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 heter ogeneity 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 changepoi nts at times T-1 and T-2, (0 < T-1 < T-2 < t(max)), with continuity of resi dual variance at these points, were assumed. Also, a nonlinear relationship between residual variance and the number of days of milking t was postulat ed. The residual variance at a time t (sigma(et)(2)) in the lactation phase i was modeled as: sigma(et)(2) = t(lambda i) sigma(ei)(2) for (i = 1, 2, 3 ), where lambda(i) is a phase-specific parameter. A Bayesian analysis using Gibbs sampling and the Metropolis-Hastings algorithm for marginalization w as implemented. After a burn-in of 20 000 iterations, 40 000 samples were d rawn to estimate posterior features. The posterior modes of T-1, T-2, lambd a(1), lambda(2), lambda(3), sigma(e1)(2), sigma(e2)(2), sigma(e3)(2) were 5 3.2 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 th e model has fewer parameters than other methods proposed to account for the heterogeneity of residual variance during lactation.