Application of multivariate heavy-tailed distributions to residuals in the estimation of genetic parameters of growth traits in beef cattle1

Abstract

Assumptions of normality in most animal breeding applications may make inferences vulnerable to the presence of outliers. Heavy-tail densities are viable alternatives to normal distributions and provide robustness against unusual or outlying observations when used to model the densities of residual effects. Our objective is to compare estimates of genetic parameters by fitting multivariate normal (MN) or heavy-tail distributions [multivariate Student's t (MSt) and multivariate slash (MS)] for residuals in data of body birth weight (BBW), weaning (WW), and yearling (YW) weight traits in beef cattle. A total of 17,019 weight records for BBW, WW, and YW from 1998 through 2010 from a large commercial cow/calf operation in the sand hills of Nebraska were analyzed. Models included fixed effects of contemporary group and sire breed whereas animal and maternal effects were random and the degrees of freedom (v) was treated as unknown for MSt and MS. Model comparisons using deviance information criteria (DIC) favored MSt over MS and MN models, respectively. The posterior means [and 95% posterior probability intervals (PPI)] of v for the MSt and MS models were 5.28 (4.80, 5.85) and 1.88 (1.76, 2.00), respectively. Smaller values of posterior densities of v for MSt and MS models confirm that the assumption of normally distributed residuals is not adequate for the analysis of BBW, WW, and YW datasets. Posterior mean (PM) and posterior median (PD) estimates of direct and maternal genetic variances were the same and posterior densities of these parameters were found to be symmetric. The 95% PPI estimates from MN and MSt models for BBW did not overlap, which indicates significant difference between PM estimates from MN or MSt models. The observed antagonistic relationship between additive direct and additive maternal effects indicated that genetic evaluation and selection strategies will be sensitive to the assumed model for residuals.