Tuning of the divergence based regression for compositional data with compositional data in the covariates side using the alpha-transformation {Compositional} R Documentation

## Tuning of the divergence based regression for compositional data with compositional data in the covariates side using the α-transformation

### Description

Tuning of the divergence based regression for compositional data with compositional data in the covariates side using the α-transformation.

### Usage

```klalfapcr.tune(y, x, covar = NULL, nfolds = 10, maxk = 50, a = seq(-1, 1, by = 0.1),
folds = NULL, graph = FALSE, tol = 1e-07, maxiters = 50, seed = FALSE)
```

### Arguments

 `y` A numerical matrix with compositional data with or without zeros. `x` A matrix with the predictor variables, the compositional data. Zero values are allowed. `covar` If you have other continuous covariates put themn here. `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. `folds` If you have the list with the folds supply it here. You can also leave it NULL and it will create folds. `graph` If graph is TRUE (default value) a filled contour plot will appear. `tol` The tolerance value to terminate the Newton-Raphson procedure. `maxiters` The maximum number of Newton-Raphson iterations. `seed` If seed is TRUE the results will always be the same.

### Details

The M-fold cross validation is performed in order to select the optimal values for α and k, the number of principal components. The α-transformation is applied to the compositional data first, the first k principal component scores are calcualted and used as predictor variables for the Kullback-Leibler divergence based regression model. This procedure is performed M times during the M-fold cross validation.

### Value

A list including:

 `mspe` A list with the KL divergence for each value of α and k in every fold. `performance` A matrix with the KL divergence for each value of α averaged over all folds. If graph is set to TRUE this matrix is plotted. `best.perf` The minimum KL divergence. `params` The values of α and k corresponding to the minimum KL divergence.

### Author(s)

Initial code by Abdulaziz Alenazi. Modifications by Michail Tsagris.

R implementation and documentation: Abdulaziz Alenazi a.alenazi@nbu.edu.sa and Michail Tsagris mtsagris@uoc.gr.

### References

Alenazi A. (2019). Regression for compositional data with compositioanl data as predictor variables with or without zero values. Journal of Data Science, 17(1): 219-238. http://www.jds-online.com/file_download/688/01+No.10+315+REGRESSION+FOR+COMPOSITIONAL+DATA+WITH+COMPOSITIONAL+DATA+AS+PREDICTOR+VARIABLES+WITH+OR+WITHOUT+ZERO+VALUES.pdf

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

```kl.alfapcr, cv.tflr, pcr, glm.pcr, alfapcr.tune ```

### Examples

```library(MASS)
y <- rdiri( 214, runif(4, 1, 3) )
x <- as.matrix( fgl[, 2:9] )
x <- x / rowSums(x)
mod <- klalfapcr.tune(y = y, x = x, a = c(0.7, 0.8) )
mod
```

[Package Compositional version 5.2 Index]