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