Another Look at Bayesian Analysis of AMMI Models for Genotype-Environment Data

Linear–bilinear models are frequently used to analyze two-way data such as genotype-by-environment data. A well-known example of this class of models is the additive main effects and multiplicative interaction effects model (AMMI). We propose a new Bayesian treatment of such models offering a proper way to deal with the major problem of overparameterization. The rationale is to ignore the issue at the prior level and apply an appropriate processing at the posterior level to be able to arrive at easily interpretable inferences. Compared to previous attempts, this new strategy has the great advantage of being directly implementable in standard software packages devoted to Bayesian statistics such as WinBUGS/OpenBUGS/JAGS. The method is assessed using simulated datasets and a real dataset from plant breeding. We discuss the benefits of a Bayesian perspective to the analysis of genotype-by-environment interactions, focusing on practical questions related to general and local adaptation and stability of genotypes. We also suggest a new solution to the estimation of the risk of a genotype not exceeding a given threshold.