Table 1. Simulated data with three traits and three environments.

	Posterior Mean of ${\widehat{\Sigma }}_t$			Posterior SD of ${\widehat{\Sigma }}_t$
	T1	T2	T3	T1	T2	T3
T1	0.591	0.458	0.530	0.094	0.078	0.090
T2	—	0.500	0.488	—	0.080	0.084
T3	—	—	0.670	—	—	0.109
	Posterior Mean of ${\widehat{R}}_e$			Posterior SD of ${\widehat{R}}_e$
	T1	T2	T3	T1	T2	T3
T1	0.151	0.115	0.119	0.003	0.002	0.003
T2	—	0.121	0.107	—	0.002	0.002
T3	—		0.131	—	—	0.003
	Posterior Mean of ${\widehat{\Sigma }}_E$			Posterior SD of ${\widehat{\Sigma }}_E$
	E1	E2	E3	E1	E2	E3
	0.854	0.740	0.937	0.167	0.184	0.210
	Posterior Mean of $\widehat{\mathit{\beta }}$			Posterior SD of $\widehat{\mathit{\beta }}$
	T1	T2	T3	T1	T2	T3
E1	15.046	8.006	7.054	0.406	0.326	0.365
E2	12.004	5.980	7.003	0.307	0.254	0.378
E3	14.104	9.003	8.053	0.464	0.407	0.434

Posterior mean and standard deviation (SD) of the β coefficients ($\widehat{\mathit{\beta }}$) of three traits (T1, T2, and T3) in three environments (E1, E2, E3) and the estimated variance–covariance components for the traits (${\widehat{\Sigma }}_t$), for the residuals (${\widehat{R}}_e$), and for the environments (${\widehat{\Sigma }}_E$).