alfareg.nr: The alpha-regression using Newton-Raphson

In CompositionalSR: Spatial Regression Models with Compositional Data

The alpha-regression using Newton-Raphson

Description

The alpha-regression using Newton-Raphson.

Usage

alfareg.nr(y, x, alpha = 1, beta_init = NULL, max_iter = 100,
tol = 1e-6, line_search = TRUE)

Arguments

y	A matrix with the compositional data.
x	A matrix with the continuous predictor variables or a data frame including categorical predictor variables.
alpha	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.
beta_init	A vector of initial parameters (optional). This is then transformed into a matrix.
max_iter	The maximum number of iterations for the Newton-Raphson algorithm.
tol	The tolerance value to terminate the Newton-Raphson algorithm.
line_search	Do you want to perform line search? The default value is TRUE.

Details

The \alpha-transformation is applied to the compositional data first and then multivariate regression is applied. This involves numerical optimisation.

Value

A list including:

runtime	The time required by the regression.
iters	The iterations of the Newton-Raphson algorithm
be	The beta coefficients.
objective	The sum of the squared residuals.
est	The fitted values.
covb	The covariance matrix of the beta coefficients, or NULL if it is singular.

Author(s)

Michail Tsagris.

R implementation and documentation: Michail Tsagris [e-mail].

References

Tsagris M. and Pantazis Y. (2026). The \alpha–regression for compositional data: a unified framework for standard, spatially-lagged, spatial autoregressive and geographically-weighted regression models. 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

alfa.reg, cv.alfareg, alfa.slx

Examples

data(fadn)
y <- fadn[, 3:7]
x <- fadn[, 8]
mod <- alfareg.nr(y, x, a = 0.2)
mod2 <- alfa.reg(y, x, 0.2)

CompositionalSR documentation built on March 28, 2026, 5:07 p.m.