Alternative parameterizations of the multiple-trait random regression model for milk yield and somatic cell score via...

Multiple-trait random regression models with recursive phenotypic link from somatic cell score (SCS) to milk yield on the same test day and with different restrictions on co-variances between these traits were fitted to the first-lactation Canadian Holstein data. Bayesian methods with Gibbs sampling were used to derive inferences about parameters for all models. Bayes factor indicated that the recursive model with uncorrelated environmental effects between traits was the most plausible specification in describing the data. Goodness of fit in terms of a within-trait weighted mean square error and correlation between observed and predicted data was the same for all parameterizations. All recursive models estimated similar negative causal effects from SCS to milk yield (up to -0.4 in 46-115 days in milk in lactation). Estimates of heritabilities, genetic and environmental correlations for the first two regression coefficients (overall level of a trait and lactation persistency) within both traits were similar among models. Genetic correlations between milk and SCS were dependent on the restrictions on genetic co-variances for these traits. Recursive model with uncorrelated system genetic effects between milk and SCS gave estimates of genetic correlations of the opposite sign compared with a regular multiple-trait model. Phenotypic recursion between milk and SCS seemed, however, to be the only source of environmental correlations between these two traits. Rankings of sires for total milk yield in lactation, average daily SCS and persistency for both traits were similar among models. Multiple-trait model with recursive links between milk and SCS and uncorrelated random environmental effects could be an attractive alternative for a regular multiple-trait model in terms of model parsimony and accuracy.