Compositional (version 5.5)

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

Value

The output of the ridge.reg.

Details

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

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

# NOT RUN {
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)
# }