A Gaussian-threshold model is described under the general framework of structural equation models for inferring simultaneous and recursive relationships between binary and Gaussian characters, and estimating genetic parameters. Relationships between clinical mastitis (CM) and test-day milk yield (MY) in first-lactation Norwegian Red cows were examined using a recursive Gaussian-threshold model. For comparison, the data were also analyzed using a standard Gaussian-threshold, a multivariate linear model, and a recursive multivariate linear model. The first 180 days of lactation were arbitrarily divided into three periods of equal length, in order to investigate how these relationships evolve in the course of lactation. The recursive model showed negative within-period effects from (liability to) CM to test-day MY in all three lactation periods, and positive between-period effects from test-day MY to (liability to) CM in the following period. Estimates of recursive effects and of genetic parameters were time-dependent. The results suggested unfavorable effects of production on liability to mastitis, and dynamic relationships between mastitis and test-dayMYin the course of lactation. Fitting recursive effects had little influence on the estimation of genetic parameters. However, some differences were found in the estimates of heritability, genetic, and residual correlations, using different types of models (Gaussian-threshold vs. multivariate linear).
Keywords: Bayesian inference, mastitis, milk yield, structural equation model, threshold model