Cross validation for the alpha-kernel regression with compositional response data {Compositional}

Cross validation for the \alpha-kernel regression with compositional response data

Description

Cross validation for the \alpha-kernel regression with compositional response data.

Usage

akernreg.tune(y, x, a = seq(0.1, 1, by = 0.1), h = seq(0.1, 1, length = 10),
type = "gauss", nfolds = 10, folds = NULL, seed = NULL)

Arguments

y

A matrix with the compositional response data. Zeros are allowed.

x

A matrix with the available predictor variables.

a

A vector with a grid of values 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.

h

A vector with the bandwidth value(s) to consider.

type

The type of kernel to use, "gauss" or "laplace".

nfolds

The number of folds. Set to 10 by default.

folds

If you have the list with the folds supply it here. You can also leave it NULL and it will create folds.

seed

You can specify your own seed number here or leave it NULL.

Details

A k-fold cross validation for the \alpha-kernel regression for compositional response data is performed.

Value

A list including:

kl

The Kullback-Leibler divergence for all combinations of \alpha and h.

js

The Jensen-Shannon divergence for all combinations of \alpha and h.

klmin

The minimum Kullback-Leibler divergence.

jsmin

The minimum Jensen-Shannon divergence.

kl.alpha

The optimal \alpha that leads to the minimum Kullback-Leibler divergence.

kl.h

The optimal h that leads to the minimum Kullback-Leibler divergence.

js.alpha

The optimal \alpha that leads to the minimum Jensen-Shannon divergence.

js.h

The optimal h that leads to the minimum Jensen-Shannon divergence.

runtime

The runtime of the cross-validation procedure.

Author(s)

Michail Tsagris.

R implementation and documentation: Michail Tsagris [e-mail].

References

Tsagris M., Alenazi A. and Stewart C. (2023). Flexible non-parametric regression models for compositional response data with zeros. Statistics and Computing, 33(106).

https://link.springer.com/article/10.1007/s11222-023-10277-5

See Also

akern.reg, aknnreg.tune, aknn.reg, alfa.rda, alfa.fda

Examples

y <- as.matrix( iris[, 1:3] )
y <- y / rowSums(y)
x <- iris[, 4]
mod <- akernreg.tune(y, x, a = c(0.4, 0.6), h = c(0.1, 0.2), nfolds = 5)