Implementing structural equation models to observational data from feedlot production systems

The objective of this study was to illustrate the implementation of a mixed-model-based structural equation modeling (SEM) approach to observational data in the context of feedlot production systems. Different from traditional multiple-trait models, SEMs allow assessment of potential causal interrelationships between outcomes and can effectively discriminate between direct and indirect effects. For illustration, we focused on feedlot performance and its relationship to health outcomes related to Bovine Respiratory Disease (BRD), which accounts for approximately 75% of morbidity and 50-80% of deaths in feedlots. Our data consisted of 1430 lots representing 178,983 cattle from 9 feedlot operations located across the US Great Plains. We explored functional links between arrival weight (AW; i = 1), BRD-related treatment costs (Trt$; as a proxy for health; i = 2) and average daily weight gain (ADG; as an indicator of productive performance i = 3), accounting for the fixed effect of sex and correlation patterns due to the clustering of lots within feedlots. We proposed competing plausible causal models based on expert knowledge. The best fitting model selected for inference supported direct effects of AW on ADG as well as indirect effects of AW on ADG mediated by Trt$. Direct effects from outcome i' to outcome i are quantified by the structural coefficient λ_ii', such that every unit increase in kg/head of AW had a direct effect of increasing ADG by approximately (estimate ± standard error) λˆ₃₁=0.002±0.0001 kg/head/day and also a direct effect of reducing Trt$ by an estimated λˆ₂₁=$0.08±0.006 USD per head. In addition, every $1 USD spent on Trt$ directly decreased ADG by an estimated λˆ₃₂=0.004±0.0006 kg/head/day. From these estimates, we show how to compute the indirect, Trt$-mediated, effect of AW on ADG, as well as the overall effect of AW on ADG, including both direct and indirect effects. We further compared estimates of SEM-based effects with those obtained from standard linear regression mixed models and demonstrated the additional advantage of explicitly distinguishing direct and indirect components of an overall regression effect using SEMs. Understanding the direct and indirect mechanisms of interplay between health and performance outcomes may provide valuable insight into production systems.