title: A robust AMMI model for the analysis of genotype-by-environment data.
abstract: BACKGROUND
  One of the most widely used models to analyse genotype-by-environment data is the additive main effects and multiplicative interaction (AMMI) model. Genotype-by-environment data resulting from multi-location trials are usually organized in two-way tables with genotypes in the rows and environments (location-year combinations) in the columns. The AMMI model applies singular value decomposition (SVD) to the residuals of a specific linear model, to decompose the genotype-by-environment interaction (GEI) into a sum of multiplicative terms. However, SVD, being a least squares method, is highly sensitive to contamination and the presence of even a single outlier, if extreme, may draw the leading principal component towards itself resulting in possible misinterpretations and in turn lead to bad practical decisions. Since, as in many other real-life studies the distribution of these data is usually not normal due to the presence of outlying observations, either resulting from measurement errors or sometimes from individual intrinsic characteristics, robust SVD methods have been suggested to help overcome this handicap.
  
  
  RESULTS
  We propose a robust generalization of the AMMI model (the R-AMMI model) that overcomes the fragility of its classical version when the data are contaminated. Here, robust statistical methods replace the classic ones to model, structure and analyse GEI. The performance of the robust extensions of the AMMI model is assessed through a Monte Carlo simulation study where several contamination schemes are considered. Applications to two real plant datasets are also presented to illustrate the benefits of the proposed methodology, which can be broadened to both animal and human genetics studies.
  
  
  METHODS
  Source code implemented in R is available in the supplementary material under the function r-AMMI.
  
  
  BACKGROUND
  paulocanas@gmail.com
  
  
  BACKGROUND
  Supplementary data are available at Bioinformatics online.
authors.affiliation: Department of Statistics, Federal University of Bahia, Salvador, Brazil, CAST-Center for Applied Statistics and Data Analytics, University of Tampere, Finland.
authors.forename: Paulo C
authors.initials: PC
authors.lastname: Rodrigues
authors.affiliation: Centro de Matemática e Aplicações (CMA), and.
authors.forename: Andreia
authors.initials: A
authors.lastname: Monteiro
authors.affiliation: Centro de Matemática e Aplicações (CMA), and Department of Mathematics, FCT-NOVA University of Lisbon, Lisbon, Portugal.
authors.forename: Vanda M
authors.initials: VM
authors.lastname: Lourenço
mesh_terms: D002874:Chromosome Mapping; D003198:Computer Simulation; D003433:Crosses, Genetic; D004777:Environment; D005838:Genotype; D001467:Hordeum / Q000235:genetics*; D008962:Models, Theoretical; D025341:Principal Component Analysis; D014908:Triticum / Q000235:genetics*