Compositional summaries, biplot and Dirichlet models

AitchisonClrCovariance: clr covariance, total variance, variation matrix and centre (Aitchison 1986). CompositionalMad: MAD of each clr coordinate. CompositionalPielou: Pielou (1966) evenness of a composition. CompositionalQuantileDist: Aitchison distance between the part-wise upper and lower quartiles. AitchisonBiplot: SVD of the centred clr matrix (Aitchison and Greenacre 2002). DirichletFitMom: method of moments (Minka 2000). DirichletSample: gamma draws by inversion of Philox uniforms (part i on stream i - 1). Identical to the Python arm morie.fn.compdir.

Usage

AitchisonClrCovariance(X)

CompositionalMad(X)

CompositionalPielou(x)

CompositionalQuantileDist(X)

AitchisonBiplot(X)

DirichletFitMom(X)

DirichletSample(alpha, n, seed = 1L)

Arguments

X

Sample (rows are compositions).

x

Composition.

alpha

Dirichlet parameters.

n

Number of draws.

seed

Philox seed.

Value

List, vector, number or matrix.

References

Aitchison, J. (1986). The Statistical Analysis of Compositional Data. Chapman and Hall.

Aitchison, J. and Greenacre, M. (2002). Biplots of compositional data. Journal of the Royal Statistical Society C 51, 375-392.

Minka, T. P. (2000). Estimating a Dirichlet distribution. Technical report, MIT.

Examples

AitchisonClrCovariance(rbind(c(1, 2, 4), c(2, 2, 2), c(4, 2, 1)))$total_variance
#> [1] 0.960906
CompositionalPielou(c(1, 1, 2))
#> [1] 0.9463946
DirichletFitMom(rbind(c(1, 2, 7), c(2, 2, 6), c(3, 1, 6)))$alpha
#> [1] 3.0 2.5 9.5
DirichletSample(c(2, 3), 1, seed = 4)
#>           [,1]      [,2]
#> [1,] 0.0586551 0.9413449