Fourteen random regression models were used to adjust 86,595 test-day milk records of 2,155 first lactation of native Caracu cows. The models include fixed effects of contemporary group and age of cow as covariable. A cubic regression on Legendre orthogonal polynomial of days in milk was used to model the mean trend and the additive genetic and permanent environmental regressions. Different structures of residual variances were tried and considered through homogeneous variances or heterogeneous variances, modeled as a step function with 10, 15 and 43 classes or variance functions, using ordinary and orthogonal polynomials of different orders (quadratic to sixty). Models were compared by Likelihood ratio test, Akaike's Information Criterion and Bayesian Information Criterion. These tests indicated that functions with higher order improved the change in log-likelihood. The models with step functions were superior to models with residual variance functions. Homogeneous residual variances were not adequate. The model using a step function with 15 heterogeneous variances presented the best fit. However, the genetic parameters estimated by the models with 10, 15 or 43 classes or with a sixty order variance function were similar.
covariance functions; genetic parameters; milk yield
