Ridge regression with the alpha-transformation plot {Compositional}

Ridge regression plot

Description

A plot of the regularised regression coefficients is shown.

Usage

alfaridge.plot(y, x, a, lambda = seq(0, 5, by = 0.1) )

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. In any case, they must be continuous only.

x

A numeric matrix containing the continuous variables.

a

The value of the \alpha-transformation. It has to be between -1 and 1. If there are zero values in the data, you must use a strictly positive value.

lambda

A grid of values of the regularisation parameter \lambda.

Details

For every value of \lambda the coefficients are obtained. They are plotted versus the \lambda values.

Value

A plot with the values of the coefficients as a function of \lambda.

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

ridge.plot, alfa.ridge

Examples

library(MASS)
y <- as.vector(fgl[, 1])
x <- as.matrix(fgl[, 2:9])
x <- x / rowSums(x)
alfaridge.plot(y, x, a = 0.5, lambda = seq(0, 5, by = 0.1) )