Table 3 Prediction performance of data set 2 in terms of mean square error (MSE), mean arctangent absolute percentage error (MAAPE) and Average Pearson Correlation (APC) without taking into consideration the genotype×environment interaction (WI) and taking it into account (I) in the 13 models. SE_1 denotes the standard error of the MSE, SE_2 denotes the standard error of the MAAPE and SE_3 denotes the standard error of the APC
ModelInteractionTraitMSESE_1MAAPESE_2APCSE_3
UPDN_1WIPTR16.6823.2680.5030.0250.3710.045
UPDN_1WISB9.6400.8160.4080.0190.4080.029
UPDN_1WISN10.9651.1440.3500.0160.5520.037
Average12.4291.7430.4200.0200.4440.037
UPDN_2WIPTR11.3231.1720.4380.0190.4580.039
UPDN_2WISB8.2440.6710.3830.0210.4490.041
UPDN_2WISN8.7860.7160.3060.0140.6220.032
Average9.4510.8530.3760.0180.5100.037
UPDN_3WIPTR12.4441.380.4620.0230.4580.043
UPDN_3WISB7.8330.5620.3790.0160.4670.044
UPDN_3WISN8.5420.6210.3130.0140.6340.033
Average9.6060.8540.3850.0180.5200.040
UPDN_4WIPTR10.6510.8630.4210.0220.4920.032
UPDN_4WISB7.3820.4930.3730.0180.4870.038
UPDN_4WISN8.3640.8350.2940.0150.640.034
Average8.7990.7300.3630.0180.5400.035
MPDN_1WISN8.2870.8150.3000.0150.6440.031
MPDN_1WIPTR11.4330.8920.4380.0190.5140.034
MPDN_1WISB8.0600.6830.3800.0160.4740.038
Average9.2600.7970.3730.0170.5440.034
MPDN_2WISN8.3620.8160.2920.0150.6490.031
MPDN_2WIPTR10.5230.7910.4290.0190.5380.033
MPDN_2WISB7.3570.5720.3690.0160.4820.037
Average8.7470.7260.3630.0170.5560.034
MPDN_3WISN8.3120.7900.3040.0150.6560.030
MPDN_3WIPTR10.2520.8010.4200.0190.5440.033
MPDN_3WISB7.6160.5640.3750.0160.4600.038
Average8.7270.7180.3660.0170.5530.034
MPDN_4WISN8.2330.7960.2780.0150.6530.030
MPDN_4WIPTR10.3710.7780.4220.0190.5280.033
MPDN_4WISB7.8550.5930.3720.0160.4490.038
Average8.8200.7220.3570.0170.5430.034
GPR_L1_0.5WISN8.3890.7870.3040.0150.6300.031
GPR_L1_0.5WIPTR10.1390.7690.4080.0190.5350.033
GPR_L1_0.5WISB7.1680.5550.3710.0160.4820.037
Average8.5650.7040.3610.0170.5490.034
GPR_L1_0.25WISN8.3840.7860.3040.0150.6310.031
GPR_L1_0.25WIPTR10.1320.7690.4080.0190.5340.033
GPR_L1_0.25WISB7.1630.5560.3710.0160.4830.037
Average8.5600.7040.3610.0170.5490.034
GPR_L1_0.75WISN8.3890.7870.3040.0150.6310.031
GPR_L1_0.75WIPTR10.1400.7690.4080.0190.5350.033
GPR_L1_0.75WISB7.1700.5550.3710.0160.4820.037
Average8.5660.7040.3610.0170.5490.034
GPR_LasssoWISN8.3900.7870.3040.0150.6310.031
GPR_LasssoWIPTR10.1400.7690.4080.0190.5350.033
GPR_LasssoWISB7.1710.5560.3710.0160.4820.037
Average8.5670.7040.3610.0170.5490.034
GPR_RidgeWISN8.3460.7850.3030.0150.6270.032
GPR_RidgeWIPTR10.2620.7670.4130.0190.5120.035
GPR_RidgeWISB7.1590.5520.3720.0160.4790.038
Average8.5890.7010.3630.0170.5390.035
UPDN_1IPTR16.2131.6770.5030.0240.3260.047
UPDN_1ISB10.0890.9230.4040.0210.3610.044
UPDN_1ISN12.3081.1130.3530.0190.4940.051
Average12.8701.2380.4200.0210.3940.047
UPDN_2IPTR13.0141.3080.450.0180.3910.046
UPDN_2ISB9.4480.7660.3820.0160.3960.046
UPDN_2ISN10.9231.0160.3220.0140.5620.038
Average11.1281.0300.3850.0160.4500.043
UPDN_3IPTR13.3461.4720.4560.0190.430.045
UPDN_3ISB9.0610.5980.3840.0150.4310.04
UPDN_3ISN10.7181.0420.3230.0180.5750.047
Average11.0421.0370.3880.0170.4790.044
UPDN_4IPTR12.4211.3640.4340.0210.4410.046
UPDN_4ISB8.0280.620.3720.0160.4510.039
UPDN_4ISN9.3170.9130.3090.0190.620.035
Average9.9220.9660.3720.0190.5040.040
MPDN_1ISN11.8781.1200.3380.0140.5350.035
MPDN_1IPTR15.2761.2310.4870.0180.3910.040
MPDN_1ISB10.0680.7760.4000.0150.3700.041
Average12.4071.0420.4080.0160.4320.039
MPDN_2ISN11.5031.0440.3230.0140.5950.031
MPDN_2IPTR12.7451.0170.4400.0180.4730.037
MPDN_2ISB9.3410.7180.3790.0150.4270.038
Average11.1960.9260.3810.0160.4980.035
MPDN_3ISN9.9420.8960.3100.0150.5850.033
MPDN_3IPTR11.6540.9100.4240.0190.4710.037
MPDN_3ISB8.2260.6220.3750.0160.4250.038
Average9.9410.8090.3700.0170.4940.036
MPDN_4ISN10.3140.9140.2970.0150.5890.033
MPDN_4IPTR12.0180.9330.4180.0190.4620.036
MPDN_4ISB8.2450.6160.3730.0160.4230.039
Average10.1920.8210.3630.0170.4910.036
GPR_L1_0.5ISN10.6490.8840.3650.0140.5270.036
GPR_L1_0.5IPTR11.5390.8640.4340.0180.4620.035
GPR_L1_0.5ISB8.4820.6220.4000.0160.3470.040
Average10.2230.7900.4000.0160.4450.037
GPR_L1_0.25ISN10.6610.8830.3660.0140.5260.036
GPR_L1_0.25IPTR11.5420.8660.4350.0180.4620.035
GPR_L1_0.25ISB8.4880.6230.4000.0160.3470.040
Average10.2300.7910.4000.0160.4450.037
GPR_L1_0.75ISN10.6540.8860.3650.0140.5280.036
GPR_L1_0.75IPTR11.5570.8650.4340.0180.4600.035
GPR_L1_0.75ISB8.4750.6210.4000.0160.3470.040
Average10.2290.7910.4000.0160.4450.037
GPR_LasssoISN10.6520.8860.3650.0140.5280.036
GPR_LasssoIPTR11.5530.8650.4340.0180.4600.035
GPR_LasssoISB8.4900.6220.4010.0160.3470.040
Average10.2320.7910.4000.0160.4450.037
GPR_RidgeISN11.7220.9620.3950.0130.6010.033
GPR_RidgeIPTR11.9860.8850.4380.0180.5030.035
GPR_RidgeISB8.4440.6590.3860.0150.4610.038
Average10.7170.8350.4060.0150.5220.035