Table 3. Maize data.

	Posterior Mean of ${\widehat{\Sigma }}_t$			Posterior SD of ${\widehat{\Sigma }}_t$
	Yield	ASI	PH	Yield	ASI	PH
Yield	1.666	−0.260	0.069	0.430	0.210	0.030
ASI	−0.158	1.631	−0.046	—	0.430	0.030
PH	0.315	−0.212	0.028	—	—	0.010
	Posterior Mean of ${\widehat{R}}_e$			Posterior SD of ${\widehat{R}}_e$
	Yield	ASI	PH	Yield	ASI	PH
Yield	0.506	−0.077	0.022	0.050	0.030	0.000
ASI	−0.151	0.512	−0.012	—	0.050	0.000
PH	0.278	−0.153	0.013	—	—	0.000
	Posterior Mean of ${\widehat{\Sigma }}_E$			Posterior SD of ${\widehat{\Sigma }}_E$
	E1	E2	E3	E1	E2	E3
	0.663	0.655	0.898	0.0369	0.0320	0.0349
	Posterior Mean of $\widehat{\mathit{\beta }}$			Posterior SD of $\widehat{\mathit{\beta }}$
	Yield	ASI	PH	Yield	ASI	PH
E1	6.445	1.872	2.354	0.210	0.280	0.030
E2	4.958	1.147	2.066	0.280	0.330	0.040
E3	6.102	2.276	2.341	0.290	0.300	0.040
	Correlation in the Entire Data			MSPE in the Entire Data
	Yield	ASI	PH	Yield	ASI	PH
E1	0.796	0.756	0.646	0.428	0.233	0.012
E2	0.769	0.798	0.757	0.245	0.605	0.007
E3	0.799	0.794	0.763	0.480	0.338	0.011

Posterior mean and SD of the β coefficients ($\widehat{\mathit{\beta }}$) for three traits, Yield, anthesis-silking interval (ASI), and plant height (PH) in three environments (E1, E2, and E3). Estimate variance–covariance components for the traits (${\widehat{\Sigma }}_t$), the environments (${\widehat{\Sigma }}_E$), and the residuals (${\widehat{R}}_e$). In ${\widehat{\Sigma }}_t$ and ${\widehat{R}}_e$, the upper triangle contains the variance–covariance components and the lower triangle contains the correlations. ${\widehat{\Sigma }}_E$ is a diagonal matrix.