Model^{a} | Form^{b} of u_{m} | Form of u_{e} | STY or MET | Log-Likelihood | AIC | |
---|---|---|---|---|---|---|

Phenotypic^{c} | E_{DIAG} | DIAG^{d} | STY | −11,074.6 | 22,163.1 | |

E_{CS} | CS^{e} | MET | −10,877.0 | 21,768.1 | ||

E_{CS+DIAG} | CS+DIAG^{f} | MET | −10,872.5 | 21,760.9 | ||

E_{FAM}, E_{1}_{US} | FAM1^{g}, US^{h} | MET | −10,872.4 | 21,760.8 | ||

Standard^{i} | S_{DIAG} | DIAG | STY | −10,924.9 | 21,863.8 | |

S_{CS} | CS | MET | −10,794.0 | 21,602.1 | ||

S_{CS+DIAG} | CS+DIAG | MET | −10,790.6 | 21,597.2 | ||

S_{FAM}, S_{1}_{US} | FAM1, US | MET | −10,787.8 | 21,591.6 | ||

Partitioned^{j} | P_{DIAG} | DIAG | DIAG | STY | −10,876.4 | 21,770.8 |

P_{CS} | CS | CS | MET | −10,747.2 | 21,512.5 | |

P_{CS+DIAG} | CS+DIAG | CS+DIAG | MET | −10,744.6 | 21,511.2 | |

P_{FAM}, P_{1}_{US} | FAM1, US | FAM1, US | MET | −10,744.2 | 21,510.4 |

STY, single trial year; MET, multi-environment trial; AIC, Akaike information criteria.

↵a All models derive from Equation 1 but are special cases of

(Equation 2).*g*↵b Details of forms of

**u**_{m}are given in Table 1.↵c Phenotypic model has

=**g****u**_{e}.↵d DIAG implies the covariance between the two trials is assumed to be zero, and is equivalent to fitting the two trials separately.

↵e CS is the compound symmetry model.

↵f CS+DIAG is the model described by Cullis

*et al.*1998.↵g FAM

*1*is the factor analytic model (Smith*et al.*2001), with main effect with*k*the number of factors equal to 1.↵h US is the unstructured model (US), for two trials this model is equivalent to the FAM

*1*model.↵i Standard RR-BLUP model has

**u**_{m}.↵j Partitioned RR-BLUP model has .