Analysis of a three-way interaction including multi-attributes

The additive main effect and multiplicative interaction ( AMMI) has been widely used for studying and interpreting genotype x environment interaction ( GEI) in agricultural experiments using multi-environment trials ( METs). When METs are performed across several years the interaction is referred to as a 3- mode ( 3- way) data array, inwhich the modes are genotypes, environments, and years. The 3- way array can be applied to other conditions or factors artificially created by the researcher, such as different sowing dates or plant densities, etc. Three-way interaction data can be studied using the AMMI analysis. The objective of this study is to apply the 3- mode AMMI to 2 datasets. Dataset 1 comprises genotype ( 25) x location ( 4) x sowing time ( 4) interaction; 8 traits were measured. The structure of dataset 2 is genotype ( 20) x irrigation regimes ( 4) x year ( 3) on grain yield. Results of the 3- way AMMI on dataset 1 show that several important 3- way interactions were not detected when condensing location ( 4) x sowing time ( 4) into environments ( 16). An alternative 3- way array, genotype x attribute x locations for the early sowing date in Year 1, is considered. Results of the 3- way AMMI on dataset 2 show that different patterns of response of genotypes can be found at different irrigation methods and years.