Epsilon Open Archive

Abstract

The additive main effects and multiplicative interaction (AMMI) model is a statistical model that is used for analysis of series of crop variety trials. This model can be fitted to a matrix of observations from a set of genotypes or crop varieties that have been investigated in a set of varying environments or locations. The model includes additive effects of genotypes and environments, and multiplicative effects of genotype-by-environment interaction. The multiplicative interaction terms are obtained through singular value decomposition. This paper describes the simple parametric bootstrap method, which can be used for testing significance of multiplicative terms. The simple parametric bootstrap method assumes that observations are normally distributed. Through simulation it is confirmed that the simple parametric bootstrap method performs well provided that the assumptions of normality and homogeneity of variance are fulfilled. However, when the distribution is non-normal, the frequency of Type I error is not maintained at the nominal significance level. The results of the simulation study suggest that a non-parametric bootstrap method would be needed.