rgr (version 1.1.0)

gx.mva: Function to undertake an Exploratory Multivariate Data Analysis

Description

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.plot, gx.rotate, gx.md.plot and gx.md.print.

Usage

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

Arguments

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.

Value

• The following are returned as an object to be saved for subsequent display, etc.:
• main
  by default (recommended) the input data matrix name.
• input
  the data matrix name, input = deparse(substitute(xx)), retained to be used by post-processing display functions.
• proc
  the procedure used, by default proc = "cov" to indicate a classical covariance matrix.
• n
  the total number of individuals (observations, cases or samples) in the input data matrix.
• nc
  the number of individuals remaining in the core data subset after trimming. At this stage of a data analysis nc = n.
• p
  the number of variables on which the multivariate operations were based.
• ifilr
  flag for gx.md.plot, set to FALSE.
• matnames
  the row numbers and column headings of the input matrix.
• wts
  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.
• mean
  the vector the weighted means for the p variables.
• cov
  the p by p weighted covariance matrix for the n by p data matrix.
• sd
  the vector of weighted standard deviations for the p variables.
• snd
  the n by p matrix of weighted standard normal deviates.
• r
  the p by p matrix of weighted Pearson product moment correlation coefficients.
• eigenvalues
  the vector of p eigenvalues of the scaled Pearson correlation matrix for RQ analysis, see Grunsky (2001).
• econtrib
  the vector of p eigenvalues each expressed as a percentage of the sum of the eigenvalues.
• eigenvectors
  the n by p matrix of eigenvectors.
• rload
  the p by p matrix of Principal Component (PC) loadings.
• rcr
  the p by p matrix containing the percentages of the variability of each variable (columns) expressed in each PC (rows).
• rqscore
  the n by p matrix of the n individuals scores on the p PCs.
• vcontrib
  a vector of p variances of the columns of rqscore.
• pvcontrib
  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.
• cpvcontrib
  the vector of p cumulative sums of pvcontrib, see above.
• md
  the vector of n Mahalanobis distances (MDs) for the n by p input matrix.
• ppm
  the vector of n predicted probabilities of population membership, see Garrett (1990).
• epm
  the vector of n empirical Chi-square probabilities for the MDs.
• nr
  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.

Details

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".

References

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.

See Also

ltdl.fix.df, remove.na, na.omit, gx.rqpca.screeplot, gx.rqpca.plot, gx.rotate, gx.md.plot, gx.md.print, gx.robmva

Examples

## Make test data available
data(sind)
attach(sind)
sind.mat <- as.matrix(sind[, -c(1:3)])
## Ensure all data are in the same units (mg/kg)
sind.mat2open <- sind.mat
sind.mat2open[, 2] <- sind.mat2open[, 2] * 10000

## Generate gx.mva object after an clr transform for a PCA
sind.save.clr <- gx.mva(clr(sind.mat2open))
gx.rqpca.screeplot(sind.save.clr)
gx.rqpca.plot(sind.save.clr)
## Display saved object with alternate main titles
gx.rqpca.screeplot(sind.save.clr,
main = "Howarth & Sinding-Larsen
Stream Sediments, clr Transformed Data",
cex.main = 0.8)
gx.rqpca.plot(sind.save.clr,
main = "Howarth & Sinding-Larsen
Stream Sediments, clr Transformed Data",
cex.main = 0.8)

## Generate gx.mva object after an ilr transform for Mahalanobis
## distance estimation
sind.save.ilr <- gx.mva(ilr(sind.mat2open))
gx.md.plot(sind.save.ilr)
## Display saved object with alternate main titles
gx.md.plot(sind.save.ilr,
main = "Howarth & Sinding-Larsen
Stream Sediments, ilr Transformed Data",
cex.main = 0.8)

## Clean-up and detach test data
rm(sind.mat)
rm(sind.mat2open)
rm(sind.save.clr)
rm(sind.save.ilr)
detach(sind)