Table 2. Prediction performance of data set 1 in terms of mean square error (MSE), mean arctangent absolute percentage error (MAAPE) and Average Pearson Correlation (APC) without taking into consideration genotype$\times$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.

Model	Interaction	Trait	MSE	SE_1	MAAPE	SE_2	APC	SE_3
UPDN_1	WI	y1	49.792	7.579	0.596	0.024	0.546	0.054
UPDN_1	WI	y2	51.319	7.742	0.662	0.015	0.523	0.06
		Average	50.556	7.661	0.629	0.020	0.535	0.057
UPDN_2	WI	y1	46.03	4.51	0.607	0.023	0.55	0.043
UPDN_2	WI	y2	46.611	7.902	0.668	0.024	0.535	0.067
		Average	46.321	6.206	0.638	0.024	0.543	0.055
UPDN_3	WI	y1	46.08	4.969	0.623	0.021	0.553	0.048
UPDN_3	WI	y2	48.441	6.686	0.681	0.021	0.524	0.061
		Average	47.261	5.828	0.652	0.021	0.539	0.055
UPDN_4	WI	y1	44.609	5.645	0.625	0.018	0.554	0.032
UPDN_4	WI	y2	49.637	7.102	0.673	0.015	0.523	0.078
		Average	47.123	6.374	0.649	0.017	0.539	0.055
MPDN_1	WI	y1	45.507	10.464	0.581	0.047	0.87	0.025
MPDN_1	WI	y2	37.971	9.21	0.583	0.048	0.865	0.026
		Average	41.739	9.837	0.582	0.048	0.868	0.026
MPDN_2	WI	y1	45.294	10.069	0.591	0.048	0.863	0.026
MPDN_2	WI	y2	36.453	9.294	0.582	0.049	0.86	0.027
		Average	40.874	9.682	0.587	0.049	0.862	0.027
MPDN_3	WI	y1	48.682	10.454	0.595	0.048	0.854	0.027
MPDN_3	WI	y2	39.857	8.977	0.612	0.047	0.853	0.028
		Average	44.270	9.716	0.604	0.048	0.854	0.028
MPDN_4	WI	y1	49.999	10.283	0.625	0.046	0.831	0.031
MPDN_4	WI	y2	41.182	8.96	0.614	0.048	0.834	0.031
		Average	45.591	9.622	0.620	0.047	0.833	0.031
GPR_L1_0.5	WI	y1	39.964	8.811	0.583	0.047	0.889	0.022
GPR_L1_0.5	WI	y2	36.945	9.926	0.592	0.048	0.861	0.025
		Average	38.455	9.369	0.588	0.048	0.875	0.024
GPR_L1_0.25	WI	y1	36.732	7.982	0.577	0.047	0.896	0.021
GPR_L1_0.25	WI	y2	35.138	9.154	0.592	0.049	0.867	0.025
		Average	35.935	8.568	0.585	0.048	0.882	0.023
GPR_L1_0.75	WI	y1	41.012	9.051	0.583	0.047	0.886	0.022
GPR_L1_0.75	WI	y2	37.738	10.202	0.592	0.049	0.859	0.026
		Average	39.375	9.627	0.588	0.048	0.873	0.024
GPR_Lassso	WI	y1	41.99	9.299	0.585	0.047	0.884	0.023
GPR_Lassso	WI	y2	37.958	10.251	0.592	0.048	0.858	0.026
		Average	39.974	9.775	0.589	0.048	0.871	0.025
GPR_Ridge	WI	y1	33.521	7.205	0.57	0.048	0.905	0.02
GPR_Ridge	WI	y2	33.701	8.817	0.594	0.049	0.888	0.02
		Average	33.611	8.011	0.582	0.049	0.897	0.020
UPDN_1	I	y1	133.047	7.442	0.695	0.024	0.373	0.055
UPDN_1	I	y2	99.26	11.279	0.711	0.021	0.402	0.05
		Average	116.154	9.361	0.703	0.023	0.388	0.053
UPDN_2	I	y1	95.62	7.786	0.669	0.025	0.409	0.053
UPDN_2	I	y2	75.986	11.879	0.691	0.019	0.389	0.051
		Average	85.803	9.833	0.680	0.022	0.399	0.052
UPDN_3	I	y1	97.618	6.255	0.687	0.023	0.389	0.064
UPDN_3	I	y2	72.15	9.406	0.698	0.017	0.397	0.051
		Average	84.884	7.831	0.693	0.020	0.393	0.058
UPDN_4	I	y1	102.29	7.787	0.679	0.02	0.346	0.061
UPDN_4	I	y2	74.66	12.035	0.7	0.014	0.356	0.057
		Average	88.475	9.911	0.690	0.017	0.351	0.059
MPDN_1	I	y1	111.247	23.885	0.662	0.044	0.766	0.04
MPDN_1	I	y2	102.691	23.825	0.668	0.044	0.758	0.043
		Average	106.969	23.855	0.665	0.044	0.762	0.042
MPDN_2	I	y1	98.646	21.658	0.653	0.046	0.782	0.041
MPDN_2	I	y2	90.899	21.828	0.643	0.046	0.771	0.04
		Average	94.773	21.743	0.648	0.046	0.777	0.041
MPDN_3	I	y1	96.984	21.958	0.66	0.046	0.766	0.042
MPDN_3	I	y2	89.359	22.391	0.638	0.047	0.769	0.041
		Average	93.172	22.175	0.649	0.047	0.768	0.042
MPDN_4	I	y1	94.62	21.06	0.651	0.046	0.779	0.039
MPDN_4	I	y2	85.397	21.374	0.632	0.047	0.78	0.038
		Average	90.009	21.217	0.642	0.047	0.780	0.039
GPR_L1_0.5	I	y1	64.279	14.495	0.624	0.046	0.825	0.031
GPR_L1_0.5	I	y2	48.417	10.777	0.623	0.048	0.783	0.04
		Average	56.348	12.636	0.624	0.047	0.804	0.036
GPR_L1_0.25	I	y1	62.199	13.912	0.61	0.046	0.83	0.03
GPR_L1_0.25	I	y2	46.086	10.418	0.621	0.048	0.787	0.04
		Average	54.143	12.165	0.616	0.047	0.809	0.035
GPR_L1_0.75	I	y1	65.515	14.917	0.627	0.045	0.824	0.032
GPR_L1_0.75	I	y2	49.455	11.066	0.624	0.048	0.781	0.039
		Average	57.485	12.992	0.626	0.047	0.803	0.036
GPR_Lassso	I	y1	67.005	15.7	0.628	0.046	0.82	0.033
GPR_Lassso	I	y2	50.073	11.395	0.624	0.048	0.78	0.04
		Average	58.539	13.548	0.626	0.047	0.800	0.037
GPR_Ridge	I	y1	116.056	22.719	0.788	0.049	0.857	0.028
GPR_Ridge	I	y2	86.785	18.019	0.775	0.049	0.826	0.032
		Average	101.421	20.369	0.782	0.049	0.842	0.030