Assessment of heterogeneity of residual variances using changepoint techniques

Several studies using test-day models show clear heterogeneity of residual variance along lactation. A changepoint technique to account for this heterogeneity is proposed. The data set included 100 744 test-day records of 10 869 Holstein-Friesian cows from northern Spain. A three-stage hierarchical model using the Wood lactation function was employed. Two unknown changepoints at times T(1 )and T(2), (0 <T(1 )<T(2 )<t(max)), with continuity of residual variance at these points, were assumed. Also, a nonlinear relationship between residual variance and the number of days of milking t was postulated. The residual variance at a time t([Image: see text]) in the lactation phase i was modeled as: [Image: see text] for (i = 1, 2, 3), where λ(ι )is a phase-specific parameter. A Bayesian analysis using Gibbs sampling and the Metropolis-Hastings algorithm for marginalization was implemented. After a burn-in of 20 000 iterations, 40 000 samples were drawn to estimate posterior features. The posterior modes of T(1), T(2), λ(1), λ(2), λ(3), [Image: see text], [Image: see text], [Image: see text] were 53.2 and 248.2 days; 0.575, -0.406, 0.797 and 0.702, 34.63 and 0.0455 kg(2), respectively. The residual variance predicted using these point estimates were 2.64, 6.88, 3.59 and 4.35 kg(2 )at days of milking 10, 53, 248 and 305, respectively. This technique requires less restrictive assumptions and the model has fewer parameters than other methods proposed to account for the heterogeneity of residual variance during lactation.