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$\times$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	PTR	16.682	3.268	0.503	0.025	0.371	0.045
UPDN_1	WI	SB	9.640	0.816	0.408	0.019	0.408	0.029
UPDN_1	WI	SN	10.965	1.144	0.350	0.016	0.552	0.037
		Average	12.429	1.743	0.420	0.020	0.444	0.037
UPDN_2	WI	PTR	11.323	1.172	0.438	0.019	0.458	0.039
UPDN_2	WI	SB	8.244	0.671	0.383	0.021	0.449	0.041
UPDN_2	WI	SN	8.786	0.716	0.306	0.014	0.622	0.032
		Average	9.451	0.853	0.376	0.018	0.510	0.037
UPDN_3	WI	PTR	12.444	1.38	0.462	0.023	0.458	0.043
UPDN_3	WI	SB	7.833	0.562	0.379	0.016	0.467	0.044
UPDN_3	WI	SN	8.542	0.621	0.313	0.014	0.634	0.033
		Average	9.606	0.854	0.385	0.018	0.520	0.040
UPDN_4	WI	PTR	10.651	0.863	0.421	0.022	0.492	0.032
UPDN_4	WI	SB	7.382	0.493	0.373	0.018	0.487	0.038
UPDN_4	WI	SN	8.364	0.835	0.294	0.015	0.64	0.034
		Average	8.799	0.730	0.363	0.018	0.540	0.035
MPDN_1	WI	SN	8.287	0.815	0.300	0.015	0.644	0.031
MPDN_1	WI	PTR	11.433	0.892	0.438	0.019	0.514	0.034
MPDN_1	WI	SB	8.060	0.683	0.380	0.016	0.474	0.038
		Average	9.260	0.797	0.373	0.017	0.544	0.034
MPDN_2	WI	SN	8.362	0.816	0.292	0.015	0.649	0.031
MPDN_2	WI	PTR	10.523	0.791	0.429	0.019	0.538	0.033
MPDN_2	WI	SB	7.357	0.572	0.369	0.016	0.482	0.037
		Average	8.747	0.726	0.363	0.017	0.556	0.034
MPDN_3	WI	SN	8.312	0.790	0.304	0.015	0.656	0.030
MPDN_3	WI	PTR	10.252	0.801	0.420	0.019	0.544	0.033
MPDN_3	WI	SB	7.616	0.564	0.375	0.016	0.460	0.038
		Average	8.727	0.718	0.366	0.017	0.553	0.034
MPDN_4	WI	SN	8.233	0.796	0.278	0.015	0.653	0.030
MPDN_4	WI	PTR	10.371	0.778	0.422	0.019	0.528	0.033
MPDN_4	WI	SB	7.855	0.593	0.372	0.016	0.449	0.038
		Average	8.820	0.722	0.357	0.017	0.543	0.034
GPR_L1_0.5	WI	SN	8.389	0.787	0.304	0.015	0.630	0.031
GPR_L1_0.5	WI	PTR	10.139	0.769	0.408	0.019	0.535	0.033
GPR_L1_0.5	WI	SB	7.168	0.555	0.371	0.016	0.482	0.037
		Average	8.565	0.704	0.361	0.017	0.549	0.034
GPR_L1_0.25	WI	SN	8.384	0.786	0.304	0.015	0.631	0.031
GPR_L1_0.25	WI	PTR	10.132	0.769	0.408	0.019	0.534	0.033
GPR_L1_0.25	WI	SB	7.163	0.556	0.371	0.016	0.483	0.037
		Average	8.560	0.704	0.361	0.017	0.549	0.034
GPR_L1_0.75	WI	SN	8.389	0.787	0.304	0.015	0.631	0.031
GPR_L1_0.75	WI	PTR	10.140	0.769	0.408	0.019	0.535	0.033
GPR_L1_0.75	WI	SB	7.170	0.555	0.371	0.016	0.482	0.037
		Average	8.566	0.704	0.361	0.017	0.549	0.034
GPR_Lassso	WI	SN	8.390	0.787	0.304	0.015	0.631	0.031
GPR_Lassso	WI	PTR	10.140	0.769	0.408	0.019	0.535	0.033
GPR_Lassso	WI	SB	7.171	0.556	0.371	0.016	0.482	0.037
		Average	8.567	0.704	0.361	0.017	0.549	0.034
GPR_Ridge	WI	SN	8.346	0.785	0.303	0.015	0.627	0.032
GPR_Ridge	WI	PTR	10.262	0.767	0.413	0.019	0.512	0.035
GPR_Ridge	WI	SB	7.159	0.552	0.372	0.016	0.479	0.038
