Uso do algoritmo Reversible Jump Markov Chain Monte Carlo para seleção de termos multiplicativos do modelo AMMI

Abstract

Additive Main effects and Multiplicative Interaction model (AMMI) has acquired great applicability for the analysis of data from multi-environmental trials. The determination of how many bilinear terms are required to explain the genotype environment interaction (GEI) has been exhaustively studied in the context of the AMMI frequentist analysis. In the Bayesian context (AMMI-Bayesian), this problem has been approached through information criteria and Bayesian factor. However, these procedures involve intensive computation, making applications impossible when model space is large. The main objective of this work is to propose the determination of the number of multiplicative terms in AMMI-Bayesian model using the Reversible Jump algorithm. For that, three versions of the AMMI-Bayesian were considered, which differ only by the assumed priori for the scale parameter of the singular values: BAMMI based on the principle of insufficient reason (uniform); BAMMIS based on the invariance principle (Jeffreys priori) and BAMMIE, which uses the concept of priori of maximum entropy. To exemplify the method, a data set was simulated in which 20 genotypes were tested in nine environments in a randomized block design, with three replicates, whose variable was productivity. The predictive evaluation indicated that AMMI analysis, in general, is robust and Reversible Jump proved to be a good method for adjustment and selection of models, and the correlation between values observed and predicted by this method was always greater in comparison to AMMI adjusted by conventional Markov chain Monte Carlo (MCMC). Biplots conditional on the most probable models, and also marginal in relation to the bilinear terms, were implemented and presented practically the same pattern. The question of the selection of models in AMMI analysis in the Bayesian perspective has not been much approached in the current literature and, in this sense, studies, as proposed here, are of great importance to encourage and to make feasible the use of AMMI-Bayesian method that, even being well-founded, has not yet become a common multi-environmental analysis procedure.