Justificativa bayesiana para efeito de encolhimento em modelos AMMI

Abstract

The main additive effect model and multiplicative interaction (AMMI) is often used to study the interaction among factors in several areas of research, particularly in the test cultivars. A key feature of this model is parsimony, so that only some bilinear components are required to represent the genotype environment interaction (GE). Several procedures have been developed for selection of components, such as F approximated tests and cross-validation methods. In the literature, examples also can be found with the use of the shrinkage estimators applied in the context of fixed effects, which provide more accurate estimates of parameters. In this study, the Bayesian methodology was applied to the AMMI model taking the variances of the singular values as random variables and incorporating into the joint prior of the model. It was found that using a priori information, the interaction effects were more important on first bilinear components and the estimates for the singular values have shrunk to zero, so that the AMMI1 model was the most appropriate for the analysis. Regions of credibility were proposals for the biplot AMMI1 with respect to the genotypes effects and genotypic scores referring to the first principal axis. With the construction of the regions of credibility, it was possible to identify homogeneous groups of genotypes and environments, enabling classify the genotypes more productive and stable and evaluate them with respect to GE interaction.