  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.
