Approximation of reliabilities for multiple-trait model with maternal effects

Reliabilities for a multiple-trait maternal model were obtained by combining reliabilities obtained from single-trait models. Single-trait reliabilities were obtained using an approximation that supported models with additive and permanent environmental effects. For the direct effect, the maternal and permanent environmental variances were assigned to the residual. For the maternal effect, variance of the direct effect was assigned to the residual. Data included 10,550 birth weight, 11,819 weaning weight, and 3,617 postweaning gain records of Senepol cattle. Reliabilities were obtained by generalized inversion and by using single-trait and multiple-trait approximation methods. Some reliabilities obtained by inversion were negative because inbreeding was ignored in calculating the inverse of the relationship matrix. The multiple-trait approximation method reduced the bias of approximation when compared with the single-trait method. The correlations between reliabilities obtained by inversion and by multiple-trait procedures for the direct effect were 0.85 for birth weight, 0.94 for weaning weight, and 0.96 for postweaning gain. Correlations for maternal effects for birth weight and weaning weight were 0.96 to 0.98 for both approximations. Further improvements can be achieved by refining the single-trait procedures.