A permutation-based F-test (Fs, with 1000 permutations) was then performed and restricted maximum likelihood was used to solve the mixed model equations.
An alternative to estimating GEBVs by summing up all the marker effects, is to estimate GEBVs directly within the framework of mixed model equations (MME).
In the framework of mixed model equations, a new best linear unbiased prediction (BLUP) method including a trait-specific relationship matrix (TA) was presented and termed TABLUP.
The main aim of this study was to present the two-step TABLUP method, which utilizes a trait-specific relationship matrix (TA) in the mixed model equations (MME), for estimating genomic breeding values in the framework of genomic selection.
With markers covering the entire genome, genetic merit of genotyped individuals can be predicted directly within the framework of mixed model equations, by using a matrix of relationships among individuals that is derived from the markers.
The solutions of mixed model equations are predicted SNP genotypes for individuals.
Hence the LHS of the mixed model equations is of size 10,680 × 10,680.
Additional file 1 Matrices for EM-REML and Mixed model equations.
The estimation of marker effects is then given by the mixed model equations [ 76].
The mixed model equations are then [ 31]: (24) Note that enter non-trivially into G.
Breeding values were predicted by solving Henderson's mixed model equations, using the R environment [ 11].