		Average	8.589	0.701	0.363	0.017	0.539	0.035
UPDN_1	I	PTR	16.213	1.677	0.503	0.024	0.326	0.047
UPDN_1	I	SB	10.089	0.923	0.404	0.021	0.361	0.044
UPDN_1	I	SN	12.308	1.113	0.353	0.019	0.494	0.051
		Average	12.870	1.238	0.420	0.021	0.394	0.047
UPDN_2	I	PTR	13.014	1.308	0.45	0.018	0.391	0.046
UPDN_2	I	SB	9.448	0.766	0.382	0.016	0.396	0.046
UPDN_2	I	SN	10.923	1.016	0.322	0.014	0.562	0.038
		Average	11.128	1.030	0.385	0.016	0.450	0.043
UPDN_3	I	PTR	13.346	1.472	0.456	0.019	0.43	0.045
UPDN_3	I	SB	9.061	0.598	0.384	0.015	0.431	0.04
UPDN_3	I	SN	10.718	1.042	0.323	0.018	0.575	0.047
		Average	11.042	1.037	0.388	0.017	0.479	0.044
UPDN_4	I	PTR	12.421	1.364	0.434	0.021	0.441	0.046
UPDN_4	I	SB	8.028	0.62	0.372	0.016	0.451	0.039
UPDN_4	I	SN	9.317	0.913	0.309	0.019	0.62	0.035
		Average	9.922	0.966	0.372	0.019	0.504	0.040
MPDN_1	I	SN	11.878	1.120	0.338	0.014	0.535	0.035
MPDN_1	I	PTR	15.276	1.231	0.487	0.018	0.391	0.040
MPDN_1	I	SB	10.068	0.776	0.400	0.015	0.370	0.041
		Average	12.407	1.042	0.408	0.016	0.432	0.039
MPDN_2	I	SN	11.503	1.044	0.323	0.014	0.595	0.031
MPDN_2	I	PTR	12.745	1.017	0.440	0.018	0.473	0.037
MPDN_2	I	SB	9.341	0.718	0.379	0.015	0.427	0.038
		Average	11.196	0.926	0.381	0.016	0.498	0.035
MPDN_3	I	SN	9.942	0.896	0.310	0.015	0.585	0.033
MPDN_3	I	PTR	11.654	0.910	0.424	0.019	0.471	0.037
MPDN_3	I	SB	8.226	0.622	0.375	0.016	0.425	0.038
		Average	9.941	0.809	0.370	0.017	0.494	0.036
MPDN_4	I	SN	10.314	0.914	0.297	0.015	0.589	0.033
MPDN_4	I	PTR	12.018	0.933	0.418	0.019	0.462	0.036
MPDN_4	I	SB	8.245	0.616	0.373	0.016	0.423	0.039
		Average	10.192	0.821	0.363	0.017	0.491	0.036
GPR_L1_0.5	I	SN	10.649	0.884	0.365	0.014	0.527	0.036
GPR_L1_0.5	I	PTR	11.539	0.864	0.434	0.018	0.462	0.035
GPR_L1_0.5	I	SB	8.482	0.622	0.400	0.016	0.347	0.040
		Average	10.223	0.790	0.400	0.016	0.445	0.037
GPR_L1_0.25	I	SN	10.661	0.883	0.366	0.014	0.526	0.036
GPR_L1_0.25	I	PTR	11.542	0.866	0.435	0.018	0.462	0.035
GPR_L1_0.25	I	SB	8.488	0.623	0.400	0.016	0.347	0.040
		Average	10.230	0.791	0.400	0.016	0.445	0.037
GPR_L1_0.75	I	SN	10.654	0.886	0.365	0.014	0.528	0.036
GPR_L1_0.75	I	PTR	11.557	0.865	0.434	0.018	0.460	0.035
GPR_L1_0.75	I	SB	8.475	0.621	0.400	0.016	0.347	0.040
		Average	10.229	0.791	0.400	0.016	0.445	0.037
GPR_Lassso	I	SN	10.652	0.886	0.365	0.014	0.528	0.036
GPR_Lassso	I	PTR	11.553	0.865	0.434	0.018	0.460	0.035
GPR_Lassso	I	SB	8.490	0.622	0.401	0.016	0.347	0.040
		Average	10.232	0.791	0.400	0.016	0.445	0.037
GPR_Ridge	I	SN	11.722	0.962	0.395	0.013	0.601	0.033
GPR_Ridge	I	PTR	11.986	0.885	0.438	0.018	0.503	0.035
GPR_Ridge	I	SB	8.444	0.659	0.386	0.015	0.461	0.038
		Average	10.717	0.835	0.406	0.015	0.522	0.035