Genetic analysis of liability to clinical mastitis, with somatic cell score and production traits using bivariate threshold–linear and linear–linear models

Inferences about genetic and residual correlation estimates and sire evaluations involving a categorical trait with linear model are ambiguous and mostly based on data simulations. In this study, estimates of variance components and prediction of breeding values in a model with a categorical and a continuous trait were compared between threshold–linear (TLM) and linear–linear models (LLM) in analysis of large clinical mastitis (CM) field data. Data on CM, somatic cell score (SCS), 305-day milk (MY), protein (PY) and fat yield (FY) from first-lactation Finnish Ayrshire cows were used. Four bivariate analyses were made using a TLM in Bayesian analysis. Each analysis fitted CM and one continuous trait at a time. Corresponding bivariate analyses were made using a Gaussian linear model. Estimates of heritabilities for CM were 0.06 and 0.02 from TLM and LLM, respectively whilst heritability estimates of the continuous traits were similar from both models. Genetic correlations between CM–SCS, CM–MY, CM–PY, and CM–FY from TLM and LLM were 0.63 and 0.63; 0.36 and 0.36; 0.32 and 0.32; 0.30 and 0.29, respectively. Estimates of residual correlations were 0.11 and 0.06; − 0.04 and − 0.02; − 0.03 and − 0.02; − 0.05 and − 0.03 between CM–SCS, CM–MY, CM–PY, and CM–FY, respectively. Comparison between the models indicates similar estimates of genetic correlations with no underestimation with the linear model analysis. In CM evaluation, the comparison of model's predictive ability showed greater improvements in accuracy with the bivariate than with the univariate models. There was, however no clear advantage of univariate threshold model over univariate linear model, except for less accuracy sires.