Compositional: alfapcr.tune – R documentation

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alfapcr.tune

Tuning the number of PCs in the PCR with compositional data using the α-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 α-transformation.

Usage

alfapcr.tune(y, x, model = "gaussian", nfolds = 10, maxk = 50, a = seq(-1, 1, by = 0.1),
folds = NULL, ncores = 1, graph = TRUE, col.nu = 15, seed = FALSE)

Arguments

`y`	A vector with either continuous, binary or count data.
`x`	A matrix with the predictor variables, the compositional data. Zero values are allowed.
`model`	The type of regression model to fit. The possible values are "gaussian", "binomial" and "poisson".
`nfolds`	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 α=0 the isometric log-ratio transformation is applied and the solution exists in a closed form, since it the classical mutivariate regression. The estimated bias correction via the (Tibshirani and Tibshirani (2009) criterion is applied.
`folds`	If you have the list with the folds supply it here. You can also leave it NULL and it will create folds.
`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. It is advisable to use it if you have many observations and or many variables, otherwise it will slow down th process.
`graph`	If graph is TRUE (default value) a filled contour plot will appear.
`col.nu`	A number parameter for the filled contour plot, taken into account only if graph is TRUE.
`seed`	If seed is TRUE the results will always be the same.

Details

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

Value

If graph is TRUE a filled contour will appear. A list including:

`mspe`	The MSPE where rows correspond to the α values and the columns to the number of principal components.
`best.par`	The best pair of α and number of principal components.
`performance`	The minimum mean squared error of prediction.
`runtime`	The time required by the cross-validation procedure.

Author(s)

Michail Tsagris

R implementation and documentation: Michail Tsagris mtsagris@uoc.gr and Giorgos Athineou <gioathineou@gmail.com>

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

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

Examples

library(MASS)
y <- as.vector(fgl[, 1])
x <- as.matrix(fgl[, 2:9])
x <- x/ rowSums(x)
mod <- alfapcr.tune(y, x, nfolds = 10, maxk = 50, a = seq(-1, 1, by = 0.1) )

Compositional

Compositional Data Analysis

v4.6

GPL (>= 2)

Authors

Michail Tsagris [aut, cre], Giorgos Athineou [aut], Abdulaziz Alenazi [ctb]

Initial release

2021-04-27