Package 'Compositionalasmr'

The alpha-Spatial Median Regression for Compositional Data

Description

The $alpha$-spatial median regression is performed via the iteretively reweighted least squares (IRLS) algorithm. At first the $alpha$-transformation is applied and then the non-linear regression model is fitted.

Details

Package:	Compositionalasmr
Type:	Package
Version:	1.0
Date:	2026-08-20

Maintainers

Michail Tsagris <[email protected]>.

Author(s)

Michail Tsagris [email protected]

References

Aitchison J. (1986). The statistical analysis of compositional data.

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Spatial median regression with compositional data using the $\alpha$-transformation

Description

Spatial median regression with compositional data using the $\alpha$-transformation.

Usage

asmr(y, x, a, yb = NULL, xnew = NULL, maxit = 100, tol = 1e-06 )
asmr2(y, x, a = c(-1, 1), xnew = NULL, maxit = 500, tol = 1e-6)

Arguments

y	A matrix with the compositional data.
x	A matrix with the continuous predictor variables or a data frame including categorical predictor variables.
a	The value of the power transformation, it has to be between -1 and 1. If zero values are present it has to be greater than 0. If $\alpha=0$ the isometric log-ratio transformation is applied and the solution exists in a closed form, since it the classical mutivariate regression. For the asmr2() this is a vector with the lower and upper value of $\alpha$ to search for.
yb	If you have already transformed the data using the $\alpha$-transformation with the same $\alpha$ as given in the argument "a", put it here. Othewrise leave it NULL.
xnew	If you have new data use it, otherwise leave it NULL.
maxit	The maximum number of iterations the IRLS algorithm will perform.
tol	The tolerance value to terminate the IRLS algorithm.

Details

The $\alpha$-transformation is applied to the compositional data first and then non-linear spatial median regression using the iteratively reqeighted least squares (IRLS) algorithm is performed.

Value

A list including:

runtime	The time required by the regression.
iters	The number of iterations required until convergence.
norm	The value of the $L_1$ norm.
be	The beta coefficients.
est	The fitted values for xnew if xnew is not NULL.

The asmr2() function also returns an extra outcome, the "alpha", which is the optimal value of $\alpha$.

Author(s)

Michail Tsagris.

R implementation and documentation: Michail Tsagris [email protected].

References

Tsagris M. and Pantazis Y. (2026). The $\alpha$–regression for compositional data: a unified framework for standard, temporal and spatial regression models including compositional predictors. https://arxiv.org/pdf/2510.12663

Tsagris M. (2015). Regression analysis with compositional data containing zero values. Chilean Journal of Statistics, 6(2): 47-57. https://arxiv.org/pdf/1508.01913v1.pdf

Tsagris M.T., Preston S. and Wood A.T.A. (2011). A data-based power transformation for compositional data. In Proceedings of the 4th Compositional Data Analysis Workshop, Girona, Spain. https://arxiv.org/pdf/1106.1451.pdf

Mardia K.V., Kent J.T., and Bibby J.M. (1979). Multivariate analysis. Academic press.

Aitchison J. (1986). The statistical analysis of compositional data. Chapman & Hall.

See Also

cv.asmr, asmr.path

Examples

y <- as.matrix(iris[, 1:3])
y <- y / rowSums(y)
x <- iris[, 4]
mod <- asmr(y, x, 0.2)

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Regression with compositional data using the $\alpha$-transformation

Description

Regression with compositional data using the $\alpha$-transformation.

Usage

asmr.path(y, x, a = seq(-1, 1, by = 0.1), xnew = NULL, maxit = 100,
tol = 1e-6, ncores = 1)

Arguments

y	A matrix with the compositional data.
x	A matrix with the continuous predictor variables or a data frame including categorical predictor variables.
a	A vector with the $\alpha$ values of the power transformation, it has to be between -1 and 1.
xnew	If you have new data use it, otherwise leave it NULL.
maxit	The maximum number of iterations the IRLS algorithm will perform.
tol	The tolerance value to terminate the IRLS algorithm.
ncores	The number of cores to use for parallel computations.

