MLE of distributions for compositional data {MLE}

MLE of distributions for compositional data

Description

MLE of distributions for compositional data.

Usage

comp.mle(x, distr = "diri", type = 1, a = NULL, tol = 1e-07)

Arguments

x

A matrix containing the compositional data. Zero values are not allowed except for the case of the ZAD which is designed for the case of zero values present.

distr

The distribution to fit. "diri" stands for the Dirichlet distribution, "zad" is the Zero Adjusted Dirichlet distribution and "afolded" for the \alpha-folded model (Tsagris and Stewart, 2020).

type

This is for the Dirichlet distribution ("diri"). Type 1 uses a vectorised version of the Newton-Raphson (Minka, 2012). In high dimensions this is to be preferred. If the data are too concentrated, regardless of the dimensions, this is also to be preferrred. Type 2 uses the regular Newton-Raphson, with matrix multiplications. In small dimensions this can be considerably faster.

a

The value of \alpha. If this is NULL, the function will estimate it internally.

tol

The tolerance level idicating no further increase in the log-likelihood.

Details

Maximum likelihood estimation of the parameters of a Dirichlet distribution is performed via Newton-Raphson. Initial values suggested by Minka (2012) are used.

Value

A list including:

loglik

The value of the log-likelihood.

param

The estimated parameters.

phi

The precision parameter. If covariates are linked with it (function "diri.reg2"), this will be a vector.

mu

The mean vector of the distribution.

runtime

The time required by the MLE.

best

The estimated optimal \alpha 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.

Author(s)

Michail Tsagris and Sofia Piperaki.

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

References

Minka Thomas (2012). Estimating a Dirichlet distribution. Technical report.

Ng Kai Wang, Guo-Liang Tian, and Man-Lai Tang (2011). Dirichlet and related distributions: Theory, methods and applications. John Wiley & Sons.

Tsagris M. and Stewart C. (2018). A Dirichlet regression model for compositional data with zeros. Lobachevskii Journal of Mathematics, 39(3): 398–412. Preprint available from https://arxiv.org/pdf/1410.5011.pdf

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

See Also

prop.mle

Examples

x <- matrix( rgamma(100 * 4, c(5, 6, 7, 8), 1), ncol = 4)
x <- x / rowSums(x)
res <- comp.mle(x)