Genomic evaluations are commonly based on models with genomic relationships. However, estimated genomic relationship matrices are often positive semi-definite and ad-hoc corrections are applied to force positive definiteness without consideration about model properties. In this contribution a hierarchical quantitative genetic model is postulated that provides a positive definite genomic relationship matrix by taking into account the amount of genetic variance captured by estimated marker effects. Based on the hierarchical formulation the proposed model also provides a system of equations to estimate marker effects and breeding values jointly without setting up and inverting covariance matrices. Further extension with pedigree information is also possible.
Proceedings of the World Congress on Genetics Applied to Livestock Production, Volume Genetic Improvement Programs: Selection using molecular information, , 068, 2014
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