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.

中文翻译：

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应用于动物生产系统的异构网络结构系数的分层建模

了解系统中绩效结果之间的相互联系对于集成管理越来越重要。结构方程模型 (SEM) 是一种多变量建模策略，它允许研究结果变量之间关联的方向性，从而深入了解它们作为定义功能网络的假定因果关系的相互联系。SEM 的一个关键假设是同质网络结构，其中定义功能联系的结构系数被假定为同质且不受环境条件或管理因素的影响。这个假设似乎有问题，因为系统经常受到明确的干预，以优化结果之间的必要权衡。使用贝叶斯方法，我们通过明确指定结构系数作为系统和非系统变异源的函数，提出了对分层 SEM 的方法扩展，以适应结构异质性。我们使用模拟研究验证了我们提出的方法的推理特性，并表明网络可以始终如一地被识别为同构或异构。我们将提议的方法扩展应用于猪生产设计实验的数据集，该实验由六个相互关联的繁殖性能结果组成，以探索因胎次而异的生理联系，同时考虑由于实验设计而导致的数据结构。全面的，我们的结果表明，基于显式分层 SEM 的异构功能网络建模可用于促进对动物生产农业中复杂系统的理解。本文随附的补充材料出现在网上。