rrcov3way (version 0.5-0)

Arno: Chemical composition of water in the main stream of Arno river

Description

Chemical composition of water in the main stream of Arno river.

Usage

data("Arno")

Format

A three-way array with dimension 23x11x4. The first dimension refers to 23 distances from the spring. The second dimension refers to the 11 chemical compositions. The third dimension refers to the time of collection - four occasions.

Details

The Arno data example was used in Gallo and Buccinati (2013) to illustrate a particular version of the Tucker model, known as the weighted principal component analysis. The Tucker3 results are usually given in the form of tables or plots and in this work for the representation of the Tucker3 results of logratio data, is proposed to use one-mode plots, clr-joint biplots (Gallo, 2015), and trajectory plots.

References

Gallo M. and Buccianti A. (2013). Weighted principal component analysis for compositional data: application example for the water chemistry of the Arno river (Tuscany, central Italy), Environmetrics, 24(4):269-277.

Gallo M. (2015). Tucker3 model for compositional data. Communications in Statistics-Theory and Methods, 44(21):4441-4453.

Examples

data(Arno)
dim(Arno)               # [1] 23 11  4
dim(Arno[,,1])          # [1] 23 11
rownames(Arno[,,1])     # the 23 distances from the spring
colnames(Arno[,,1])     # the 11 chemical compositions
dim(Arno[,1,])          # [1] 23  4
colnames(Arno[,1,])     # the four occasions

res <- Tucker3(Arno, robust=FALSE, coda.transform="ilr")
res

## Distance-distance plot
plot(res, which="dd", main="Distance-distance plot")

## Paired component plot, mode A
plot(res, which="comp", main="Paired component plot (mode A)")

## Paired component plot, mode B
plot(res, which="comp", mode="B", main="Paired component plot (mode B)") 

## Joint biplot
plot(res, which="jbplot", main="Joint biplot") 

## Trajectory
plot(res, which="tjplot", main="Trajectory biplot")