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 T1 and T2, (0<T1<T2<tmax), 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 (sigma2(et)) in the lactation phase i was modeled as: sigma2(et) = t(lambda)(i)sigma2(ei) 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 was implemented. After a burn-in of 20,000 iterations, 40,000 samples were drawn to estimate posterior features. The posterior modes of T1, T2, lambda1, lambda2, lambda3, sigma2(e1), sigma2(e2), sigma2(e3) were 53.2 and 248.2 days; 0.575, -0.406, 0.797 and 0.702, 34.63 and 0.0455 kg2, respectively. The residual variance predicted using these point estimates were 2.64, 6.88, 3.59 and 4.35 kg2 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.

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