In this study, the smallest validation RMSPD value has been used to select the number of PC axes involved in the best AMMI model (Gauch and Zobel, 1988, 1989; Crossa et al.
As the error associated with the cell means decreased, and the number of replications involved in the estimates increased, the RMSPD decreased, indicating better precision of predicted means.
Abbreviations: AMMI, additive main effect and multiplicative interaction; BLUP, best linear unbiased predictor; COMM, completely multiplicative model; EVP, eigenvalue partition; GEAR, genotypes, environment, attribute regression model: GREG, genotypes regression model; GEI, genotype x environment interaction; PC, principal component; SREG, sites regression model; SHMM, shifted multiplicative model; RMSPD, root mean square predictive difference.
These four estimation methods were compared by cross validation using the RMSPD.
The RMSPD between the shrunken predicted means and the validation cell means was computed by taking the square root of the average of the squared predictive differences [([y.
The RMSPD cross validation criterion was also applied to the BLUP estimates.
They computed the RMSPD of PRESS by adjusting the value of PRESS as [[PRESS/ge + 3[s.
The full cross validation yields minimum RMSPD at four components, although the RMSPD values for three, four, and five components are very similar in size and any could be chosen to represent the optimum number of components for the model.
Abbreviations: AMMI, additive main effects and multiplicative interaction model; COMM, completely multiplicative model; DF, degrees of freedom; GEI, genotype x environment interaction; GREG; genotype regression model; IPCA, interaction principal component analysis; MET, multi-environment trials; NID, normally and independently distributed; PCA, principal components analysis; PRESS, predictive sum of squares; PRECORR, predictive correlation; RMSPD, root mean square predictive difference; SHMM, shifted multiplicative model; SREG, sites regression model: SS, sum of squares: SVD, singular value decomposition.
After determining the maximum number of data splittings required to meet the program's stopping rule on the computer runs for the five model forms (for each trial, one run for each model form), those model forms for which the program terminated at an earlier stage were rerun to complete a balanced set of RMSPD values for all data splitting X model and method combinations.
1997) with an unstructured covariance matrix in order to allow for heterogeneous variances and covariances among RMSPD values obtained by different model forms and methods.
For each trial, the method, and the model form X method combinations, with the smallest mean RMSPD were identified a priori.