alpha.mle: MLE of the folded model for a given value of alpha

In Compositional: Compositional Data Analysis

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. The function alpha.mle() had a bug which was noticed by Wang, Yu and Yu (2026) and it is now fixed. The function now returns the correct log-likelihood and not the log-likelihood of the Q function in the EM algorithm. Also, the case of negative or positive \alpha is being treated properly. The function a.mle() returns the value of the Q function, deliberately, because it used as internal function in the a.est function.

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

Wang X., Yu L. and Yu, H. (2026). Data-driven small area estimation for compositional proportions based on parametric transformations. Statistical Methods & Applications, 1-41.

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 <- rdiri(100, runif(4, 5, 8))
alpha.mle(x, 0.5)

Compositional documentation built on Sept. 15, 2026, 9:07 a.m.