Inferring Upon Heterogeneous Associations in Dairy Cattle Performance Using a Bivariate Hierarchical Model

Multivariate hierarchical Bayesian models provide a flexible framework for comprehensive study of biological systems with more than one outcome. Recent methodological developments facilitate modeling of heterogeneous associations between outcomes by specifying a linear mixed model on (co)variances at different levels of the data structure. Motivated by previous evidence for heterogeneous correlations in animal agriculture, we apply the proposed hierarchical Bayesian models to study the nature of the correlations between key performance outcomes in dairy cattle production systems, namely milk yield and reproduction. That is, the association between these outcomes might depend upon various fixed and random effect sources of heterogeneity both at the individual cow (residual) level as well as the herd (cluster) level. We thus propose a sequential modeling approach based on the deviance information criterion to select relevant explanatory variables on both types of associations. Furthermore, we extend the proposed methodology to accommodate right-censored outcomes, as common for dairy reproduction data, and use it to analyze field data from the Michigan dairy industry. The nature of the associations between milk production and reproduction in dairy cattle was inferred to be strongly heterogeneous and driven by multiple farm management practices and herd attributes, as well as by random clustering effects, at both cow and herd levels, thereby suggesting potential between-herd and within-herd intervention strategies to optimize performance of dairy production systems. Supplementary materials are available online.