Research involving diverse but related data sets, where associations between covariates and outcomes may vary, is prevalent in various fields including agronomic studies. In these scenarios, hierarchical models, also known as multilevel models, are frequently employed to assimilate information from different data sets while accommodating their distinct characteristics. However, their structure extend beyond simple heterogeneity, as variables often form complex networks of causal relationships. Bayesian networks (BNs) provide a powerful framework for modelling such relationships using directed acyclic graphs to illustrate the connections between variables. This study introduces a novel approach that integrates random effects into BN learning. Rooted in linear mixed-effects models, this approach is particularly well-suited for handling hierarchical data. Results from a real-world agronomic trial suggest that employing this approach enhances structural learning, leading to the discovery of new connections and the improvement of improved model specification. Furthermore, we observe a reduction in prediction errors from 28% to 17%. By extending the applicability of BNs to complex data set structures, this approach contributes to the effective utilisation of BNs for hierarchical agronomic data. This, in turn, enhances their value as decision-support tools in the field.

翻译：涉及变量与结果间关联可能不同的多样化但相关数据集的研究，在农学研究等众多领域普遍存在。在此类场景中，分层模型（亦称多水平模型）常被用于整合不同数据集的信息，同时兼顾其独特特征。然而，这些模型的结构已超越简单的异质性，变量间往往形成复杂的因果网络关系。贝叶斯网络（BNs）通过有向无环图刻画变量间关联，为建模此类关系提供了强大框架。本研究提出一种将随机效应融入贝叶斯网络学习的新方法。该方法根植于线性混合效应模型，尤其适用于处理分层数据。真实农学试验结果表明，采用该方法可增强结构学习，发现新连接并改进模型规范。此外，我们观察到预测误差从28%降至17%。通过将贝叶斯网络的应用范围拓展至复杂数据结构，该方法有效推动了贝叶斯网络在分层农学数据中的应用，进而提升其作为领域决策支持工具的价值。