Table 1 Summary of the special cases of the general form of Embedded Imagea
ModelDescriptionskEmbedded ImageEmbedded ImageEmbedded ImageSTY or METReference
Single trialDiagonal (s = 1)10Embedded ImageSTY
DIAGDiagonals0Embedded ImagebSTY
USUnstructureds0Embedded ImageMET
CSCompound symmetrys1Embedded ImageEmbedded ImageEmbedded ImageMETPatterson et al. (1977)
CS+DIAGCS+DIAGs1Embedded ImageEmbedded ImageEmbedded ImageMETCullis et al. (1998)
FAMkc,dFactor analytic (main effect)sEmbedded ImageEmbedded ImageEmbedded ImageEmbedded ImageMETSmith 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 Embedded Image with Embedded Image, Embedded Image and Embedded Image.

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

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

  • d For FAMk let Embedded Image where Embedded Image, varEmbedded Image and Embedded Image.