PCA {easyCODA}

Principal component analysis

Description

Computation of weighted or unweighted principal component analysis of a matrix of interval-scale data (e.g. a matrix of logratios).

Usage

PCA(data, nd = 2, weight = TRUE, row.wt = NA, suprow = NA)

Arguments

data

A data frame or matrix of interval-scale data, or logratio object from functions ALR, CLR or LR

nd

Number of dimensions for summary solution if not 2

weight

TRUE (default) for column weighting, FALSE for unweighted analysis, or a vector of user-defined column weights

row.wt

Optional user-defined set of positive weights for the rows (samples) (default: equal weights)

suprow

Indices of rows that are supplementary points (NOTE: this option is not implemented in this version)

Details

The function PCA computes an unstandardized principal component analysis, based on the singular value decomposition, of a matrix of interval-scale data, usually a matrix of logratios in the context of this package (but it can be used for general data as well). For general usage the unweighted option weight = FALSE might be preferred, but the default is weighted in the present context of compositional data.

User-specified weights can be supplied, for the rows and/or the columns. Usually row weights are not specified, and are equal unless intentional weighting of the samples is desired. User-specified part weights can be provided using the weight option.

Supplementary rows and columns can be declared (also known as passive points) – these do not contribute to the solution but are positioned on the solution axes. Notice that this optyion is not implemented in the present version, but will appear in the next one.

The function borrows the structure and functions of the ca package, which is required, and produces a ca object, and the same print, summary and plot methods can be used, as for a ca object.

Value

sv

Singular values

nd

Dimenson of the solution

rownames

Row names

rowmass

Row weights

rowdist

Row logratio distances to centroid

rowinertia

Row variances

rowcoord

Row standard coordinates

rowpcoord

Row principal coordinates

rowsup

Indices of row supplementary points

colnames

Column names

colmass

Column weights

coldist

Column logratio distances to centroid

colinertia

Column variances

colcoord

Column standard coordinates

colpcoord

Column principal coordinates

N

The data table

Author(s)

Michael Greenacre

References

Aitchison, J. and Greenacre, M. (2002), Biplots of compositional data, Applied Statistics 51, 375-392.
Greenacre, M. (2010), Biplots in Practice, BBVA Foundation, Bilbao. Free download from www.multivariatestatistics.org

See Also

, PLOT.PCA, plot.ca, summary.ca, print.ca

Examples

# compute logratios of Vegetables data set
data(veg)
veg.LR <- LR(veg)
# unweighted PCA biplot of the results
veg.PCA <- PCA(veg.LR$LR, weight=FALSE)
PLOT.PCA(veg.PCA, map="asymmetric")