The function carries out a Principal Components Analysis (PCA) and estimates the Mahalanobis distances for a dataset and places them in an object to be saved and post-processed for display and further manipulation. Classical procedures are used, for robust procedures see `gx.robmva`

. For results display see `gx.rqpca.screeplot`

, `gx.rqpca.loadplot`

, `gx.rqpca.plot`

, `gx.rqpca.print`

, `gx.md.plot`

and `gx.md.print`

. For Kaiser varimax rotation see `gx.rotate`

. For closed. compositional, data use `gx.mva.closed`

.

`gx.mva(xx, main = deparse(substitute(xx)))`

xx

a `n`

by `p`

data matrix to be processed.

main

by default the name of the object `xx`

, `main = deparse(substitute(xx))`

, it may be replaced by the user, but this is not recommended, see Details below.

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

by default (recommended) the input data matrix name.

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

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

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

to indicate a classical covariance matrix.

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

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

.

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

flag for `gx.md.plot`

, set to `FALSE`

.

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

the vector of weights for the `n`

individuals used to compute the covariance matrix and means. At this stage of the data analysis all weights are set to ‘1’.

the vector the weighted means for the `p`

variables.

the `p`

by `p`

weighted covariance matrix for the `n`

by `p`

data matrix.

the vector of weighted standard deviations for the `p`

variables.

the `n`

by `p`

matrix of weighted standard normal deviates.

the `p`

by `p`

matrix of weighted Pearson product moment correlation coefficients.

the vector of `p`

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

the vector of `p`

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

.

the `n`

by `p`

matrix of `eigenvectors`

.

the `p`

by `p`

matrix of Principal Component (PC) loadings.

the `p`

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

the `n`

by `p`

matrix of the n individuals scores on the `p`

PCs.

a vector of `p`

variances of the columns of `rqscore`

.

the vector of `p`

variances of the columns of `rqscore`

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

, the values should be identical.

the vector of `p`

cumulative sums of `pvcontrib`

, see above.

the vector of `n`

Mahalanobis distances (MDs) for the n by `p`

input matrix.

the vector of `n`

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

the vector of `n`

empirical Chi-square probabilities for the MDs.

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

in order to control PC plot axis labelling.

If `main`

is undefined the name of the matrix object passed to the function is used to identify the object. This is the recommended procedure as it helps to track the progression of a data analysis. Alternate plot titles are best defined when the saved object is passed to `gx.rqpca.plot`

, `gx.rqpca.screeplot`

or `gx.md.plot`

for display. If no plot title is required set `main = " "`

, or if a user defined plot title is required it may be defined, e.g., `main = "Plot Title Text"`

.

Garrett, R.G., 1990. A robust multivariate allocation procedure with applications to geochemical data. In Proc. Colloquium on Statistical Applications in the Earth Sciences (Eds F.P. Agterberg & G.F. Bonham-Carter). Geological Survey of Canada Paper 89-9, pp. 309-318.

Garrett, R.G., 1993. Another cry from the heart. Explore - Assoc. Exploration Geochemists Newsletter, 81:9-14.

Grunsky, E.C., 2001. A program for computing RQ-mode principal components analysis for S-Plus and R. Computers & Geosciences, 27(2):229-235.

Reimann, C., Filzmoser, P., Garrett, R. and Dutter, R., 2008. Statistical Data Analysis Explained: Applied Environmental Statistics with R. John Wiley & Sons, Ltd., 362 p.

`ltdl.fix.df`

, `remove.na`

, `na.omit`

, `gx.rqpca.screeplot`

, `gx.rqpca.loadplot`

, `gx.rqpca.plot`

, `gx.rqpca.print`

, `gx.md.plot`

, `gx.md.print`

, `gx.robmva`

, `gx.robmva.closed`

, `gx.rotate`

# NOT RUN { ## Make test data available data(sind.mat2open) ## Generate gx.mva object, for demonstration purposes only ## These are compositional data - gx.mva.closed should be used sind.save <- gx.mva(sind.mat2open) gx.rqpca.screeplot(sind.save) gx.rqpca.loadplot(sind.save) gx.rqpca.plot(sind.save) ## Display saved object with alternate main titles gx.rqpca.loadplot(sind.save, main = "Howarth & Sinding-Larsen\nStream Sediments, clr Transformed Data", cex.main = 0.8) gx.rqpca.plot(sind.save, main = "Howarth & Sinding-Larsen\nStream Sediments, clr Transformed Data", cex.main = 0.8) ## Display Mahalanobis distances in a Chi-square plot gx.md.plot(sind.save) ## Display saved object with alternate main titles gx.md.plot(sind.save, main = "Howarth & Sinding-Larsen\nStream Sediments, ilr Transformed Data", cex.main = 0.8) ## Clean-up rm(sind.save) # }