Data on 17258 weaning weight records of calves from a crossbreeding project were utilized to investigate the problem of collinearity and its effect on the estimation of direct, maternal and the non-additive genetic effects. Several criteria were used to detect the near-dependency among the independent variables. The results indicated that there was a near-dependency among both the direct and the maternal genetic effects causing unstable estimates. It was attempted to solve the collinearity problem using ridge regression. An improved model fit was evident at a ridge value of k = 0.8 with large reductions in standard errors and estimates with more meaningful biological interpretation. Ridge regression is recommended for the estimation of crossbreeding effects where inevitable collinearity amongst the independent variables are evident.