Table 1 Summary of the special cases of the general form of a
ModelDescriptionskSTY or METReference
Single trialDiagonal (s = 1)10STY
DIAGDiagonals0bSTY
USUnstructureds0MET
CSCompound symmetrys1METPatterson et al. (1977)
CS+DIAGCS+DIAGs1METCullis et al. (1998)
FAMkc,dFactor analytic (main effect)sMETSmith et al. (2001)
• STY, single trial year (note the DIAG model is equivalent to analyzing each trial year separately); MET, multi-environment trial.

• a A similar table could be constructed for with , and .

• b ⊕ represents a kronecker sum, so that results in a diagonal matrix with elements for the specific variance of trial t.

• c is a matrix of k factor loadings at each of the s trials.

• d For FAMk let where , var and .