Hierarchical Modeling of Structural Coefficients for Heterogeneous Networks with an Application to Animal Production Systems

Understanding the interconnections between performance outcomes in a system is increasingly important for integrated management. Structural equation models (SEMs) are a type of multiple-variable modeling strategy that allows investigation of directionality in the association between outcome variables, thereby providing insight into their interconnections as putative causal links defining a functional network. A key assumption underlying SEMs is that of a homogeneous network structure, whereby the structural coefficients defining functional links are assumed homogeneous and impervious to environmental conditions or management factors. This assumption seems questionable as systems are regularly subjected to explicit interventions to optimize the necessary trade-offs between outcomes. Using a Bayesian approach, we propose methodological extensions to hierarchical SEMs that accommodate structural heterogeneity by explicitly specifying structural coefficients as functions of systematic and non-systematic sources of variation. We validate the inferential properties of our proposed approach using a simulation study and show that networks can be consistently identified as homogeneous or heterogeneous. We apply the proposed methodological extensions to a dataset from a designed experiment in swine production consisting of six interrelated reproductive performance outcomes to explore physiological links that differed by parity, while accounting for data architecture due to experimental design. Overall, our results indicate that explicit hierarchical SEM-based modeling of heterogeneous functional networks can be used to advance understanding of complex systems in animal production agriculture. Supplementary materials accompanying this paper appear online.