Table 2. Simulated data with three traits and three environments.

Method	E-T	Low Correlation Between Traits (0.20)						High Correlation Between Traits (0.85)
		Correlation			MSPE			Correlation			MSPE
		Mean	SE	Ra	Mean	SE	Ra	Mean	SE	Ra	Mean	SE	Ra
	E1-T1	0.17	0.15	2	1.27	0.15	2	0.54	0.17	1	0.96	0.21	2
	E1-T2	0.30	0.22	1	0.74	0.11	1	0.66	0.11	1	0.88	0.12	1
	E1-T3	0.51	0.12	1	0.93	0.15	1	0.59	0.09	1	1.10	0.22	1
	E2-T1	0.69	0.09	2	0.87	0.17	2	0.72	0.06	2	0.85	0.14	1
U	E2-T2	0.66	0.10	1	0.73	0.08	2	0.74	0.07	1	0.79	0.08	1
	E2-T3	0.72	0.04	1	0.79	0.14	1	0.70	0.07	2	0.99	0.18	2
	E3-T1	0.59	0.14	3	1.51	0.30	2	0.66	0.10	3	1.27	0.22	2
	E3-T2	0.80	0.06	1	0.95	0.15	1	0.77	0.07	1	1.11	0.16	1
	E3-T3	0.66	0.05	2	1.79	1.79	1	0.67	0.07	3	1.70	0.36	1
	Ave	0.57	0.11	1.56	1.06	0.34	1.44	0.67	0.09	1.67	1.07	0.19	1.33
	E1-T1	0.14	0.16	3	1.07	0.13	1	0.48	0.18	3	0.84	0.14	1
	E1-T2	0.24	0.20	3	0.78	0.07	2	0.43	0.17	3	1.01	0.11	2
	E1-T3	0.25	0.12	3	1.18	0.12	2	0.55	0.09	3	1.21	0.22	2
	E2-T1	0.71	0.07	1	0.85	0.16	1	0.76	0.04	1	0.92	0.14	2
D	E2-T2	0.64	0.07	2	0.71	0.16	1	0.70	0.05	2	0.90	0.13	2
	E2-T3	0.67	0.08	3	0.91	0.18	3	0.66	0.08	3	1.15	0.24	3
	E3-T1	0.65	0.11	2	1.26	0.35	1	0.73	0.06	2	1.19	0.27	1
	E3-T2	0.61	0.16	3	1.43	0.26	3	0.63	0.13	3	1.66	0.24	3
	E3-T3	0.66	0.04	3	2.02	2.02	3	0.69	0.07	2	1.81	0.34	3
	Ave	0.51	0.11	2.56	1.13	0.38	1.89	0.63	0.10	2.44	1.19	0.20	2.11
	E1-T1	0.22	0.17	1	1.32	0.20	3	0.53	0.18	2	1.08	0.23	3
	E1-T2	0.27	0.19	2	0.99	0.25	3	0.52	0.16	2	1.22	0.30	3
	E1-T3	0.43	0.09	2	1.23	0.18	3	0.55	0.13	2	1.48	0.38	3
	E2-T1	0.66	0.07	3	1.10	0.23	3	0.70	0.06	3	1.17	0.20	3
S	E2-T2	0.52	0.11	3	1.02	0.13	3	0.60	0.07	3	1.16	0.13	3
	E2-T3	0.71	0.07	2	0.91	0.19	2	0.73	0.07	1	0.94	0.18	1
	E3-T1	0.70	0.09	1	1.54	0.32	3	0.77	0.05	1	1.34	0.23	3
	E3-T2	0.71	0.10	2	1.03	0.18	2	0.69	0.09	2	1.17	0.18	2
	E3-T3	0.69	0.06	1	1.96	0.39	2	0.73	0.07	1	1.72	0.36	2
	Ave	0.55	0.11	1.89	1.23	0.23	2.67	0.65	0.10	1.89	1.25	0.24	2.56

Mean and standard error (SE) of the estimated correlations and Mean Squared Prediction Error (MSPE) from the 10-fold cross-validation CV1. The BMTME model was fitted using unstructured (U), diagonal (D), and standard (S) variance–covariance matrix. Environment (E1, E2, E3)–trait (T1, T2, T3) combination. Method stands for the variance–covariance matrix used with the BMTME, E-T for the environment–trait combination, R for rank, and Ave for average.

^aSince three conditions are compared (unstructured, diagonal, and standard), the values of the ranks range from 1 to 3, and the lower the values, the better the prediction accuracy. For ties, we assigned the average of the ranks that would have been assigned had there been no ties.