CompositionalML (version 1.0)

alfa-PPR with compositional predictor variables: \(\alpha\)-PPR with compositional predictor variables

Description

\(\alpha\)-PPR with compositional predictor variables.

Usage

alfa.ppr(xnew, y, x, a = seq(-1, 1, by = 0.1), nterms = 1:10)

Value

A list including:

mod

A list with the results of the PPR model for each value of \(\alpha\) that includes the PPR output as provided by the function "ppr", for each value of "nterms".

est

A list with the predicted response values of "xnew" for each value of \(\alpha\) and number of "nterms".

Arguments

xnew

A matrix with the new compositional data whose group is to be predicted. Zeros are allowed, but you must be careful to choose strictly positive vcalues of \(\alpha\).

y

The response variable, a numerical vector.

x

A matrix with the compositional data.

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 a=0, the isometric log-ratio transformation is applied.

nterms

The number of terms to include in the model.

Author

Michail Tsagris.

R implementation and documentation: Michail Tsagris .

Details

This is the standard projection pursuit regression (PPR) applied to the \(\alpha\)-transformed compositional predictors. See the built-in function "ppr" for more details.

References

Friedman J. H. and Stuetzle W. (1981). Projection pursuit regression. Journal of the American Statistical Association, 76, 817-823. doi: 10.2307/2287576.

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

alfappr.tune

Examples

x <- as.matrix(iris[, 1:3])
x <- x/ rowSums(x)
y <- iris[, 4]
mod <- alfa.ppr(x, y, x, a = c(0, 0.5, 1), nterms = c(2, 3))
mod