SummaryThe genotype by environment interaction (GEI)) has an influence on the selection and recommendation of cultivars. The aim of this work is to study the effect of GEI and evaluate the adaptability and stability of productivity (kg/ha) of nine maize genotypes using AMMI model (Additive Main effects and Multiplicative Interaction). The AMMI model is one of the most widely used statistical tools in the analysis of multiple-environment trials. It has two purposes, namely understanding complex GEI and increasing accuracy. Nevertheless, the AMMI model is a widely used tool for the analysis of multiple-environment trials, where the data are represented by a two-way table of GEI means. In the complete tables, least squares estimation for the AMMI model is equivalent to fitting an additive two-way ANOVA model for the main effects and applying a singular value decomposition to the interaction residuals. It assumes equal weights for all GEI means implicitly. The experiments were conducted in twenty environments, and the experimental design was a randomized complete block design with four repetitions. The AMMI model identified the best combinations of genotypes and environments with respect to the response variable. This paper concerns a basic and a common application of AMMI: yield-trial analysis without consideration of special structure or additional data for either genotypes or environments.Key words: genotype environment interaction (GEI), adaptability and stability, additive main effects and multiplicative interaction model, multienvironment trials
SummaryA common problem in multi-environment trials arises when some genotypeby-environment combinations are missing. In Arciniegas-Alarcón et al. (2010) we outlined a method of data imputation to estimate the missing values, the computational algorithm for which was a mixture of regression and lower-rank approximation of a matrix based on its singular value decomposition (SVD). In the present paper we provide two extensions to this methodology, by including weights chosen by cross-validation and allowing multiple as well as simple imputation. The three methods are assessed and compared in a simulation study, using a complete set of real data in which values are deleted randomly at different rates. The quality of the imputations is evaluated using three measures: the Procrustes statistic, the squared correlation between matrices and the normalised root mean squared error between these estimates and the true observed values. None of the methods makes any distributional or structural assumptions, and all of them can be used for any pattern or mechanism of the missing values.
A common problem in the analysis of data from multi‐environment trials is imbalance caused by missing observations. To get around this problem, Yan proposed a method for imputing the missing values based on the singular‐value decomposition (SVD) of a matrix. However, this SVD can be affected by outliers and produce low quality imputations. In this article, we propose four extensions of the Yan method that are resistant to outliers, replacing the standard SVD method with four robust SVD extensions. We evaluate these methods, using exclusively numerical criteria in a simulation study and in a cross‐validation study based on real data. We conclude that in the presence of outliers, the standard SVD method should not be used; instead, the best alternatives are the robust SVD methods based on sub‐sampling when the percentage of contamination is less than 2% following a completely random missing data mechanism. In any other case, methods that either minimize the L2 norm or that involve L1 regressions are preferable.
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