Compositional (version 1.0)

alfapcr.tune: Tuning the number of PCs in the PCR with compositional data using the $\alpha$-transformation

Description

This is a cross-validation procedure to decide on the number of principal components when using regression with compositional data (as predictor variables) using the $\alpha$-transformation.

Usage

alfapcr.tune(y, x, M = 10, maxk = 50, a = seq(-1, 1, by = 0.1), oiko = "normal",
seed = FALSE, ncores = 2)

Arguments

y

A vector with either continuous, binary or count data.

x

The predictor variables, the compositional data. Zero values are allowed.

M

The number of folds for the K-fold cross validation, set to 10 by default.

maxk

The maximum number of principal components to check.

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 and the solution exists in a closed form, since it the classical

oiko

The family to be used, "normal" for a continuous variable, "binomial" for a binary or "poisson" for a count vaiable.

seed

If seed is TRUE the same folds will always be generated.

ncores

How many cores to use. If you have heavy computations or do not want to wait for long time more than 1 core (if available) is suggested.

Value

• A matrix including:
• mspe
  The rows correspond to the $\alpha$ values and the columns to the number of principal components.

Details

The $\alpha$-transformation is applied to the compositional data first and the function "pcr.tune" or "glmpcr.tune" is called.

References

Tsagris M. (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 Jolliffe I.T. (2002). Principal Component Analysis.

See Also

alfa, profile, alfa.pcr, pcr.tune, glmpcr.tune, glm

Examples

library(MASS)
y <- fgl[, 1]
x <- fgl[, 2:9]
mod <- alfapcr.tune(y, x, M = 10, maxk = 50, a = seq(-1, 1, by = 0.1), oiko = "normal",
seed = FALSE, ncores = 1)