Mixture model selection with the alpha-transformation using BIC {Compositional}

Mixture model selection with the \alpha-transformation using BIC

Description

Mixture model selection with the \alpha-transformation using BIC.

Usage

bic.alfamixnorm(x, G, a = seq(-1, 1, by = 0.1), veo = FALSE, graph = TRUE)

Arguments

x

A matrix with compositional data.

G

A numeric vector with the number of components, clusters, to be considered, e.g. 1:3.

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.

veo

Stands for "Variables exceed observations". If TRUE then if the number variablesin the model exceeds the number of observations, but the model is still fitted.

graph

A boolean variable, TRUE or FALSE specifying whether a graph should be drawn or not.

Details

The \alpha-transformation is applied to the compositional data first and then mixtures of multivariate Gaussian distributions are fitted. BIC is used to decide on the optimal model and number of components.

Value

A list including:

abic

A list that contains the matrices of all BIC values for all values of \alpha.

optalpha

The value of \alpha that leads to the highest BIC.

optG

The number of components with the highest BIC.

optmodel

The type of model corresponding to the highest BIC.

If graph is set equal to TRUE a plot with the BIC of the best model for each number of components versus the number of components and a list with the results of the Gaussian mixture model for each value of \alpha.

Author(s)

Michail Tsagris.

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

References

Ryan P. Browne, Aisha ElSherbiny and Paul D. McNicholas (2018). mixture: Mixture Models for Clustering and Classification. R package version 1.5.

Ryan P. Browne and Paul D. McNicholas (2014). Estimating Common Principal Components in High Dimensions. Advances in Data Analysis and Classification, 8(2), 217-226.

Aitchison J. (1986). The statistical analysis of compositional data. Chapman & Hall.

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.mix.norm, mix.compnorm, mix.compnorm.contour, rmixcomp, alfa, alfa.knn, alfa.rda, comp.nb

Examples

x <- as.matrix( iris[, 1:4] )
x <- x/ rowSums(x)
bic.alfamixnorm(x, 1:3, a = c(0.4, 0.5, 0.6), graph = FALSE)