Figure 1
General representation of stage-wise approaches to compare year-effect adjustment. Factors were genotype (G), tester (T), location (L), year (A), trial (S), replicate (R) and block (B). Grain dry matter yield (Y) is the response variable in the first stage, M(1) is the adjusted mean of genotypes across locations used in the second stage, M(1∗) is the year effect-corrected genotype adjusted mean, represents the simple mean of genotypes of the r-th year. In the genomic prediction (GP) stage, M(2) is the n×1 vector of adjusted means of genotypes by year for Approach 1a and across years for Approach 2, M(2∗) is the n×1 vector of adjusted means of year effect-corrected genotypes in Approach 1b, X and β are respectively the design matrix and parameter vector of fixed effects, Z is the n×p marker matrix, u is the p-dimensional vector of SNP effects and e the error vector. Y=G·T:S/R/B is the shorthand notation of the model eq. (1) in the text: Y h i j k v =(G T) h v +S i +R i j +B i j k +e h i j k v , M(1)=G×L×T stands for the model eq. (2) in the text: , and M(1)=(A/T)×G×L represents the extended model eq. (4) in the text: . The final predictive abilities (ρ) are presented in the ellipses.