Johannes Forkman: A simple parametric bootstrap method for AMMI analysis of genotype-by-environment data

The additive main effects and multiplicative interaction (AMMI) model is a statistical model for analysis of genotype-by-environment data. This model is frequently used by agronomists, plant breeders, geneticists and statisticians for analysis of multi-environment trials. In such trials, a set of genotypes, e.g. crop cultivars, are compared across a range of environments, e.g. locations. The AMMI model uses singular value decomposition to partition genotype-by-environment interaction into an ordered sum of multiplicative terms. This presentation discusses the problem of testing the significance of these multiplicative terms in order to decide how many terms to retain in the final model. A simple parametric bootstrap method is proposed. This method involves repeated sampling of standard normally distributed values. In a simulation study, the simple parametric bootstrap method performed well with regard to Type I error rate and power. The method can also be used for testing components in principal component analysis.