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 procedure used, by default `proc = "cov"`

to indicate a classical covariance matrix.

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

ncthe number of individuals remaining in the ‘core’ data subset after trimming. At this stage of a data analysis `nc = n`

.

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 used to compute the covariance matrix and means. For a classical, non-robust, estimation all weights are set to ‘1’.

meanthe vector the clr means for the `p`

variables.

covthe `p`

by `p`

clr covariance matrix for the `n`

by `p`

data matrix.

sdthe vector of clr standard deviations for the `p`

variables.

sndthe `n`

by `p`

matrix of clr standard normal deviates.

rthe `p`

by `p`

matrix of clr Pearson product moment correlation coefficients.

eigenvaluesthe vector of `p`

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

econtribthe vector of `p`

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

eigenvectorsthe `n`

by `p`

matrix of `eigenvectors`

.

rloadthe `p`

by `p`

matrix of Principal Component (PC) loadings.

rcrthe `p`

by `p`

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

rqscorethe `n`

by `p`

matrix of the n individuals scores on the `p`

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.

cpvcontribthe vector of `p`

cumulative sums of `pvcontrib`

, see above.

mdthe vector of n Mahalanobis distances (MDs) for the `n`

by `p`

, now `(p-1)`

, input matrix.

ppmthe vector of `n`

predicted probabilities of population membership, see Garrett (1990).

epmthe vector of `n`

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.