A flexible Bayesian tool for CoDa mixed models: logistic-normal distribution with Dirichlet covariance

TL;DR

This paper introduces the logistic-normal Dirichlet Model (LNDM), a flexible Bayesian approach for compositional data analysis that effectively handles structured random effects and integrates into R-INLA for improved model fitting and prediction.

Contribution

The paper presents the LNDM, a novel Bayesian model for CoDa that incorporates structured random effects and is seamlessly integrated into R-INLA, enhancing analysis capabilities.

Findings

LNDM effectively models structured random effects in CoDa.

The approach facilitates model selection using DIC, WAIC, and CPO.

Demonstrated success in ecological case study with Arabidopsis thaliana.

Abstract

Compositional Data Analysis (CoDa) has gained popularity in recent years. This type of data consists of values from disjoint categories that sum up to a constant. Both Dirichlet regression and logistic-normal regression have become popular as CoDa analysis methods. However, fitting this kind of multivariate models presents challenges, especially when structured random effects are included in the model, such as temporal or spatial effects. To overcome these challenges, we propose the logistic-normal Dirichlet Model (LNDM). We seamlessly incorporate this approach into the R-INLA package, facilitating model fitting and model prediction within the framework of Latent Gaussian Models (LGMs). Moreover, we explore metrics like Deviance Information Criteria (DIC), Watanabe Akaike information criterion (WAIC), and cross-validation measure conditional predictive ordinate (CPO) for model selection in R-INLA for CoDa. Illustrating LNDM through a simple simulated example and with an ecological case study on Arabidopsis thaliana in the Iberian Peninsula, we underscore its potential as an effective tool for managing CoDa and large CoDa databases.