Details

The $\alpha$-transformation is applied to the compositional data first and then non-linear spatial median regression using the iteratively reqeighted least squares (IRLS) algorithm is performed. This takes place for each value of $\alpha$.

Value

For the alfa.reg() function a list including:

runtime	The time required by the regression.
res	A list with two components: "be", the estimated regression coefficients, and "est", the fitted values, both for each value of $\alpha$.
covbe	The covariance matrix if covb was set to TRUE, otherwise NULL.

Author(s)

Michail Tsagris.

R implementation and documentation: Michail Tsagris [email protected].

References

Tsagris M. and Pantazis Y. (2026). The $\alpha$–regression for compositional data: a unified framework for standard, temporal and spatial regression models including compositional predictors. https://arxiv.org/pdf/2510.12663

Tsagris M. (2015). Regression analysis with compositional data containing zero values. Chilean Journal of Statistics, 6(2): 47-57. https://arxiv.org/pdf/1508.01913v1.pdf

Tsagris M.T., Preston S. and Wood A.T.A. (2011). A data-based power transformation for compositional data. In Proceedings of the 4th Compositional Data Analysis Workshop, Girona, Spain. https://arxiv.org/pdf/1106.1451.pdf

Mardia K.V., Kent J.T., and Bibby J.M. (1979). Multivariate analysis. Academic press.

Aitchison J. (1986). The statistical analysis of compositional data. Chapman & Hall.

See Also

asmr, cv.asmr

Examples

y <- as.matrix(iris[, 1:3])
y <- y / rowSums(y)
x <- iris[, 4]
mod <- asmr.path(y, x, a = c(0.1, 0.2))

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K-fold cross-validation for the $\alpha$-smr

Description

K-fold cross-validation for the $\alpha$-smr.

Usage

cv.asmr(y, x, a = seq(0.1, 1, by = 0.1), maxit = 500, tol = 1e-6,
nfolds = 10, folds = NULL, ncores = 1, seed = NULL)

Arguments

y	A matrix with compositional data. zero values are allowed.
x	A matrix with the continuous predictor variables or a data frame including categorical predictor variables.
a	The value of the power transformation, it has to be between -1 and 1. If zero values are present it has to be greater than 0. If $\alpha=0$ the isometric log-ratio transformation is applied.
maxit	The maximum number of iterations the IRLS algorithm will perform.
tol	The tolerance value to terminate the IRLS algorithm.
nfolds	The number of folds to split the data.
folds	If you have the list with the folds supply it here. You can also leave it NULL and it will create folds.
ncores	The number of cores to use. IF you have a multicore computer it is advisable to use more than 1. It makes the procedure faster. It is advisable to use it if you have many observations and or many variables, otherwise it will slow down th process.
seed	You can specify your own seed number here or leave it NULL.

Details

Tuning the value of $\alpha$ in the $\alpha$-smr takes place using K-fold cross-validation.

Value

A list including:

runtime	The runtime required by the cross-validation.
perf	A vector with the average Kullback-Leibler divergence, for every value of $\alpha$.
opt	A vector with the minimum Kullback-Leibler divergence and the optimal value of $\alpha$.

Author(s)

Michail Tsagris.

R implementation and documentation: Michail Tsagris [email protected].

References

Tsagris M. and Pantazis Y. (2026). The $\alpha$–regression for compositional data: a unified framework for standard, temporal and spatial regression models including compositional predictors. https://arxiv.org/pdf/2510.12663

Tsagris M. (2015). Regression analysis with compositional data containing zero values. Chilean Journal of Statistics, 6(2): 47-57. https://arxiv.org/pdf/1508.01913v1.pdf

Tsagris M.T., Preston S. and Wood A.T.A. (2011). A data-based power transformation for compositional data. In Proceedings of the 4th Compositional Data Analysis Workshop, Girona, Spain. https://arxiv.org/pdf/1106.1451.pdf

See Also

asmr, asmr.path

Examples

y <- as.matrix(iris[, 1:3])
y <- y / rowSums(y)
x <- iris[, 4]
mod <- cv.asmr(y, x, a = c(0.5, 1))

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