Ridge regression with compositional data in the covariates side using the alpha-transformation {Compositional}

Ridge regression with compositional data in the covariates side using the \alpha-transformation

Description

Ridge regression with compositional data in the covariates side using the \alpha-transformation.

Usage

alfa.ridge(y, x, a, lambda, B = 1, xnew = NULL)

Arguments

y

A numerical vector containing the response variable values. If they are percentages, they are mapped onto R using the logit transformation.

x

A matrix with the predictor variables, the compositional data. Zero values are allowed, but you must be careful to choose strictly positive vcalues of \alpha.

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.

lambda

The value of the regularisation parameter, \lambda.

B

If B > 1 bootstrap estimation of the standard errors is implemented.

xnew

A matrix containing the new compositional data whose response is to be predicted. If you have no new data, leave this NULL as is by default.

Details

The \alpha-transformation is applied to the compositional data first and then ridge components regression is performed.

Value

The output of the ridge.reg.

Author(s)

Michail Tsagris.

R implementation and documentation: Michail Tsagris [e-mail] and Giorgos Athineou <[e-mail]>.

References

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

ridge.reg, alfaridge.tune, alfaridge.plot

Examples

library(MASS)
y <- as.vector(fgl[, 1])
x <- as.matrix(fgl[, 2:9])
x <- x/ rowSums(x)
mod1 <- alfa.ridge(y, x, a = 0.5, lambda = 0.1, B = 1, xnew = NULL)
mod2 <- alfa.ridge(y, x, a = 0.5, lambda = 1, B = 1, xnew = NULL)