MLE of the folded model for a given value of alpha {Compositional}

MLE of the folded model for a given value of \alpha

Description

MLE of the folded model for a given value of \alpha.

Usage

alpha.mle(x, a)
a.mle(a, x)

Arguments

x

A matrix with the compositional data. No zero vaues are allowed.

a

A value of \alpha.

Details

This is a function for choosing or estimating the value of \alpha in the folded model (Tsagris and Stewart, 2020). It is called by a.est.

Value

If "alpha.mle" is called, a list including:

iters

The nubmer of iterations the EM algorithm required.

loglik

The maximimized log-likelihood of the folded model.

p

The estimated probability inside the simplex of the folded model.

mu

The estimated mean vector of the folded model.

su

The estimated covariance matrix of the folded model.

If "a.mle" is called, the log-likelihood is returned only.

Author(s)

Michail Tsagris.

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

References

Tsagris M. and Stewart C. (2022). A Review of Flexible Transformations for Modeling Compositional Data. In Advances and Innovations in Statistics and Data Science, pp. 225–234. https://link.springer.com/chapter/10.1007/978-3-031-08329-7_10

Tsagris M. and Stewart C. (2020). A folded model for compositional data analysis. Australian and New Zealand Journal of Statistics, 62(2): 249-277. https://arxiv.org/pdf/1802.07330.pdf

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.profile, alfa, alfainv, a.est

Examples

x <- as.matrix(iris[, 1:4])
x <- x / rowSums(x)
mod <- alfa.tune(x)
mod
alpha.mle(x, mod[1])