A major challenge in the analysis of plant breeding multi-environment datasets is the provision of meaningful and concise information for variety selection in the presence of variety by environment interaction (VEI). This is addressed in the current paper by fitting a factor analytic linear mixed model (FALMM) then using the fundamental factor analytic parameters to define groups of environments in the dataset within which there is minimal crossover VEI, but between which there may be substantial crossover VEI. These groups are consequently called interaction classes (iClasses). Given that the environments within an iClass exhibit minimal crossover VEI, it is then valid to obtain predictions of overall variety performance (across environments) for each iClass. These predictions can then be used not only to select the best varieties within each iClass but also to match varieties in terms of their patterns of VEI across iClasses. The latter is aided with the use of a new graphical tool c