cv.alfapcreg: K-fold cross-validation the alpha-regression with...

In CompositionalSR: Spatial Regression Models with Compositional Data

K-fold cross-validation the \alpha-regression with compositional predictors

Description

K-fold cross-validation the \alpha-regression with compositional predictors.

Usage

cv.alfapcreg(y, x, a = seq(0.1, 1, by = 0.1), nfolds = 10, folds = NULL, seed = NULL)

Arguments

y	A matrix with compositional response data. Zero values are allowed.
x	A matrix with the compositional predictor variables. Zero values are allowed.
a	A numerical vector with the values 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.
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.
seed	You can specify your own seed number here or leave it NULL.

Details

Tuning the value of \alpha and k, the number of principal components in the \alpha-regression with compositional predictors takes place using the classical K-fold cross-validation.

Value

A list including:

runtime	The runtime required by the cross-validation.
perf	A matrix with the average Kullback-Leibler divergence, for every value of \alpha and k.
kl	The minimum average value of the Kullback-Leibler divergence.
opt_a	The optimal value of \alpha.
opt_k	The optimal value of k, the number of principal components.

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

See Also

alfa.pcreg, cv.alfareg

Examples

data(fadn)
y <- fadn[, 3:7]
x <- fadn[, 8:11]
x <- x / rowSums(x)
mod <- cv.alfapcreg(y, x, a = c(0.5, 1))

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