Comparing methodologies to estimate fixed genetic effects and to predict genetic values for an Angus x Nellore cattle population

The study assesses the need for and effectiveness of using ridge regression when estimating regression coefficients of covariates representing genetic effects due to breed proportion in a crossbreed genetic evaluation. It also compares 2 ways of selecting the ridge parameters. A large crossbred Angus x Nellore population with 294,045 records for weaning gain and 148,443 records for postweaning gain was used. Phenotypic visual scores varying from 1 to 5 for weaning and postweaning conformation, weaning and postweaning precocity, weaning and postweaning muscling, and scrotal circumference were analyzed. Three models were used to assess the need for ridge regression, having 4, 6, and 8 genetic covariates. All 3 models included the fixed contemporary group effect and random animal, maternal, and permanent environment effects. Model AH included fixed direct and maternal breed additive and the direct and maternal heterosis covariates, model AHE also included direct and maternal epistatic loss covariates, and model AHEC further included direct and maternal complementarity effects. The normal approach is to include these covariates as fixed effects in the model. However, being all derived from breed proportions, they are highly collinear and, consequently, may be poorly estimated. Ridge regression has been proposed as a method of reducing the collinearity. We found that collinearity was not a problem for models AH and AHE. We found a high variance inflation factor, >20, associated with some maternal covariates in the AHEC model reflecting instability of the regression coefficients and that this instability was well addressed by using ridge regression using a ridge parameter calculated from the variance inflation factor.