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 \alpha-folded model (Tsagris and Stewart, 2020). It is called by a.est.

Value

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

iters

The number of iterations the EM algorithm required.

loglik

The maximimized log-likelihood of the folded model.

p

The estimated probability inside the simplex of the \alpha-folded model.

mu

The estimated mean vector of the \alpha-folded model.

su

The estimated covariance matrix of the \alpha-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])