe vector of `n`

robust ilr-based empirical Chi-square probabilities for the MDs.

nrthe number of PCs that have been rotated. At this stage of a data analysis `nr = NULL`

in order to control PC plot axis labelling.