Table 2 Simulated data with three traits and three environments
MethodE-TLow Correlation Between Traits (0.20)High Correlation Between Traits (0.85)
Correlation MSPECorrelation MSPE
MeanSERaMeanSERaMeanSERaMeanSERa
E1-T10.170.1521.270.1520.540.1710.960.212
E1-T20.300.2210.740.1110.660.1110.880.121
E1-T30.510.1210.930.1510.590.0911.100.221
E2-T10.690.0920.870.1720.720.0620.850.141
UE2-T20.660.1010.730.0820.740.0710.790.081
E2-T30.720.0410.790.1410.700.0720.990.182
E3-T10.590.1431.510.3020.660.1031.270.222
E3-T20.800.0610.950.1510.770.0711.110.161
E3-T30.660.0521.791.7910.670.0731.700.361
Ave0.570.111.561.060.341.440.670.091.671.070.191.33
E1-T10.140.1631.070.1310.480.1830.840.141
E1-T20.240.2030.780.0720.430.1731.010.112
E1-T30.250.1231.180.1220.550.0931.210.222
E2-T10.710.0710.850.1610.760.0410.920.142
DE2-T20.640.0720.710.1610.700.0520.900.132
E2-T30.670.0830.910.1830.660.0831.150.243
E3-T10.650.1121.260.3510.730.0621.190.271
E3-T20.610.1631.430.2630.630.1331.660.243
E3-T30.660.0432.022.0230.690.0721.810.343
Ave0.510.112.561.130.381.890.630.102.441.190.202.11
E1-T10.220.1711.320.2030.530.1821.080.233
E1-T20.270.1920.990.2530.520.1621.220.303
E1-T30.430.0921.230.1830.550.1321.480.383
E2-T10.660.0731.100.2330.700.0631.170.203
SE2-T20.520.1131.020.1330.600.0731.160.133
E2-T30.710.0720.910.1920.730.0710.940.181
E3-T10.700.0911.540.3230.770.0511.340.233
E3-T20.710.1021.030.1820.690.0921.170.182
E3-T30.690.0611.960.3920.730.0711.720.362
Ave0.550.111.891.230.232.670.650.101.891.250.242.56
  • Mean and standard error (SE) of the estimated correlations and Mean Squared Prediction Error (MSPE) from the 10-fold cross-validation CV1. The BMTME model was fitted using unstructured (U), diagonal (D), and standard (S) variance–covariance matrix. Environment (E1, E2, E3)–trait (T1, T2, T3) combination. Method stands for the variance–covariance matrix used with the BMTME, E-T for the environment–trait combination, R for rank, and Ave for average.

  • a Since three conditions are compared (unstructured, diagonal, and standard), the values of the ranks range from 1 to 3, and the lower the values, the better the prediction accuracy. For ties, we assigned the average of the ranks that would have been assigned had there been no ties.