Cross validation for the ridge regression with compositional data as predictor using the alpha-transformation {Compositional}

Cross validation for the ridge regression with compositional data as predictor using the \alpha-transformation

Description

Cross validation for the ridge regression is performed. There is an option for the GCV criterion which is automatic. The predictor variables are compositional data and the \alpha-transformation is applied first.

Usage

alfaridge.tune(y, x, nfolds = 10, a = seq(-1, 1, by = 0.1),
lambda = seq(0, 2, by = 0.1), folds = NULL, ncores = 1,
graph = TRUE, col.nu = 15, seed = NULL)

Arguments

y

A numeric vector containing the values of the target variable. If the values are proportions or percentages, i.e. strictly within 0 and 1 they are mapped into R using the logit transformation.

x

A numeric matrix containing the compositional data, i.e. the predictor variables. Zero values are allowed.

nfolds

The number of folds in the cross validation.

a

A vector with the a grid of values of \alpha to be used.

lambda

A vector with the a grid of values of \lambda to be used.

folds

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

ncores

The number of cores to use. If it is more than 1 parallel computing is performed. 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

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

Details

A k-fold cross validation is performed.

Value

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

mspe

The MSPE where rows correspond to the \alpha values and the columns to the number of principal components.

best.par

The best pair of \alpha and \lambda.

performance

The minimum mean squared error of prediction.

runtime

The run time of the cross-validation procedure.

Author(s)

Michail Tsagris.

R implementation and documentation: Giorgos Athineou <[e-mail]> and Michail Tsagris [e-mail].

References

Hoerl A.E. and R.W. Kennard (1970). Ridge regression: Biased estimation for nonorthogonal problems. Technometrics, 12(1):55-67.

Brown P. J. (1994). Measurement, Regression and Calibration. Oxford Science Publications.

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

See Also

alfa.ridge, ridge.tune

Examples

library(MASS)
y <- as.vector(fgl[, 1])
x <- as.matrix(fgl[, 2:9])
x <- x / rowSums(x)
alfaridge.tune( y, x, nfolds = 10, a = seq(0.1, 1, by = 0.1),
lambda = seq(0, 1, by = 0.1) )