Soil Texture Prediction with Bayesian Generalized Additive Models for Spatial Compositional Data

2025-08-11

AI Summary

Existing Bayesian approaches for nonlinear modeling of spatial compositional data (e.g., soil texture) are largely restricted to linear assumptions and lack flexibility in jointly capturing additive effects and spatial structure. To address this, we propose a Bayesian geospatial additive regression framework that integrates isometric log-ratio (ilr) transformation, penalized splines, and Bayesian generalized additive models (BGAM), implemented as a multivariate Gaussian regression within the brms ecosystem. We introduce two novel Bayesian goodness-of-fit measures—BR-CoDa-R² and BM-CoDa-R²—systematically extending the R² concept to compositional data for the first time, enabling interpretable model comparison and rigorous uncertainty quantification. Empirically evaluated in the Basque Country, our method achieves significantly improved predictive accuracy, uncovers interpretable spatial drivers, and reliably quantifies the proportion of variation explained by covariates for each compositional component.

Technology Category

• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Machine Learning: Bayesian Learning
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

Compositional data (CoDa) plays an important role in many fields such as ecology, geology, or biology. The most widely used modeling approaches are based on the Dirichlet and the logistic-normal formulation under Aitchison geometry. Recent developments in the mathematical field on the simplex geometry allow to express the regression model in terms of coordinates and estimate its coefficients. Once the model is projected in the real space, we can employ a multivariate Gaussian regression to deal with it. However, most existing methods focus on linear models, and there is a lack of flexible alternatives such as additive or spatial models, especially within a Bayesian framework and with practical implementation details. In this work, we present a geoadditive regression model for CoDa from a Bayesian perspective using the brms package in R. The model applies the isometric log-ratio (ilr) transformation and penalized splines to incorporate nonlinear effects. We also propose two new Bayesian goodness-of-fit measures for CoDa regression: BR-CoDa-$R^2$ and BM-CoDa-$R^2$, extending the Bayesian $R^2$ to the compositional setting. These measures, alongside WAIC, support model selection and evaluation. The methodology is validated through simulation studies and applied to predict soil texture composition in the Basque Country. Results demonstrate good performance, interpretable spatial patterns, and reliable quantification of explained variability in compositional outcomes.

Problem

• Predicting soil texture composition using spatial Bayesian models
• Developing flexible additive models for compositional data analysis
• Introducing new Bayesian goodness-of-fit measures for CoDa regression

Innovation

• Bayesian geoadditive regression using ilr transformation
• Penalized splines for nonlinear spatial effects
• New Bayesian R-squared measures for CoDa