This work applies the three mode principal components analysis to analyze simultaneously the multiple attributes; to fit of models with additive main effects and multiplicative interaction effects (AMMI models) and the regressions models on sites (SREG models); to evaluate, respectively, the multivariate response of the genotype × environment interaction and the mean response of 36 genotypes of corn tested in 4 locations in Brazil. The results were presented by joint plots to identify the best genotypes for their adaptability and performance in the set of attributes. 1. Introduction The multienvironment trials are conducted to estimate the genetic stability, to evaluate the performance of the genotypes in different environmental conditions, and to quantify and interpret the genotype × environment interaction (GEI), in such a way to select the best genotypes that will be recombined and planted in other years and other environments in the next selection cycle. Some statistical models are used to evaluate the behavior of the genotypes; the most recently proposed methods are based on the singular value decomposition of the GEI matrix. In [1], the two-way interaction using the principal components analysis (PCA) are explained and considered in their model only one multiplicative term. An extension of these models was made in [2], which applies the PCA to decompose the two-way interaction in several multiplicative terms. This model was called as additive main effects and multiplicative interaction effects model (AMMI) by Gauch [3]. Another class of the Linear-bilinear model used in multienvironment trials is the sites regression model (SREG) described by [4]. In this case, the main objective is to evaluate the response of the genotype in each environment. The basic difference in relation to AMMI models is that the effect of genotype is introduced into the residual interaction. This model was used in [5] for clustering of environmental data with no cross-interaction. Gabriel [6] describes the least-square adjustment of the AMMI model, first estimating the additive effects of the model and then making the decomposition in singular values of the matrix ( ) of interaction residuals. The results can be interpreted by graphics called biplot [7] that reflects in reduced dimensions the most important aspects of the GEI, in the case the AMMI model, or the performance of genotypes in different environments, for the case of the model SREG. The researchers in the multienvironmental trials evaluate multiple attributes and must select the best genotypes taking in to
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