Hierarchical Bayesian modeling of heterogeneous cluster‐ and subject‐level associations between continuous and binary outcomes in dairy production |
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Authors: | Nora M Bello Juan P Steibel Robert J Tempelman |
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Institution: | 1. Department of Statistics, Kansas State University, , Manhattan, KS, 66506 USA;2. Department of Animal Science, Michigan State University, , East Lansing, MI, 28824 USA;3. Department of Fisheries and Wildlife, Michigan State University, , East Lansing, MI, 28824 USA |
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Abstract: | The augmentation of categorical outcomes with underlying Gaussian variables in bivariate generalized mixed effects models has facilitated the joint modeling of continuous and binary response variables. These models typically assume that random effects and residual effects (co)variances are homogeneous across all clusters and subjects, respectively. Motivated by conflicting evidence about the association between performance outcomes in dairy production systems, we consider the situation where these (co)variance parameters may themselves be functions of systematic and/or random effects. We present a hierarchical Bayesian extension of bivariate generalized linear models whereby functions of the (co)variance matrices are specified as linear combinations of fixed and random effects following a square‐root‐free Cholesky reparameterization that ensures necessary positive semidefinite constraints. We test the proposed model by simulation and apply it to the analysis of a dairy cattle data set in which the random herd‐level and residual cow‐level effects (co)variances between a continuous production trait and binary reproduction trait are modeled as functions of fixed management effects and random cluster effects. |
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Keywords: | Bivariate Bayesian model Dairy production systems Generalized linear mixed model Heterogeneous covariance Mixed outcomes |
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