This study was carried out to evaluate the use of different residual variance structures to estimate covariance functions for weight of Canchim beef cattle. The covariance functions were estimated by the Restricted Maximum Likelihood method, in an animal model with fixed effect of contemporary group (year and month of birth and sex), age of dam at calving as covariable (linear and quadratic effects) and mean growth trajectory while the random effects considered were the direct additive genetic and maternal effects, permanent individual environment and maternal and residual effects. Different structures were used for residual variance: ordinary polynomials of different orders (linear to fifth) and step functions with 1, 5, 10, 15 and 20 classes. Homogeneous residual variance was not adequate. The four-ordered variance function and the step function with 20 classes presented the best fit and the class division was more efficient than residual functions. The estimated heritabilities were between 0.16 and 0.25, and the greatest ones were obtained close to 360 days and at the end of the study period. The estimated heritabilities were similar for models with homogeneous residual variance, four-ordered residual function and step model with 20 classes of heterogeneous variances. The best description of residual variance, for weights at different ages of Canchim beef cattle, was by step function with 20 classes of heterogeneous variances. However, as existing classes with the same variances, they can be grouped to reduce the number of parameters to be estimated.
correlation; heritability; random regression
