Compositional (version 1.2)

alfareg.tune: Tuning the value of $\alpha$ in the $\alpha$-regression

Description

Tuning the value of $\alpha$ in the $\alpha$-regression.

Usage

alfareg.tune(y, x, a = seq(0.1, 1, by = 0.1), K = 10,
mat = NULL, nc = 1, graph = FALSE)

Arguments

y

A matrix with the compositional data. zero values are allowed.

x

A matrix with the continuous 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.

K

The number of folds to split the data.

mat

You can specify your own folds by giving a mat, where each column is a fold. Each column contains indices of the observations. You can also leave it NULL and it will create folds.

nc

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.

graph

If grpah is TRUE a plot of the performance for each fold along the values of $\alpha$ will appear.

Value

• A plot of the estimated Kullback-Leibler divergences (multiplied by 2) along the values of $\alpha$ (if graph is set to TRUE). A list including:
• runtime
  The runtime required by the cross-validation.
• kl
  Twice the Kullback-Leibler divergence of the observed from the fitted values.
• opt
  The optimal value of $\alpha$.
• value
  The minimum value of twice the Kullback-Leibler with the estimated bias added.
• bias
  The stimated bias.

Details

The $\alpha$-transformation is applied to the compositional data and the numerical otpimiation is performed for the regression, unless $\alpha=0$, where the coefficients are available in closed form. The estimated bias correction via the Tibshirani and Tibshirani (2009) criterion is applied.

References

Tsagris Michail (2015). Regression analysis with compositional data containing zero values. Chilean Journal of Statistics, 6(2): 47-57. http://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. http://arxiv.org/pdf/1106.1451.pdf Tibshirani and Tibshirani (2009). A bias correction for the minimum error rate in cross-validation. The Annals of Applied Statistics, 3(1):822-829.

See Also

alfa, alfa.reg

Examples

library(MASS)
y <- fgl[1:40, 2:4]
x <- fgl[1:40, 1]
mod <- alfareg.tune(y, x, a = c(0.2, 0.25, 0.3), K = 5, nc = 1)