Table 4.

Parameter estimates and prediction performance obtained with simulated dataset 2

	${\tilde{\mathbf{\ell }}}_{\mathbf{y}\mid {\mathbf{m}}^{\mathbf{o}}}\mathbf{+}{\stackrel{\mathbf{~}}{\mathbf{\ell }}}_{\mathit{\text{mark}}}$	${\stackrel{\mathbf{~}}{\mathbf{\ell }}}_{\mathit{\text{mark}}}$&${\stackrel{\mathbf{~}}{\mathbf{\ell }}}_{\mathbf{y}\mathbf{\mid }{\mathbf{m}}^{\mathbf{o}}}$	G-adjust
$\widehat{\gamma }$	0.4605	0.4615
$\widehat{\tilde{s}}/(p/2)$	0.9996	1.0003
α			0.0134
β			1.0074
$\widehat{\omega }$	0.375	0.375	0.60
${\widehat{\sigma }}_a$	6.507	6.512	5.084
${\widehat{\sigma }}_e$	15.816	15.816	15.797
$\text{Cor}(\widehat{\mathbf{a}},\mathbf{a})$	0.536	0.536	0.493
reg	1.17	1.17	1.34

Parameters were estimated either, jointly using the full log-likelihood $\tilde{\ell }={\tilde{\ell }}_{\mathbf{y}\mid {\mathbf{m}}^o}+{\tilde{\ell }}_{\mathit{\text{mark}}}$, or by first estimating γ and $\tilde{s}$ using ${\tilde{\ell }}_{\mathit{\text{mark}}}$ and then the other parameters using ${\tilde{\ell }}_{\mathbf{y}\mid {\mathbf{m}}^o}$; the last column contains parameter values estimated with the single-step method with an adjusted marker-based relationship matrix, in which first α and β were estimated using equation (6) and then the remaining parameters were estimated using $\left({\ell }_{\mathbf{y}\mid {\mathbf{m}}^o}\right)$; the last two rows show the correlation between predicted and true breeding values, $\text{Cor}(\widehat{\mathbf{a}},\mathbf{a})$, for candidate boars, which is a measure of prediction performance, and the regression coefficient (reg) for the regression of aon $\widehat{\mathbf{a}}$.