easyCODA (version 0.40.2)

FINDALR: Find the best ALR transformation

Description

Searching over every possible reference part for choosing an optimal ALR transformation.

Usage

FINDALR(data, weight=FALSE)

Value

An object which describes the tree produced by the clustering process on the n objects. The object is a list with components:

totvar

Total logratio variance

procrust.cor

The Procrustes correlations of the ALRs using each reference

procrust.max

The value of the highest Procrustes correlation

procrust.ref

The reference corresponding to the highest correlation

var.log

Variances of the log-transformed references

var.min

The value of the lowest variance

var.ref

The reference corresponding to the lowest variance

Arguments

data

Compositional data matrix, with the parts as columns

weight

FALSE (default) for equally weighted parts, TRUE when weights are in data list object, or a vector of user-defined part weights

Author

Michael Greenacre

Details

The function FINDALR considers every possible set of additive logratio (ALR) transformations, by trying each of the references. For each set the closeness to isometry is measured by the Procrustes correlation. In addition, the variance of the log-transformed reference is also computed. The reference with highest Procrustes correlation and the reference with the lowest variance of its log-transform are identified. The number of ALRs computed is equal to 1 less than the number of rows or columns, whichever is the smallest.

References

Greenacre, M., Martinez-Alvaro, M. and Blasco, A. (2021), Compositional data analysis of microbiome and any-omics datasets: a validation of the additive logratio transformation, Frontiers in Microbiology 12: 2625
Gower, J. and Dijksterhuis, G.B. (2004), Procrustes Problems. Oxford University Press
Greenacre, M. (2018), Compositional Data Analysis in Practice, Chapman & Hall / CRC

See Also

ALR

Examples

# For the fish morphometric data, first close (normalize) 
# then loop over the 26 possible references
data(fish)
FINDALR(CLOSE(fish[,4:29]))
# Note that for the default option weight=FALSE closing the data is not necessary