Modelos GGE: estimadores de encolhimento e heterocedasticidade

Abstract

Multiplicative (or linear-bilinear) models are useful in different areas of knowledge to analyze data in two-way tables in which both factors and their interaction are studied. This is particularly important in the final stages of plant breeding programs, where several genotypes are evaluated in different environments and the interaction between genotypes environments (GEI) generally makes it difficult to select and widely recommend cultivars. Among these models, the Main Effects of Genotypes (G) plus GEI, referred to in the literature as GGE or SERG (Sites “environments” Regression Model) has wide applicability by researchers and breeders in the analysis of data resulting from multi-environmental experiments (MET). Of main relevance is its graphical interpretation that considers only the first two main components called GGE biplot. Many authors have pointed out the advantages of applying Bayesian inference in these models, avoiding standard analysis which considers the parameters to be fixed effects. Shrinking estimates of the parameters that model the GEI and the heterogeneity of variances between locations were modeled directly under the Bayesian methodology for the AMMI model (Additive Main Effects and Multiplicative Interaction), another model belonging to the general class of multiplicative models and provided flexibility in the analysis of MET data. The main objective of this thesis was to extend the Bayesian version of the GGE model in two directions: a) to study maximum entropy principle to derive objective a priori distributions to G + GEI effects and b) to implement the heteroscedastic version. These proposals were exemplified with both simulated and actual data. We showed that maximum entropy prior distributions for variance components of singular values makes the GGE model more flexible. Furthermore, considering the specific variance in each location, a better fit of the model is obtained, allowing, on the other hand, to evaluate the genotypes with different precision, retrieving experimental information present in different tests from the biplot graphical representation. The versatility of Bayesian modeling to incorporate inference to the biplot was also shown, with many aspects such as credibility regions for medium environment and ideal genotype, correlations between environments and for the representation “who won where”, that are all difficult to obtain in the standard biplot analysis. In this sense, the method presented here looks quite promising and his implementation on statistical packages suitable for researchers is a work in progress.