Multicollinearity in genetic effects for weaning weight in a beef cattle composite population

Abstract

In the genetic evaluation of composite cattle or multiracial populations, the additive and non-additive genetic effects need to be estimated given their importance in developing strategies for crossing. However, multicollinearity, defined as the presence of strong linear correlations between the explanatory variables, is an obstacle to obtaining these estimates, since it produces unstable regression coefficients with large standard errors when the least square method is used, leading to erroneous inferences. Thus, the objective of this study was to detect possible collinearity involving the covariates of genetic effects, to assess them by the ridge regression (RR) method, and to compare results with estimates obtained by the least squares (LS) method. Weaning weight data of composite Montana Tropical bovine born between 1994 and 2008 were used. Some covariates from the model were involved in two strong and three weak collinearities. The RR method was used as an alternative to the LS method and showed better results. After using RR, the average variance inflation factors reduced from 16 to 5.3 and yielded more accurate estimates, with smaller standard errors than those obtained by the LS.