robCompositions (version 2.4.1)

pcaCoDa: Robust principal component analysis for compositional data

Description

This function applies robust principal component analysis for compositional data.

Usage

pcaCoDa(
  x,
  method = "robust",
  mult_comp = NULL,
  external = NULL,
  solve = "eigen"
)
# S3 method for pcaCoDa
print(x, ...)
# S3 method for pcaCoDa
summary(object, ...)

Value

scores

scores in clr space

loadings

loadings in clr space

eigenvalues

eigenvalues of the clr covariance matrix

method

method

princompOutputClr

output of princomp needed in plot.pcaCoDa

Arguments

x

compositional data

method

must be either “robust” (default) or “classical”

mult_comp

a list of numeric vectors holding the indices of linked compositions

external

external non-compositional variables

solve

eigen (as princomp does, i.e. eigenvalues of the covariance matrix) or svd (as prcomp does with single value decomposition instead of eigen). Only for method classical.

...

additional parameters for print method passed through

object

object of class pcaCoDa

Author

Karel Hron, Peter Filzmoser, Matthias Templ and a contribution for dimnames in external variables by Amelia Landre.

Details

The compositional data set is expressed in isometric logratio coordinates. Afterwards, robust principal component analysis is performed. Resulting loadings and scores are back-transformed to the clr space where the compositional biplot can be shown.

mult_comp is used when there are more than one group of compositional parts in the data. To give an illustrative example, lets assume that one variable group measures angles of the inner ear-bones of animals which sum up to 100 and another one having percentages of a whole on the thickness of the inner ear-bones included. Then two groups of variables exists which are both compositional parts. The isometric logratio coordinates are then internally applied to each group independently whenever the mult_comp is set correctly.

References

Filzmoser, P., Hron, K., Reimann, C. (2009) Principal component analysis for compositional data with outliers. Environmetrics, 20, 621-632.

Kynclova, P., Filzmoser, P., Hron, K. (2016) Compositional biplots including external non-compositional variables. Statistics: A Journal of Theoretical and Applied Statistics, 50, 1132-1148.

See Also

print.pcaCoDa, summary.pcaCoDa, biplot.pcaCoDa, plot.pcaCoDa

Examples

data(arcticLake)

## robust estimation (default):
res.rob <- pcaCoDa(arcticLake)
res.rob
summary(res.rob)
plot(res.rob)

## classical estimation:
res.cla <- pcaCoDa(arcticLake, method="classical", solve = "eigen")
biplot(res.cla)

## just for illustration how to set the mult_comp argument:
data(expenditures)
p1 <- pcaCoDa(expenditures, mult_comp=list(c(1,2,3),c(4,5)))
p1

## example with external variables:
data(election)
# transform external variables
election$unemployment <- log((election$unemployment/100)/(1-election$unemployment/100))
election$income <- scale(election$income)

res <- pcaCoDa(election[,1:6], method="classical", external=election[,7:8])
res
biplot(res, scale=0)