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United States Department of Agriculture

Agricultural Research Service

Title: Normality and Skewness of Genetic Evaluations

Author
item Vanraden, Paul

Submitted to: Interbull Annual Meeting Proceedings
Publication Type: Proceedings
Publication Acceptance Date: June 4, 2006
Publication Date: July 1, 2006
Citation: Van Raden, P.M. 2006. Normality and skewness of genetic evaluations. Interbull Annual Meeting Proceedings. Interbull Bull. 35:164-167.

Interpretive Summary: Linear models are used for evaluation of linear, normally distributed traits such as milk yield. Traits (e.g. somatic cell count) with skewed distributions are normalized through log or other simple transformation. Traits with nonlinear, non-normal distributions have gained importance, and alternative (e.g. Baysian and threshold) models for evaluation have been developed. These can increase accuracy of EBVs within an evaluation system, but differences in distributions of EBVs among countries may affect the accuracy of international (MACE) EBVs. May 2006 Interbull evaluations were examined for skewness and kurtosis of EBVs on each national scale. Kurtosis was small and positive for most traits and scales, with larger values for calving traits. Some positive kurtosis is expected due to differing reliabilities. For yield traits, skewness was generally small and the larger values may be the result of selection, whereby a country has a small number of very inferior bulls, or has imported a few superior bulls. In almost all countries somatic cell score (SCS) had a moderate, consistent skewness. Clinical mastitis data is binomial, but EBVs are relatively normally distributed, and skewness was similar to that of SCS. Longevity and fertility EBVs are fairly normally distributed although raw data is not. Longevity EBVs had little skewness except in the countries using survival analysis. Fertility EBVs had only slight skewness. Skewness of calving ease (CE) EBVs ranged from –.81 to –.01. Snell score EBVs (Canada) and EBVs on the underlying scale of threshold models (3 other countries), which are reported to Interbull, are more normally distributed than EBVs from the linear models used elsewhere. Rankings for EBVs from linear models are also skewed, and this skewness is doubled when these EBVs are finally transformed to the observed (published) scales in countries exchanging Snell or underlying scores with Interbull. The effect of mixing EBV distributions with different skewness was evaluated by examining sources of extreme bulls for CE. The U.S. supplied 34% of all bulls for direct CE and although the U.S. mean was lower, 45% of the top 100 bulls but only 20% of the poorest were from the U.S. Skewness of stillbirth evaluations is uniform across countries, because only linear models are currently used. Implementation of a threshold model by the U.S. would result in reduced skewness of EBV relative to EBV from other countries. Although elimination of skewness may not be appropriate, uniformity of skewness among contributing populations would improve the accuracy of international evaluations.

Technical Abstract: Linear models are used for evaluation of linear, normally distributed traits such as milk yield. Traits (e.g. somatic cell count) with skewed distributions are normalized through log or other simple transformation. Traits with nonlinear, non-normal distributions have gained importance, and alternative (e.g. Baysian and threshold) models for evaluation have been developed. These can increase accuracy of EBVs within an evaluation system, but differences in distributions of EBVs among countries may affect the accuracy of international (MACE) EBVs. May 2006 Interbull evaluations were examined for skewness and kurtosis of EBVs on each national scale. Kurtosis was small and positive for most traits and scales, with larger values for calving traits. Some positive kurtosis is expected due to differing reliabilities. For yield traits, skewness was generally small and the larger values may be the result of selection, whereby a country has a small number of very inferior bulls, or has imported a few superior bulls. In almost all countries somatic cell score (SCS) had a moderate, consistent skewness. Clinical mastitis data is binomial, but EBVs are relatively normally distributed, and skewness was similar to that of SCS. Longevity and fertility EBVs are fairly normally distributed although raw data is not. Longevity EBVs had little skewness except in the countries using survival analysis. Fertility EBVs had only slight skewness. Skewness of calving ease (CE) EBVs ranged from –.81 to –.01. Snell score EBVs (Canada) and EBVs on the underlying scale of threshold models (3 other countries), which are reported to Interbull, are more normally distributed than EBVs from the linear models used elsewhere. Rankings for EBVs from linear models are also skewed, and this skewness is doubled when these EBVs are finally transformed to the observed (published) scales in countries exchanging Snell or underlying scores with Interbull. The effect of mixing EBV distributions with different skewness was evaluated by examining sources of extreme bulls for CE. The U.S. supplied 34% of all bulls for direct CE and although the U.S. mean was lower, 45% of the top 100 bulls but only 20% of the poorest were from the U.S. Skewness of stillbirth evaluations is uniform across countries, because only linear models are currently used. Implementation of a threshold model by the U.S. would result in reduced skewness of EBV relative to EBV from other countries. Although elimination of skewness may not be appropriate, uniformity of skewness among contributing populations would improve the accuracy of international evaluations.

Last Modified: 9/21/2014
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