Accounting for Outliers and Heteroskedasticity in Multibreed Genetic Evaluations of Post-Weaning Gain of Hereford-Nelore Cattle

¹ EMBRAPA Pecuária Sul (Brazilian Agricultural Research Corporation South - Cattle & Sheep Center) - Bagé, RS 96401-970, Brazil
² Department of Dairy Science, University of Wisconsin, Madison, WI 53706, USA
³ Department of Animal Science, Michigan State University, East Lansing, MI 48824, USA

^* To whom correspondence should be addressed. E-mail: fcardoso{at}cppsul.embrapa.br.

	Abstract

The objectives of this study were to demonstrate the utility of hierarchical Bayes models combining residual heteroskedasticity with robustness for outlier detection and muting and to evaluate the effects of such joint modeling in multibreed genetic evaluations. A 3 x 2 factorial specification of six residual variance models based on different distributional (Gaussian, Student t or Slash) and variability (homoskedastic or heteroskedastic) assumptions was used to analyze 22,717 post weaning gain records from a Nelore-Hereford population (40,082 animals in the pedigree). To illustrate the utility of the two robust distributional specifications (Student t and Slash) for outlier detection and muting, three records from the same contemporary group (an extreme residual outlier, a mild residual outlier and a near zero residual) were chosen for further study. The posterior densities of these records' corresponding weighting variables were used to assess their degree of Gaussian outlyingness and the ability of the robust models to mute the effects of deviant records. The Student t heteroskedastic provided the best model fit among the six specifications and was preferred for genetic merit inference. Kendall rank correlations of the posterior means of animals' additive genetic effects, used to compare Student t and Gaussian models selection order, were reasonably high across all animals within the most frequent genotypes, ranging from 0.83 to 0.91 and from 0.89 to 0.95, for the homoskedastic and the heteroskedastic versions, respectively. However, when considering only animals ranked in the top 10% by the customary Gaussian homoskedastic model, these rank correlations dropped considerably, ranging from 0.29 to 0.57 and from 0.72 to 0.85, between the two residual densities within the homoskedastic and heteroskedastic versions, respectively. Rank correlations between the homoskedastic and heteroskedastic versions within each of the Gaussian and Student t error models tended to be smaller, with a range between 0.68 and 0.90 across all animals and between 0.28 and 0.67 for animals ranked in the top 10%. These results support the implementation of robust models accounting for sources of heteroskedasticity to increase the precision and stability of multibreed genetic evaluations with proper statistical treatment of deviant records.

Key Words: Bayesian inference, beef cattle, genetic evaluation, heteroskedasticity, multibreed, robust models