A folded model for compositional data analysis

TL;DR

This paper introduces a new folded model for compositional data analysis that extends the alpha-transformation, offering a flexible distribution class with efficient EM-based estimation, outperforming logistic normal models in capturing data structure.

Contribution

The paper develops a novel folded model extending the alpha-transformation, providing a flexible distribution for compositional data analysis with efficient estimation methods.

Findings

The folded model outperforms logistic normal in data structure capture.

EM algorithm enables efficient parameter estimation.

Simulation studies validate the model's effectiveness.

Abstract

A folded type model is developed for analyzing compositional data. The proposed model involves an extension of the $\alpha$-transformation for compositional data and provides a new and flexible class of distributions for modeling data defined on the simplex sample space. Despite its rather seemingly complex structure, employment of the EM algorithm guarantees efficient parameter estimation. The model is validated through simulation studies and examples which illustrate that the proposed model performs better in terms of capturing the data structure, when compared to the popular logistic normal distribution, and can be advantageous over a similar model without folding.