A total of 19,770 body weight records of Guzera cattle, measured from birth to 365 days of age and supplied by the Brazilian Zebu Breeders Association, was analyzed with the following objectives of: 1) to compare different residual variances through step functions with 1, 18, 28 and 53 classes and through variance functions with orders ranging from two to five using ordinary polynomials and 2) to estimate covariance functions considering different orders for direct additive genetic effects, animal permanent environmental and maternal permanent environmental effects, using random regression models. The random effects included were modeled by regression on Legendre Polynomials with orders ranging from linear to quartic. The models were compared through the likelihood ratio test, Akaike's information criterion and the Schwarz's Bayesian information criterion. The model with 18 heterogeneous classes was the one that best fitted the residual variances, according to the statistical tests; however, the model with variance function of 5th order also showed to be appropriate. The direct heritability estimates were higher than those found in literature, ranging from 0.04 to 0.53, showing similar trends when compared to those estimated using univariate models. Selection on body weight in any age should improve the body weight in all ages in the studied interval.
covariance function; orthogonal polynomials; residual variance classes
