Table 3. Wheat data sets.

Trait	Environment	BL	BRR	Bayes A	Bayes B	BIRR	BAI	BIR1	BIR2
DTH	1	0.59 (0.11)	0.59 (0.11)	0.59 (0.11)	0.56 (0.11)	0.60 (0.11)	0.60 (0.11)	0.60 (0.11)	0.59 (0.11
	2	0.58 (0.14)	0.57 (0.14)	0.61 (0.12)	0.57 (0.13)	0.62 (0.14)	0.61 (0.14)	0.62 (0.14)	0.65 (0.12)
	3	0.60 (0.13)	0.60 (0.12)	0.62 (0.11)	0.60 (0.12)	0.62 (0.12)	0.62 (0.12)	0.62 (0.12)	0.63 (0.12)
	4	0.02 (0.18)	0.07 (0.17)	0.06 (0.17)	0.06 (0.17)	0.06 (0.18)	0.01 (0.18)	0.06 (0.18)	0.04 (0.20)
	5	0.65 (0.09)	0.64 (0.10)	0.66 (0.09)	0.66 (0.09)	0.65 (0.09)	0.65 (0.09)	0.65 (0.09)	0.65 (0.09)
	8	0.36 (0.15)	0.37 (0.15)	0.36 (0.15)	0.35 (0.14)	0.38 (0.15)	0.39 (0.15)	0.38 (0.15)	0.36 (0.15)
	9	0.59 (0.12)	0.59 (0.11)	0.53 (0.12)	0.52 (0.11)	0.60 (0.11)	0.60 (0.11)	0.60 (0.11)	0.57 (0.11)
	10	0.54 (0.14)	0.52 (0.14)	0.56 (0.13)	0.54 (0.14)	0.55 (0.13)	0.54 (0.14)	0.55 (0.13)	0.56 (0.12)
	11	0.52 (0.15)	0.52 (0.16)	0.53 (0.13)	0.51 (0.13)	0.54 (0.15)	0.54 (0.16)	0.54 (0.15)	0.52 (0.13)
	12	0.45 (0.19)	0.42 (0.18)	0.45 (0.18)	0.45 (0.18)	0.47 (0.18)	0.47 (0.18)	0.48 (0.18)	0.49 (0.19)
	Average	0.49	0.49	0.50	0.48	0.51	0.50	0.510	0.51
	% increase	−4.0%	−4.3%	−2.6%	−5.8%	−0.1%	−1.1%	0%	-0.7%
GY	1	0.48 (0.13)	0.43 (0.14)	0.48 (0.13)	0.46 (0.13)	0.48 (0.13)	0.48 (0.14)	0.48 (0.13)	0.47 (0.13)
	2	0.48 (0.14)	0.41 (0.17)	0.48 (0.14)	0.48 (0.14)	0.47 (0.15)	0.47 (0.15)	0.47 (0.15)	0.48 (0.13)
	3	0.20 (0.21)	0.29 (0.22)	0.20 (0.22)	0.18 (0.22)	0.24 (0.22)	0.25 (0.21)	0.24 (0.22)	0.21 (0.20)
	4	0.45 (0.15)	0.46 (0.13)	0.43 (0.15)	0.42 (0.15)	0.46 (0.14)	0.46 (0.14)	0.46 (0.14)	0.43 (0.14)
	5	0.59 (0.14)	0.56 (0.16)	0.75 (0.11)	0.74 (0.12)	0.58 (0.15)	0.58 (0.15)	0.59 (0.15)	0.58 (0.13)
	6	0.70 (0.10)	0.67 (0.11)	0.73 (0.08)	0.71 (0.08)	0.71 (0.1)	0.71 (0.10)	0.71 (0.1)	0.71 (0.1)
	7	0.46 (0.14)	0.50 (0.14)	0.42 (0.14)	0.40 (0.15)	0.48 (0.14)	0.48 (0.15)	0.48 (0.14)	0.42 (0.15)
	Average	0.48	0.474	0.499	0.484	0.489	0.49	0.489	0.473
	% increase	−1.7%	−2.9%	2.1%	−0.8%	0.2%	0.5%	0%	−3.5%

Mean predictive correlations (SD in parentheses) for GY and DTH by environment for eight models: BL, BRR, Bayes A, Bayes B (Pérez-Rodríguez et al. 2012), BIRR, BAI, and BIR1 and BIR2. Average correlation for each model and % increase correlation with respect to model BIR1 is shown. The largest values for each trait-environment combination are in boldface. DTH, days to heading; GY, grain yield; BL, Bayesian least absolute shrinkage and selection operator; BRR, RR-BLUP; BIRR, Bayesian inverse ridge regression; BAI, Bayes A inverse; BIR1, Bayesian inverse regression model 1; BIR2, Bayesian inverse regression model 2.