Abstract

Constrained principal component analysis (C-PCA) describes a two-dimensional data table and assumes a linear dependence of the principal component scores on known additional parameters (i.e., explanatory matrices). In this study, we used C-PCA to generalize the additive main effects and multiplicative interaction (AMMI) model and propose the constrained AMMI model. The constrained AMMI model is interpreted and illustrated when (i) only the environmental principal component parameters have an explanatory data matrix, (ii) only the genotype principal component parameters have an explanatory data matrix, and (iii) both types of parameters have explanatory data matrices. The cross-validation procedure is adapted for model diagnosis. Data for winter wheat (Triticum aestivum L.) genotype x location x management x year grain yield, recorded in Poland from multienvironment trials conducted in the post-registration variety testing system, were analyzed and used for model comparison.