Learning Bayesian networks with heterogeneous agronomic data sets via mixed-effect models and hierarchical clustering

Maize, a crucial crop globally cultivated across vast regions, especially in sub-Saharan Africa, Asia, and Latin America, occupies 197 million hectares as of 2021. Various statistical and machine learning models, including mixed-effect models, random coefficients models, random forests, and deep learning architectures, have been devised to predict maize yield. These models consider factors such as genotype, environment, genotype-environment interaction, and field management. However, the existing models often fall short of fully exploiting the complex network of causal relationships among these factors and the hierarchical structure inherent in agronomic data. This study introduces an innovative approach integrating random effects into Bayesian networks (BNs), leveraging their capacity to model causal and probabilistic relationships through directed acyclic graphs. Rooted in the linear mixed-effects models framework and tailored for hierarchical data, this novel approach demonstrates enhanced BN learning. Application to a real-world agronomic trial produces a model with improved interpretability, unveiling new causal connections. Notably, the proposed method significantly reduces the error rate in maize yield prediction from 28% to 17%. These results advocate for the preference of BNs in constructing practical decision support tools for hierarchical agronomic data, facilitating causal inference.