Nonparametric Resampling Methods for Testing Multiplicative Terms in AMMI and GGE Models for Multienvironment Trials

TL;DR: This paper proposes tests based on nonparametric bootstrap and permutation methods for testing the significance of multiplicative terms in additive main effects and multiplicative interaction models and proposes a test that can handle heterogeneity of variance between environments.

Abstract: The additive main effects and multiplicative interaction (AMMI) and genotype and genotype 'environment interaction (GGE) models have been extensively used for the analysis of genotype 'environment experiments in plant breeding and variety testing. Since their introduction, several tests have been proposed for testing the significance of the multiplicative terms, including a parametric bootstrap procedure. However, all of these tests are based on the assumptions of normality and homogeneity variance of the errors. In this paper, we propose tests based on nonparametric bootstrap and permutation methods. The proposed tests do not require any strong distributional assumptions. We also propose a test that can handle heterogeneity of variance between environments. The robustness of the proposed tests is compared with the robustness of other competing tests. The simulation study shows that the proposed tests always perform better than the parametric bootstrap method when the distributional assumptions of normality and homogeneity of variance are violated. The stratified permutation test can be recommended in case of heterogeneity of variance between environments.