Table 2. Average correlation (SE in parentheses) between observed and predicted values for grain yield (GY) and days to heading (DTH) in 12 environments for seven models.

Trait	Environment	BL	BRR	Bayes A	Bayes B	RKHS	RBFNN	BRNN
	1	0.59 (0.11)	0.59 (0.11)	0.59 (0.11)	0.56 (0.11)	0.66 (0.09)	0.66 (0.10)	0.64 (0.11)
	2	0.58 (0.14)	0.57 (0.14)	0.61 (0.12)	0.57 (0.13)	0.63 (0.13)	0.61 (0.13)	0.62 (0.13)
	3	0.60 (0.13)	0.60 (0.12)	0.62 (0.11)	0.60 (0.12)	0.68 (0.10)	0.69 (0.10)	0.67 (0.11)
	4	0.02 (0.18)	0.07 (0.17)	0.06 (0.17)	0.06 (0.17)	0.12 (0.18)	0.16 (0.18)	0.02 (0.19)
DTH	5	0.65 (0.09)	0.64 (0.10)	0.66 (0.09)	0.66 (0.09)	0.69 (0.08)	0.68 (0.08)	0.68 (0.08)
	8	0.36 (0.15)	0.37 (0.15)	0.36 (0.15)	0.35 (0.14)	0.46 (0.13)	0.46 (0.14)	0.39 (0.15)
	9	0.59 (0.12)	0.59 (0.11)	0.53 (0.12)	0.52 (0.11)	0.62 (0.11)	0.63 (0.11)	0.61 (0.12)
	10	0.54 (0.14)	0.52 (0.14)	0.56 (0.13)	0.54 (0.14)	0.61 (0.13)	0.62 (0.12)	0.57 (0.13)
	11	0.52 (0.15)	0.52 (0.16)	0.53 (0.13)	0.51 (0.13)	0.58 (0.14)	0.59 (0.13)	0.55 (0.14)
	12	0.45 (0.19)	0.42 (0.18)	0.45 (0.18)	0.45 (0.18)	0.47 (0.18)	0.39 (0.19)	0.35 (0.19)
	Average	0.59 (0.12)	0.58 (0.12)	0.60 (0.12)	0.57 (0.12)	0.65 (0.10)	0.48 (0.14)	0.48 (0.14)
	1	0.48 (0.13)	0.43 (0.14)	0.48 (0.13)	0.46 (0.13)	0.51 (0.12)	0.51 (0.12)	0.50 (0.13)
	2	0.48 (0.14)	0.41 (0.17)	0.48 (0.14)	0.48 (0.14)	0.50 (0.14)	0.43 (0.16)	0.43 (0.16)
	3	0.20 (0.21)	0.29 (0.22)	0.20 (0.22)	0.18 (0.22)	0.37 (0.20)	0.42 (0.21)	0.32 (0.24)
GY	4	0.45 (0.15)	0.46 (0.13)	0.43 (0.15)	0.42 (0.15)	0.53 (0.12)	0.55 (0.11)	0.49 (0.14)
	5	0.59 (0.14)	0.56 (0.16)	0.75 (0.11)	0.74 (0.12)	0.64 (0.13)	0.66 (0.13)	0.63 (0.13)
	6	0.70 (0.10)	0.67 (0.11)	0.73 (0.08)	0.71 (0.08)	0.73 (0.08)	0.71 (0.08)	0.69 (0.10)
	7	0.46 (0.14)	0.50 (0.14)	0.42 (0.14)	0.40 (0.15)	0.53 (0.13)	0.54 (0.14)	0.50 (0.14)
	Average	0.62 (0.10)	0.57 (0.14)	0.69 (0.10)	0.70 (0.09)	0.67 (0.09)	0.56 (0.12)	0.65 (0.10)

Fitted models were Bayesian LASSO (BL), RR-BLUP (BRR), Bayes A, Bayes B, reproducing kernel Hilbert spaces regression (RKHS), radial basis function neural networks (RBFNN) and Bayesian regularized neural networks (BRNN) across 50 random partitions of the data with 90% in the training set and 10% in the validation set. The models with highest correlations are underlined.