Cross validation for the alpha-k-NN regression with compositional predictor variables: Cross validation for the \(\alpha\)-k-NN regression with compositional predictor variables
Description
Cross validation for the \(\alpha\)-k-NN regression with compositional predictor variables.
Usage
alfaknnreg.tune(y, x, a = seq(-1, 1, by = 0.1), k = 2:10, nfolds = 10,
apostasi = "euclidean", method = "average", folds = NULL, seed = NULL, graph = FALSE)
Arguments
y
The response variable, a numerical vector.
x
A matrix with the available compositional data. Zeros are allowed.
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.
k
The number of nearest neighbours to consider. It can be a single number or a vector.
nfolds
The number of folds. Set to 10 by default.
apostasi
The type of distance to use, either "euclidean" or "manhattan".
method
If you want to take the average of the reponses of the k closest observations, type "average".
For the median, type "median" and for the harmonic mean, type "harmonic".
folds
If you have the list with the folds supply it here. You can also leave it NULL and it will create folds.
seed
If seed is TRUE the results will always be the same.
graph
If graph is TRUE (default value) a filled contour plot will appear.
Value
A list including:
mspe
The mean square error of prediction.
performance
The minimum mean square error of prediction.
opt_a
The optimal value of \(\alpha\).
opt_k
The optimal value of k.
runtime
The runtime of the cross-validation procedure.
Details
A k-fold cross validation for the \(\alpha\)-k-NN regression for compositional response data is performed.
References
Michail Tsagris, Abdulaziz Alenazi and Connie Stewart (2020).
Non-parametric regression models for compositional data.
https://arxiv.org/pdf/2002.05137.pdf
# NOT RUN {library(MASS)
x <- as.matrix(fgl[, 2:9])
x <- x / rowSums(x)
y <- fgl[, 1]
mod <- alfaknnreg.tune(y, x, a = seq(0.2, 0.4, by = 0.1), k = 2:4, nfolds = 5)
# }