Compute the transformation matrix to express a composition using the oblique additive log-ratio coordinates.
alr_basis(dim, denominator = dim, numerator = which(denominator != 1:dim))number of parts
part used as denominator (default behaviour is to use last part)
parts to be used as numerator. By default all except the denominator parts are chosen following original order.
matrix
Aitchison, J. (1986) The Statistical Analysis of Compositional Data. Monographs on Statistics and Applied Probability. Chapman & Hall Ltd., London (UK). 416p.
alr_basis(5)
#> alr1 alr2 alr3 alr4
#> c1 1 0 0 0
#> c2 0 1 0 0
#> c3 0 0 1 0
#> c4 0 0 0 1
#> c5 -1 -1 -1 -1
# Third part is used as denominator
alr_basis(5, 3)
#> alr1 alr2 alr3 alr4
#> c1 1 0 0 0
#> c2 0 1 0 0
#> c3 -1 -1 -1 -1
#> c4 0 0 1 0
#> c5 0 0 0 1
# Third part is used as denominator, and
# other parts are rearranged
alr_basis(5, 3, c(1,5,2,4))
#> alr1 alr2 alr3 alr4
#> c1 1 0 0 0
#> c2 0 0 1 0
#> c3 -1 -1 -1 -1
#> c4 0 0 0 1
#> c5 0 1 0 0