robCompositions (version 1.9.1)

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)

Arguments

x

compositional data

method

either robust (default) or standard

mult_comp

a list of numeric vectors holding the indices of linked compositions

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

Details

The compositional data set is transformed using the ilr tranformation. 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 ilr-transformation is 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.

See Also

print.pcaCoDa, plot.pcaCoDa

Examples

data(expenditures)
p1 <- pcaCoDa(expenditures)
p1
plot(p1)

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