Likelihood analysis for a class of spatial geostatistical compositional models

TL;DR

This paper introduces a likelihood-based geostatistical method for modeling and predicting regionalized compositional data, effectively handling the correlation structure inherent in compositions like soil particle fractions.

Contribution

It combines additive-log-ratio transformation with multivariate geostatistical models to enable standard likelihood estimation for compositional spatial data.

Findings

Effective spatial prediction of soil composition fractions.

Maximum likelihood estimators perform well in small samples.

Method successfully accounts for compositional correlation structures.

Abstract

We propose a model-based geostatistical approach to deal with regionalized compositions. We combine the additive-log-ratio transformation with multivariate geostatistical models whose covariance matrix is adapted to take into account the correlation induced by the compositional structure. Such specification allows the usage of standard likelihood methods for parameters estimation. For spatial prediction we combined a back-transformation with the Gauss-Hermite method to approximate the conditional expectation of the compositions. We analyze particle size fractions of the top layer of a soil for agronomic purposes which are typically expressed as proportions of sand, clay and silt. Additionally a simulation study assess the small sample properties of the maximum likelihood estimator.