Difference between revisions of "Genomic data in lmt"
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==Single step SNP-BLUP== | ==Single step SNP-BLUP== | ||
lmt's Single step SNP-BLUP model uses the approach described in Liu and Goddard 2014, where the adverse of the singe step SN-PBLUP variance structure can be written as | |||
$$ | |||
\left( | |||
\begin{array}{ccc} | |||
(A^{n,n})^{-1}\otimes \Sigma_g +\xi (A_{g,g}\otimes \Sigma_g \lambda + M\zeta M^{'}\gamma)\xi^{'} & \xi (A_{g,g}\otimes \Sigma_g \lambda + M\zeta M^{'}\gamma) & \xi M\zeta\gamma \\ | |||
(A_{g,g}\otimes \Sigma_g \lambda + M\zeta M^{'}\gamma)\xi^{'} & A_{g,g}\otimes \Sigma_g \lambda + M\zeta M^{'}\gamma & M\zeta\gamma \\ | |||
\gamma \zeta M^{'}\xi^{'} & \gamma \zeta M^{'}& \zeta\gamma | |||
\end{array} | |||
\right) | |||
$$ | |||
where $$\zeta = \Omega_{m}(\Gamma_m \otimes I)\Omega_{m}^{'}$$ and $$\xi = A_{n,g}A_{g,g}^{-1}$$, $$\Sigma_g$$ is the global genetic co-variance matrix, $$\lambda$$ is the polygenic weight and $$\gamma$$ is the genomic weight. Note that when parametrizing this variance structure the following equality should hold $$\gamma 1'\zeta 1==\gamma \Sigma_g$$ | |||
Revision as of 00:20, 4 March 2022
lmt can account for genomic data via genomic relationship matrices $$G$$ and single step relationship matrices $$H$$ where single step G-BLUP, single step GT-BLUP, and single step SNP-BLUP are supported
Single step SNP-BLUP
lmt's Single step SNP-BLUP model uses the approach described in Liu and Goddard 2014, where the adverse of the singe step SN-PBLUP variance structure can be written as
$$ \left( \begin{array}{ccc} (A^{n,n})^{-1}\otimes \Sigma_g +\xi (A_{g,g}\otimes \Sigma_g \lambda + M\zeta M^{'}\gamma)\xi^{'} & \xi (A_{g,g}\otimes \Sigma_g \lambda + M\zeta M^{'}\gamma) & \xi M\zeta\gamma \\ (A_{g,g}\otimes \Sigma_g \lambda + M\zeta M^{'}\gamma)\xi^{'} & A_{g,g}\otimes \Sigma_g \lambda + M\zeta M^{'}\gamma & M\zeta\gamma \\ \gamma \zeta M^{'}\xi^{'} & \gamma \zeta M^{'}& \zeta\gamma \end{array} \right) $$
where $$\zeta = \Omega_{m}(\Gamma_m \otimes I)\Omega_{m}^{'}$$ and $$\xi = A_{n,g}A_{g,g}^{-1}$$, $$\Sigma_g$$ is the global genetic co-variance matrix, $$\lambda$$ is the polygenic weight and $$\gamma$$ is the genomic weight. Note that when parametrizing this variance structure the following equality should hold $$\gamma 1'\zeta 1==\gamma \Sigma_g$$